Question 1

In this numerical analogy question, select the related number from the given alternatives to complete the proportion: 0.04 : 0.2 :: 0.09 : ?

Accepted Answer

Introduction / Context: This numerical analogy question uses decimal numbers and a square root relationship. The pair 0.04 and 0.2 is given, and you must determine which number completes the analogy 0.04 : 0.2 :: 0.09 : ?. Recognising square roots and squares of small decimal values is important in many quantitative reasoning questions, especially when dealing with proportions or analogy patterns. Given Data / Assumptions: The first pair is 0.04 and 0.2. The second pair starts with 0.09, and we must find the related number. The answer options are 0.3, 0.6, 0.9, 2, and 0.04. We assume the same numerical relationship that links 0.04 to 0.2 must link 0.09 to the correct answer. Concept / Approach: Note that 0.2 * 0.2 = 0.04, which means 0.2 is the square root of 0.04 and 0.04 is the square of 0.2. This suggests a clear square root or squaring relationship between the terms of the pair. To maintain the analogy, we must apply the same type of relationship between 0.09 and the unknown number. Since 0.3 * 0.3 = 0.09, it follows that the square root of 0.09 is 0.3. Therefore, the pattern likely maps each decimal to its square root or vice versa in a consistent direction. Step-by-Step Solution: Step 1: Express the first pair using squares. 0.04 can be written as 0.2^2.Step 2: This means that 0.2 is the square root of 0.04, so the mapping is 0.04 mapped to sqrt(0.04) which equals 0.2, or equivalently 0.2 mapped to its square 0.04 depending on direction.Step 3: For consistency with the order 0.04 : 0.2, we see that the first term is the square of the second term.Step 4: Apply the same idea to the second pair. We must find a number whose square equals 0.09.Step 5: We know that 0.3 * 0.3 = 0.09, so 0.09 is 0.3^2, and thus 0.3 is the square root of 0.09.Step 6: Therefore, to preserve the pattern, 0.09 must be paired with 0.3, just as 0.04 is paired with 0.2. Verification / Alternative check: We can verify the pattern by comparing both pairs in terms of square roots. In the first pair, sqrt(0.04) = 0.2. In the second pair, sqrt(0.09) must be equal to the unknown number. Since sqrt(0.09) = 0.3, the second pair becomes 0.09 : 0.3, which mirrors the structure 0.04 : 0.2. None of the other options squared equals 0.09, confirming that 0.3 is uniquely correct. For instance, 0.6^2 = 0.36, 0.9^2 = 0.81, and 2^2 = 4, all of which are inconsistent with 0.09. Why Other Options Are Wrong: Option 0.6 has a square of 0.36, not 0.09, so it breaks the square relationship used in the first pair. Option 0.9 squared gives 0.81, which is far from 0.09 and clearly does not mirror the original pattern. Option 2 squared is 4, which is completely unrelated to the small decimal value 0.09 in the context of this analogy. Option 0.04, if paired with 0.09, would create a pattern based on different squared values and does not serve as the square root of 0.09. Common Pitfalls: Some candidates may attempt to treat the relationship as simple multiplication or division by a factor of 5 or 2 because the numbers are decimals, but quick checks show these factors do not hold consistently for both pairs. Another mistake is to confuse 0.3 with 0.03, leading to incorrect squares. To avoid these issues, it is helpful to remember squares of small decimals like 0.1, 0.2, and 0.3, or to rewrite the decimals as fractions and square them to verify the pattern accurately. Final Answer: Following the same square and square root relationship as 0.04 : 0.2, the correct completion of the analogy 0.04 : 0.2 :: 0.09 : ? is 0.3.

Question 2

In this simple verbal analogy question, select the related word from the given alternatives to complete the pair: Tongue : Taste :: Nose : ?

Accepted Answer

Introduction / Context: This is a basic verbal analogy that checks your understanding of human sense organs and the senses they are associated with. The pair Tongue and Taste is given, and you must determine which word stands to Nose in the same way. Such questions are common in early level reasoning and general intelligence tests, reinforcing basic science knowledge about the five senses. Given Data / Assumptions: The first pair is Tongue and Taste. The second pair is Nose and an unknown word to be selected from the options. The options are Smell, Face, Touch, Chin, and Ear. We assume that the first word in each pair is a sense organ and the second word is the corresponding sense it perceives. Concept / Approach: The Tongue is the primary sense organ responsible for detecting Taste. Similarly, the Nose is the organ responsible for detecting Smell. Therefore, the relationship is sense organ to associated sense. To maintain this pattern consistently, we must pair Nose with Smell. Recognising such direct one to one associations is key to quickly solving this kind of analogy. Step-by-Step Solution: Step 1: Interpret the first pair. Tongue is the organ, and Taste is the sense detected by that organ.Step 2: Express the relationship as sense organ to sensory perception.Step 3: Apply the same relationship to Nose. It is a sense organ.Step 4: The sense associated with Nose is Smell, since the Nose detects odours and fragrances.Step 5: Hence, the correct completion of the analogy is Nose : Smell. Verification / Alternative check: We can verify by checking all five primary senses. Eyes are associated with Sight, Ears with Hearing, Nose with Smell, Tongue with Taste, and Skin with Touch. The given pair uses Tongue and Taste, so the second pair should mirror this pattern using Nose and its direct sense, Smell. No other option besides Smell represents a sense, and none fits as accurately with Nose as Smell does, confirming our choice. Why Other Options Are Wrong: Option Face is a body part surrounding many sense organs but is not itself a specific sense. Option Touch is a sense, but it is associated primarily with the skin and surface receptors, not with the Nose. Option Chin is another external facial part and does not represent a sense for which the Nose is the organ. Option Ear is a sense organ, but it is associated with Hearing, not with Smell, so pairing it with Nose would mix two different organs instead of organ and sense. Common Pitfalls: Some candidates may mechanically match body parts instead of focusing on organ and sense pairs, leading them to choose another facial feature such as Face or Chin. Others may confuse Touch and Smell as general sensations. The safest method is to recall the standard mapping of five senses to their organs and then select the option that fits this mapping exactly for the given organ. Final Answer: Therefore, in the analogy Tongue : Taste :: Nose : ?, the correctly related word is Smell.

Question 3

In this letter analogy question, select the related group of letters from the given alternatives to complete the pattern: FDH : LJN :: RPT : ?

Accepted Answer

Introduction / Context: This letter analogy problem asks you to identify a straightforward forward shift in alphabet positions. The relationship between FDH and LJN is shown, and you must apply the same transformation to RPT to select the correct answer from the options. Letter shift questions like this are a staple in non verbal reasoning sections and reward a systematic approach using alphabet positions. Given Data / Assumptions: The first pair is FDH and LJN. The second starting group is RPT. The options are XYZ, WUY, XVZ, SUV, and TVX. We assume that a fixed positive shift in alphabet positions converts FDH into LJN and that the same shift must be applied to RPT. Concept / Approach: As usual with letter analogies, we convert each letter into its numeric alphabet position and search for a consistent shift, either forward or backward. When moving from FDH to LJN, we will check how many steps we move forward. Once we find that the shift is constant across all letters, we will apply the same shift to each letter of RPT and see which option matches the resulting group exactly. Step-by-Step Solution: Step 1: Determine the positions of FDH. F = 6, D = 4, H = 8.Step 2: Determine the positions of LJN. L = 12, J = 10, N = 14.Step 3: Calculate the shift from F to L: 6 to 12 is plus 6.Step 4: Calculate the shift from D to J: 4 to 10 is plus 6.Step 5: Calculate the shift from H to N: 8 to 14 is plus 6 as well.Step 6: Thus, the mapping from FDH to LJN involves adding 6 to the position of each letter.Step 7: Now take RPT and note positions: R = 18, P = 16, T = 20. Add 6 to each: 18 + 6 = 24 (X), 16 + 6 = 22 (V), 20 + 6 = 26 (Z). The result is XVZ. Verification / Alternative check: We can verify by counting forward in the alphabet. From R, moving forward six steps gives S, T, U, V, W, X. From P, six steps forward give Q, R, S, T, U, V. From T, six steps forward give U, V, W, X, Y, Z. This forward counting confirms that the transformation RPT to XVZ uses a consistent plus 6 shift, exactly mirroring the example FDH to LJN. None of the other options results from this same uniform shift, so XVZ must be the correct answer. Why Other Options Are Wrong: Option XYZ would require R to become X, a plus 6 shift, but P to become Y is a plus 9 shift, so the pattern is not consistent. Option WUY produces different shifts for each letter and does not use a constant increment of plus 6 from R, P, and T. Option SUV comes from a smaller shift and does not move T all the way to Z by plus 6, so it fails the uniform shift test. Option TVX again mixes different step sizes and does not correspond to a fixed plus 6 movement for all three letters. Common Pitfalls: Some candidates rely on visual similarity of letter shapes or positions instead of calculating exact numeric shifts, which leads them to choose distractor options such as XYZ or TVX. Others may determine the correct shift for the first letter but forget to verify the pattern for the remaining letters. A consistent procedure of converting letters to numeric positions, checking the shift for every letter in the example pair, and then applying that same shift to the new group will minimise such mistakes. Final Answer: Therefore, applying the same plus six shift as from FDH to LJN, the correct completion of the analogy RPT : ? is XVZ.

Question 4

In this numerical analogy question, select the related number from the given alternatives to complete the proportion: 39 : 52 :: 51 : ?

Accepted Answer

Introduction / Context: This numerical analogy question uses multiplication with a fixed factor to build a consistent pattern. The pair 39 and 52 is provided, and you must find the number that corresponds to 51 in the same way. Unlike simple addition or subtraction, this problem involves recognising that both numbers in each pair are multiples of a common prime, which makes it a slightly more challenging reasoning exercise. Given Data / Assumptions: The first pair is 39 and 52. The second pair starts with 51, and we must find the related number. The options are 53, 40, 68, 38, and 65. We assume that there is a common structure behind 39 and 52 and that the same structure must be applied to 51 and the unknown number. Concept / Approach: First, factorise the numbers in the given pair. The number 39 can be written as 3 * 13, and 52 can be written as 4 * 13. This suggests that the underlying pattern is to take a common prime factor, here 13, and multiply it by 3 and then by 4. To extend this pattern, we look at the second starting number 51. Factorising 51 gives 3 * 17. To maintain the same pattern, we would expect the partner of 51 to be 4 * 17, since 39 corresponds to 3 * 13 and 52 to 4 * 13. This structure leads directly to the correct answer. Step-by-Step Solution: Step 1: Factorise the numbers in the first pair. 39 = 3 * 13, and 52 = 4 * 13.Step 2: Observe that both numbers share the same prime factor 13, and the multipliers are 3 and 4.Step 3: Recognise the pattern: first number is 3 times a prime, second number is 4 times the same prime.Step 4: Factorise 51. We have 51 = 3 * 17.Step 5: To keep the same structure, we should multiply 17 by 4 to obtain the partner of 51.Step 6: Compute 4 * 17 = 68.Step 7: Check the options and confirm that 68 is listed, so it is the only number that fits the pattern. Verification / Alternative check: We can also check the analogy using ratios. In the first pair, 52 / 39 = (4 * 13) / (3 * 13) = 4 / 3. Thus, the multiplier from the first to the second number is 4/3. Applying the same multiplier to 51, we get 51 * (4 / 3) = 17 * 4 = 68. This confirms again that 68 preserves the same proportional relationship between the terms, so it is the correct answer. Why Other Options Are Wrong: Option 53 is a prime number that does not relate to 51 through a factor of 4/3 or a shared prime factor structure similar to 13. Option 40 cannot be expressed as 4 times 17 or in a form that mirrors the 3 times prime and 4 times prime pattern used in the first pair. Option 38 lies close to 39 but does not match any ratio such as 4/3 when related to 51, so it fails the analogy. Option 65 equals 5 * 13 and does not maintain the pairing of 3 times prime and 4 times the same prime that we observed for 39 and 52 with factor 13 and for 51 and 68 with factor 17. Common Pitfalls: Many candidates glance at the numbers and attempt to use simple addition or subtraction, for example noticing that 39 increases by 13 to become 52 and then incorrectly adding 13 to 51. While this sometimes works in easier questions, here it does not lead to a consistent factor structure involving a common prime and the 4/3 ratio. The more robust strategy is to factorise the numbers to see if a hidden multiplicative pattern exists, especially when two numbers share a meaningful common factor. Final Answer: Therefore, in the analogy 39 : 52 :: 51 : ?, the number that correctly completes the pair is 68.

Question 5

In this verbal analogy question, select the related word from the given alternatives to complete the pair: Yellow : Lemon :: Purple : ?

Accepted Answer

Introduction / Context: This is a colour based verbal analogy. The pair Yellow and Lemon is given, and you must select the word that stands to Purple in the same way. These questions draw on common visual associations between colours and familiar objects, such as fruits or vegetables, and are frequently used in basic reasoning tests to check everyday knowledge and observation skills. Given Data / Assumptions: The first pair is Yellow and Lemon. The second pair is Purple and an unknown word from the options. The options are Apple, Brinjal, Mango, Onion, and Banana. We assume that Lemon is an object that is typically Yellow and that we need to find an object that is typically Purple. Concept / Approach: In the first pair, Yellow : Lemon, the relationship is colour to object that is commonly recognised by that colour. Lemons are widely known as yellow fruits. To preserve the structure, we must find an object among the options that is normally associated with the colour Purple. In everyday life, a very common example is Brinjal, also known as eggplant, which usually has a deep purple skin. Therefore, Purple should correspond to Brinjal. Step-by-Step Solution: Step 1: Interpret the first pair as colour to common object. Yellow is the colour, and Lemon is a fruit that is generally Yellow.Step 2: Apply the same relationship to the second pair. Purple is the colour, and we must choose a common object that is usually Purple.Step 3: Among the options, Brinjal is a vegetable that is characteristically Purple in appearance.Step 4: Therefore, Purple should be paired with Brinjal, just as Yellow is paired with Lemon.Step 5: Confirm that no other option has such a strong and typical association with the colour Purple. Verification / Alternative check: We can check each option against the colour Purple. Apples are most commonly red, green, or sometimes yellow, not Purple. Mangoes are usually green or yellow when ripe. Onions come in various types, but the most basic association in simple questions is often with white or light colours. Bananas are typically yellow. In contrast, Brinjal is almost universally visualised as a Purple vegetable in basic science and general knowledge. This confirms that Brinjal is the only choice that fits the colour object pattern, just as Lemon fits Yellow. Why Other Options Are Wrong: Option Apple does not have a standard Purple form in basic general knowledge; its common colours are red and green. Option Mango is associated more with green and yellow shades rather than Purple. Option Onion can have a reddish or purplish outer layer in some varieties, but exam questions at this level usually expect the direct and primary Purple association with Brinjal, not a less obvious association. Option Banana is almost always thought of as Yellow, which would repeat the colour used in the first pair rather than complement Purple in the second. Common Pitfalls: Some candidates may overthink and consider rare varieties of fruits and vegetables with unusual colours, but reasoning questions like this aim at the most common and widely taught associations. Another mistake is to look only for any food item without checking the colour link carefully. A systematic approach is to identify the nature of the relationship, in this case colour to object, and then choose the option that best reflects the most common real world pairing with the second colour. Final Answer: Thus, in the analogy Yellow : Lemon :: Purple : ?, the correctly related word is Brinjal.

Question 6

In this verbal reasoning question on family relationships, select the one word that is odd or different from the other given alternatives.

Accepted Answer

Introduction / Context: This question belongs to the category of verbal reasoning and tests your understanding of basic family relationships. You are given a list of close relatives and asked to select the odd one out. To answer correctly, you must identify the common property that most of the words share and then find the single option that does not follow that property. Such questions are very common in government and bank exams because they quickly check conceptual clarity and observation skills. Given Data / Assumptions: - Sister is a female sibling. - Daughter is a female child. - Aunt is a female relative (father's or mother's sister, or uncle's wife). - Mother is a female parent. - Nephew is the son of one's brother or sister and is male. - The task is to select the odd word from these alternatives. Concept / Approach: The standard approach in odd one out questions is to first group the given words based on gender, type of relation, or generation. Here, all the options are family relationships, so the deciding factor will not be whether they are relatives but what specific type of relatives they are. The most natural property to check is gender, because four of the words generally describe female relatives, while one word describes a male relative. The option that does not match the predominant gender category becomes the odd one. Step-by-Step Solution: Step 1: List all the words and identify whether each term usually refers to a male or a female relative. Step 2: Sister, daughter, aunt and mother all clearly refer to female relations in a family. Step 3: Nephew refers to the male child of one's brother or sister, so it is a male relation. Step 4: Since four of the given words describe female relatives and only one word describes a male relative, the male relation is the odd one out. Step 5: Therefore, 'Nephew' is the only term that does not fit into the group of female relatives and is the correct answer. Verification / Alternative check: An alternative way to verify the answer is to check whether the relationship is direct or indirect. Sister, daughter and mother are direct relations, while aunt is a slightly extended relation. However, both aunt and nephew are extended relations, so that criterion does not uniquely isolate any one term. The gender-based classification clearly isolates only nephew as male, while the remaining four words point to female family members. This confirms that our chosen answer is consistent and logically sound. Why Other Options Are Wrong: Sister is a female sibling and matches the majority female category, so it cannot be the odd one out. Daughter is a female child and again belongs to the female group of relations, so it matches the pattern. Aunt is a female relative and therefore still falls in the predominant female category. Mother is also a female relation and does not stand out as different when compared with sister, daughter and aunt. Common Pitfalls: Candidates sometimes overcomplicate this type of question by looking for subtle distinctions such as generational level or whether the relation comes from the mother's or father's side. While such distinctions can sometimes be relevant, here the simplest and most robust criterion is gender. Another common mistake is not checking all options carefully and quickly guessing one that feels slightly less familiar. Always verify that exactly one option is different on a clear, objective property. Final Answer: The only male relation among the options is Nephew, so it is the odd word out.

Question 7

In this analogy question, Lips are related to Smile, so you must select the word that best completes the pair Eyes : ? from the given alternatives.

Accepted Answer

Introduction / Context: This is a classic verbal analogy question where you are given a relationship between two words and asked to find a word that creates a similar relationship with a new base word. The pair "Lips : Smile" describes an action performed using a body part. To solve the analogy, you must determine which of the given options describes an action commonly performed using the eyes, in the same way that smiling is an action performed using the lips. Given Data / Assumptions: - Lips are a part of the mouth and are used when a person smiles. - Smile is an expression or action made mainly with the lips and face. - Eyes are organs of vision and can also be used to express emotions or signals. - The options are Black, Wink, Two, Spectacles and Vision. - We assume standard meanings of all the words in the context of human body parts and their common actions. Concept / Approach: The logical connection in the first pair "Lips : Smile" is that lips are used to produce a smile. Thus, the pattern is "body part : action performed using that body part". For the second pair, we need to find an action typically associated with eyes. Among the options, "Wink" is a deliberate action done with the eyes, used to signal or communicate. Other options are either objects related to eyes, numerical descriptions, or general concepts, not specific actions performed by the eyes. Step-by-Step Solution: Step 1: Identify the relationship between Lips and Smile. A person uses lips to form a smile, so the relationship is body part to its expressive action. Step 2: Apply the same logic to Eyes. We need an action that is normally carried out using the eyes. Step 3: Examine each option. "Black" is a colour and not an action. "Two" is a number and not an action. "Spectacles" are objects worn on the eyes. "Vision" is a capability rather than a distinct action. Step 4: "Wink" is clearly an intentional action performed using the eyes, similar to how a smile is formed with the lips. Step 5: Therefore, the pair "Eyes : Wink" mirrors the structure of "Lips : Smile". Verification / Alternative check: We can verify by attempting to frame sentences. One can say, "You smile with your lips" and "You wink with your eyes." Both sentences show a clear body part to action relationship. None of the other options work naturally in this kind of sentence. For example, "You black with your eyes" or "You spectacles with your eyes" do not make sense as actions. This verification confirms that Wink is the only correct choice. Why Other Options Are Wrong: Black is just a colour and has no direct action relationship with eyes in the way smiling relates to lips. Two only indicates a number and does not represent an activity or expression carried out by the eyes. Spectacles are objects worn with the help of the eyes and nose, not an action performed by the eyes themselves. Vision is the ability to see, which is a function of the eyes, but it is not a discrete voluntary action like winking or smiling. Common Pitfalls: A common mistake is to pick a word loosely associated with eyes, such as Spectacles or Vision, instead of focusing on a strict analogy of action. Students sometimes confuse function and action, but analogy questions demand a very precise parallel. Another pitfall is ignoring the grammatical nature of the second term; Smile and Wink are both verbs or verbal nouns representing actions, not static objects or qualities. Final Answer: The correct completion of the analogy is Eyes : Wink.

Question 8

In this letter analogy question, EHJ is related to KNP, so you must select the group of letters that stands in the same relation to SVX from the given alternatives.

Accepted Answer

Introduction / Context: This question tests your ability to recognise patterns in the positions of letters of the English alphabet. The pair "EHJ : KNP" shows a specific shift from one group of letters to another. You must detect that rule and apply it to the group "SVX" to find the correctly related set of letters from the options. Letter analogy questions like this are very common in competitive exams and require careful observation of alphabet positions. Given Data / Assumptions: - The first pair given is EHJ and KNP. - The second pair to be completed is SVX and ?. - We consider A as the 1st letter, B as the 2nd, and so on up to Z as the 26th letter. - The answer must follow the same pattern of positional shifts that transforms EHJ into KNP. Concept / Approach: The usual approach is to convert each letter into its alphabet position, find the numeric pattern, and then apply the same transformation. By comparing corresponding letters in EHJ and KNP, we can determine how many steps forward in the alphabet each letter has moved. Once we find this constant shift, we apply it to S, V and X to generate the correct answer. Finally, we compare our result with the options to identify the exact matching triplet. Step-by-Step Solution: Step 1: Note the alphabet positions. E is 5, H is 8 and J is 10. K is 11, N is 14 and P is 16. Step 2: Compute the shifts. From E (5) to K (11) is +6. From H (8) to N (14) is also +6. From J (10) to P (16) is again +6. Step 3: Conclude that each letter in EHJ is moved 6 places forward in the alphabet to obtain KNP. Step 4: Apply the same +6 rule to SVX. S is 19, so 19 + 6 = 25, which is Y. V is 22, so 22 + 6 = 28. Since the alphabet has 26 letters, 28 wraps around to 2 (28 - 26), which is B. X is 24, so 24 + 6 = 30; 30 - 26 = 4, which is D. Step 5: Therefore, SVX becomes YBD after shifting each letter six positions forward in the alphabet. Verification / Alternative check: We can verify the wrap around logic for letters beyond Z. After Z (26), we cycle back to A (1), B (2), C (3) and so on. Hence, adding 6 to V (22) gives 28, which is correctly interpreted as 2 (B). Similarly, adding 6 to X (24) produces 30, which wraps around to 4 (D). Now we compare YBD to the options. Option B exactly matches YBD, while all other options differ in at least one letter. This confirms that YBD is the correctly related group for SVX. Why Other Options Are Wrong: XZZ does not follow the uniform +6 shift from SVX and introduces repeated Zs, which are not consistent with the pattern. BDF arises from very small shifts and does not align with the +6 movement observed between EHJ and KNP. ZBD partly resembles the wrapping pattern but would require a different shift from S and V than the one used to get from EHJ to KNP, so it breaks the analogy. WAC also fails to maintain the consistent +6 shift for all three letters and therefore cannot be accepted as a valid analogy. Common Pitfalls: A frequent error is to miscount alphabet positions or forget to wrap around after Z. Another common mistake is to focus only on approximate patterns, such as any forward shift, instead of insisting on an exact and consistent numerical shift for each letter. Aspirants might also incorrectly assume different shifts for different letters, but a standard letter analogy in this format almost always uses the same shift for all positions. Final Answer: Using a uniform shift of six letters forward in the alphabet, SVX becomes YBD.

Question 9

In this analogy question, Umbrella is related to Rain, so you must select the word that shows a similar relationship with Sweater from the given alternatives.

Accepted Answer

Introduction / Context: This is a simple everyday life analogy that tests practical reasoning. In the pair "Umbrella : Rain", the umbrella is an object used for protection against rain. The question asks for a similar relationship with "Sweater" on the left side. Therefore, you must identify what a sweater is mainly used against or for, in the same way an umbrella is used against rain. Given Data / Assumptions: - Umbrella is commonly used during rain to protect a person from getting wet. - Sweater is a warm garment usually worn in winter or cold weather. - The options are Wool, Wear, Summer, Cold and Cloth. - We assume general, practical meanings of these words as used in daily life. Concept / Approach: The relationship in the first pair is "object used for protection against a particular environmental condition". An umbrella protects us from rain. Similarly, a sweater protects us from cold. The focus is not on what the object is made of (material), but on the natural condition it is used to guard against. With this understanding, we check which option best completes "Sweater : ?". Step-by-Step Solution: Step 1: Interpret the first pair. Umbrella is used during rain to keep a person dry, which means it protects against rain. Step 2: Apply the same idea to sweater. A sweater is mainly worn to keep the body warm. Step 3: Identify the environmental factor a sweater protects against. It protects against low temperature or cold. Step 4: Look at the options. Wool is the material used to make many sweaters. Wear is a verb. Summer is a hot season, opposite to when sweaters are worn. Cold is the weather condition that sweaters protect against. Step 5: Conclude that the correct relation is "Sweater : Cold". Verification / Alternative check: We can verify by forming meaningful statements. "We use an umbrella in rain" matches "We wear a sweater in cold." Both have the same structure of object used in a particular condition. If we try to use other options, the parallel breaks. For example, "Umbrella : Rain" does not parallel "Sweater : Wool" because rain is not the material of an umbrella. Thus, only Cold gives a proper functional relationship. Why Other Options Are Wrong: Wool is a common material used for making sweaters, but the original analogy focuses on the situation of use, not on material. Wear is a verb describing the act of putting on clothes and cannot stand in the same relationship that rain has with umbrella. Summer is a hot season when sweaters are usually not needed, so it does not fit the protective role that rain plays with umbrella. Cloth is a general term for fabric and again relates to material, not to the environmental condition that triggers sweater usage. Common Pitfalls: Candidates sometimes get confused between material and usage. In many analogy questions, especially with clothing and tools, the relationship is about function or purpose, not composition. Another pitfall is selecting an opposite concept like Summer because sweaters are not worn then, but analogies require a direct and positive relation similar to the first pair, not a contrary one. Final Answer: The correct completion of the analogy is Sweater : Cold.

Question 10

In this conceptual analogy question, Sound is related to Medium, so you must select the term that shows a similar scientific relationship with Light from the given alternatives.

Accepted Answer

Introduction / Context: This question checks your basic understanding of physics concepts related to wave propagation. Sound waves require a material medium like air, water or solids to travel. Light, however, is an electromagnetic wave and behaves differently. The analogy "Sound : Medium" describes a necessary condition for the propagation of sound. You must identify which option completes the analogy by giving the correct essential condition or characteristic environment for light in a comparable way. Given Data / Assumptions: - Sound waves are mechanical vibrations that cannot travel in a perfect vacuum and require a medium such as air, water or solids. - Light is an electromagnetic wave that does not require a material medium for propagation. - Light can travel through vacuum as well as through media like air, water and glass, but its speed changes with the medium. - The options are Air, Vacuum, Water, Glass and Space. Concept / Approach: The key difference is that sound needs a medium, whereas light does not. The relation "Sound : Medium" emphasises that a medium is essential for sound propagation. To create a parallel, we should use a word that captures the essential characteristic of light propagation. The most important fact is that light can travel through a vacuum, which is not possible for sound. Therefore, the most appropriate completion is "Light : Vacuum". This highlights the contrasting but equally fundamental condition for light, just as "medium" is fundamental for sound. Step-by-Step Solution: Step 1: Understand the first pair. Sound is a mechanical wave, and its propagation requires a material medium such as air, water or solid objects. Step 2: Recall the basic physics of light. Light is an electromagnetic wave and can travel even where there is no material medium. Step 3: Specifically, light can travel through the vacuum of outer space. This is why we can receive sunlight on Earth despite the emptiness of space. Step 4: Examine the options. Air, water and glass are all media through which light can travel, but they are not essential in the same sense that a medium is essential for sound. Step 5: Vacuum uniquely captures the fundamental property that light does not require a medium, so "Light : Vacuum" best mirrors the importance of "Medium" for sound. Verification / Alternative check: We can verify by contrasting the situations. If all air is removed from a container to form a near vacuum, a ringing bell inside cannot be heard because sound cannot travel without a medium. However, if a light source is placed inside the same vacuum chamber, its light can still be seen outside through a transparent window, because light can travel through the vacuum. This thought experiment clearly supports the analogy "Sound : Medium :: Light : Vacuum". None of the other options directly express this defining property. Why Other Options Are Wrong: Air is indeed a medium for both sound and light, but the pair "Light : Air" would focus on one particular medium and not on the essential fact that light can travel without any medium. Water is another medium that can transmit both sound and light, but it plays no unique or fundamental role for light propagation. Glass is a transparent medium used in lenses and prisms, yet it is just one of many media and does not express the key contrast with sound. Space is often used informally to refer to outer space, but scientifically the important concept is vacuum, which precisely indicates absence of material medium. Common Pitfalls: A common mistake is to select Air, since both sound and light frequently travel through air in daily life. However, analogy questions require the relationship to match at a conceptual level, not just based on common examples. Another pitfall is not recalling that sound cannot propagate in a vacuum, whereas light can, which is a fundamental high school physics concept. Final Answer: The relationship "Sound : Medium" is most closely mirrored by Light : Vacuum.

Question 11

In this letter analogy question, TR is related to VX, so you must select the pair of letters that stands in the same relation to MK from the given alternatives.

Accepted Answer

Introduction / Context: This question is a two-letter analogy based on positions in the English alphabet. The pair "TR : VX" is formed by shifting each letter of the first pair by a certain number of positions to obtain the second pair. Your task is to recognise this pattern and apply it to the pair "MK" in order to find the corresponding pair from the options. Given Data / Assumptions: - First analogy pair: TR and VX. - Second pair to complete: MK and ?. - Alphabet positions: A = 1, B = 2, ..., Z = 26. - Options are QP, QR, OQ, OP and NR. - The same transformation that converts TR to VX must be used to convert MK to the correct answer. Concept / Approach: The usual technique with letter analogies is to convert each letter to its numeric position, find the shift for each letter in the first pair, and then apply the same shifts to the second pair. We will examine how T changes to V and how R changes to X, then use those observed increments to transform M and K. Only the option that exactly matches the resulting letters can be the correct answer. Step-by-Step Solution: Step 1: Determine numeric positions. T is the 20th letter, R is the 18th, V is the 22nd and X is the 24th. Step 2: Find the shift from T to V. From 20 to 22 is an increase of +2. Step 3: Find the shift from R to X. From 18 to 24 is an increase of +6. Step 4: Conclude that the pattern is: first letter +2, second letter +6. Step 5: Apply the same rule to MK. M is the 13th letter, so 13 + 2 = 15, which is O. K is the 11th letter, so 11 + 6 = 17, which is Q. Step 6: Therefore, MK becomes OQ under the same transformation, and we select the option OQ. Verification / Alternative check: To verify, quickly test whether any other option could fit the observed pattern. Suppose we choose OP: that would give M to O (+2) and K to P (+5), which does not match the +6 shift for the second letter observed in the TR to VX mapping. Similarly, QP or QR require different shifts for one or both letters, violating the consistency of the analogy. Only OQ gives the exact +2 and +6 increments for the first and second letters respectively, fully matching the original pattern. Why Other Options Are Wrong: QP would require M to become Q (+4) and K to become P (+5), which does not follow the +2, +6 pattern. QR would correspond to shifts of +4 and +7 respectively, again inconsistent with the established mapping from TR to VX. OP arises from shifts of +2 for M and +5 for K, which does not match the second letter shift of +6 seen in the first pair. NR would represent shifts of +1 and +7, which are not observed in the transformation from TR to VX and thus cannot be correct. Common Pitfalls: A common pitfall in such questions is to guess based on rough similarity rather than precise numeric shifts. Some students notice that many options are alphabetically near one another and choose one that superficially seems close. However, letter analogy questions require exact mapping. Another mistake is to assume the same shift for both letters when the first pair clearly shows different shifts for each position. Final Answer: Applying the same +2 and +6 shifts that map TR to VX, the pair MK becomes OQ.

Question 12

In this letter analogy question, ZY is related to CD, so you must select the pair of letters that stands in the same relationship to SR from the given alternatives.

Accepted Answer

Introduction / Context: This question requires you to identify a symmetrical pattern in alphabet positions. The pair "ZY : CD" involves letters near the end of the alphabet mapped to letters near the beginning. Your task is to find the same kind of mapping for the pair "SR" from the given alternatives. Such questions test whether you can recognise hidden numerical relationships between letter positions. Given Data / Assumptions: - First pair: ZY and CD. - Second pair to complete: SR and ?. - Alphabet positions: A = 1, B = 2, ..., Z = 26. - Options are RS, JK, JP, PQ and LM. - The transformation used for both letters in ZY must be applied consistently to S and R. Concept / Approach: The key idea is to look for complementary positions in the alphabet. When we convert ZY to CD, we notice that Z and C are symmetric about a certain central value, and the same is true for Y and D. Specifically, if we add the position numbers of each pair of corresponding letters, the sum is constant. We can use this property to find the letters that pair with S and R. Step-by-Step Solution: Step 1: Determine alphabet positions. Z is 26, Y is 25, C is 3 and D is 4. Step 2: Add paired positions. For Z and C, 26 + 3 = 29. For Y and D, 25 + 4 = 29. So each pair sums to 29. Step 3: This shows that each letter in ZY is mapped to a letter whose position gives a total of 29 when added to the original letter's position. Step 4: Apply the same idea to S and R. S is 19, so we need a letter whose position plus 19 equals 29. That letter has position 10, which is J. R is 18, so we need a letter whose position plus 18 equals 29. That letter has position 11, which is K. Step 5: Thus, SR maps to JK under the same complementary-to-29 rule. Verification / Alternative check: We can verify by checking sums again. For S (19) and J (10), 19 + 10 = 29. For R (18) and K (11), 18 + 11 = 29. The pattern is exactly the same as for ZY to CD. Now examine the options. Only the pair JK gives both sums equal to 29. Other options either do not use the correct positions or break the constancy of the sum. Therefore, JK is the only pair fully consistent with the rule discovered from the first analogy. Why Other Options Are Wrong: RS simply repeats the letters and does not produce complementary pairs; the sums would be 19 + 18, which does not match the required pattern. JP would give sums 19 + 10 and 18 + 16, which are different and do not match the constant total of 29 seen in the first pair. PQ would produce 19 + 16 and 18 + 17, again failing to give a consistent fixed sum for both positions. LM similarly does not produce the constant-sum property observed in ZY and CD, so it cannot be the correct match. Common Pitfalls: Many candidates try to find a simple shift such as adding or subtracting a fixed number of positions, which does not always work for symmetrical analogies. Another error is to look only at one letter of the pair and ignore whether the same rule applies to the second letter. Symmetry questions require checking all letters and ensuring that the same numeric relationship holds throughout. Final Answer: Using the complementary-to-29 mapping, "SR" converts to JK.

Question 13

In this numerical analogy question, 8 is related to 27, so you must select the number that shows the same relationship with 64 from the given alternatives.

Accepted Answer

Introduction / Context: This question belongs to the category of numerical analogies where you must detect a mathematical relationship between two numbers and then apply the same rule to another given number. The pair "8 : 27" suggests a relationship involving powers or cubes because these numbers are familiar as 2 cube and 3 cube. You must check this idea and then apply it to 64 to find the missing number. Given Data / Assumptions: - First pair of numbers: 8 and 27. - Second pair to be completed: 64 and ?. - Options: 75, 65, 100, 125 and 216. - We assume standard arithmetic operations: addition, subtraction, multiplication, division and powers such as squares and cubes. Concept / Approach: The key concept is recognising perfect cubes. In many reasoning questions, the numbers 8 and 27 immediately hint at cubes, since 8 = 2^3 and 27 = 3^3. Once we observe this, it is natural to check whether 64 is also a cube and then continue the pattern using the next integer. This approach avoids unnecessary complex operations and uses standard number properties that are frequently examined in aptitude tests. Step-by-Step Solution: Step 1: Express 8 and 27 as powers. 8 = 2^3 and 27 = 3^3. Step 2: Observe the pattern: the first term is the cube of 2, and the second term is the cube of the next integer, 3. So the rule is: n^3 is related to (n + 1)^3. Step 3: Check 64. 64 = 4^3, so it fits into the sequence of cubes: 2^3, 3^3, 4^3, 5^3 and so on. Step 4: Apply the same rule to 64. If 64 = 4^3, then the related number should be the cube of the next integer, 5, that is 5^3. Step 5: Compute 5^3. 5 * 5 * 5 = 125. Step 6: Therefore, 64 is related to 125, just as 8 is related to 27. Verification / Alternative check: To double-check, there is no simple consistent rule such as multiplication by a constant or addition of a fixed number that can convert 8 into 27. However, the cube idea works elegantly and extends naturally to 64. Also, among the options, only 125 is a perfect cube, which further supports the cube pattern. The sequence 8, 27, 64, 125 can be recognised as consecutive cubes of 2, 3, 4 and 5. Why Other Options Are Wrong: 75 is not a perfect cube and does not fit any natural extension of the pattern created by 8 and 27. 65 is close to 64 but again has no cube property or simple relation that mirrors the original pair. 100 is a square (10^2), not a cube, and does not follow the consecutive cube pattern. 216 is 6^3 and would correspond to continuing the cube sequence even further, but the immediate next cube after 64 is 125 (5^3), not 216. Common Pitfalls: Many students do not immediately recognise 8 and 27 as cubes and instead try to apply ad hoc operations such as adding 19 or multiplying by fractions. Another common mistake is to think that 64 should be doubled or increased by some fixed difference. In analogy questions, always check for familiar patterns like squares, cubes and factorials before resorting to complex calculations. Final Answer: The correct completion of the analogy is 64 : 125, following the pattern of consecutive cubes.

Question 14

In this sports-based analogy, Sachin Tendulkar is related to Cricket, so you must select the sport that stands in the same relation to Roger Federer from the given alternatives.

Accepted Answer

Introduction / Context: This question tests general knowledge about famous sportspersons and the games for which they are best known. The pair "Sachin Tendulkar : Cricket" connects a legendary Indian player with the sport in which he achieved worldwide fame. You must identify the sport that has the same relationship with Roger Federer, an equally famous international player. Given Data / Assumptions: - Sachin Tendulkar is widely known as one of the greatest cricketers in history. - Roger Federer is an internationally acclaimed professional athlete. - The sports given in the options are Lawn Tennis, Football, Basketball, Volleyball and Hockey. - We assume we are matching each person to the sport in which they are primarily recognised as champions. Concept / Approach: The relationship in the first pair is "sportsperson : primary sport". We know that Sachin Tendulkar is associated with cricket. In the same manner, we must associate Roger Federer with his main sport. A basic level of sports general knowledge tells us that Roger Federer is one of the most successful and famous players in tennis, especially in men's singles Grand Slam tournaments. Therefore, the correct sport to pair with his name is Lawn Tennis. Step-by-Step Solution: Step 1: Identify the relation in the given pair. Sachin Tendulkar is a legendary player of cricket, so the relation is player to sport. Step 2: Recall who Roger Federer is. He is a Swiss professional tennis player. Step 3: Check the options. Lawn Tennis, Football, Basketball, Volleyball and Hockey are all popular sports, but only Lawn Tennis matches Roger Federer's field of achievement. Step 4: Confirm that Federer is known for winning many titles in Lawn Tennis, especially in major tournaments like Wimbledon, Australian Open and others. Step 5: Therefore, the pair for the second part must be "Roger Federer : Lawn Tennis". Verification / Alternative check: We can verify by elimination. There is no famous connection of Roger Federer with football, basketball, volleyball or hockey as a professional player. His career, records and titles are all from tennis. Only Lawn Tennis correctly associates a champion with his sport, just as Cricket does for Sachin Tendulkar. Thus, the analogy structure remains consistent across both pairs. Why Other Options Are Wrong: Football is associated with players such as Lionel Messi or Cristiano Ronaldo, not with Roger Federer. Basketball is connected with athletes like Michael Jordan or LeBron James, so it does not match Federer. Volleyball and Hockey are also unrelated to Federer's professional career, and pairing them with his name would be factually incorrect. Common Pitfalls: If a candidate is not familiar with international sports figures, they might randomly guess another game. Exam aspirants should maintain a basic awareness of major world sportspersons and their fields, as such questions are frequently asked in aptitude and general awareness sections. It is also important to focus on the primary, not secondary, association of a person's name with a sport. Final Answer: The correct analogy is Roger Federer : Lawn Tennis.

Question 15

In this letter analogy question, TC is related to EV, so you must select the pair of letters that stands in the same relation to NS from the given alternatives.

Accepted Answer

Introduction / Context: This is a letter analogy problem that checks your ability to observe patterns involving simple transformations like reversing pairs and shifting letters. The given pair is "TC : EV", and you need to determine which option forms a similar relationship with the pair "NS". A careful look at letter positions and order reveals the rule used to generate the second pair from the first. Given Data / Assumptions: - First pair: TC becomes EV. - Second pair to be completed: NS becomes ?. - Alphabet positions: A = 1, B = 2, ..., Z = 26. - Options: QT, LK, PU, UP and RV. - We assume the same pattern is applied to both letter pairs. Concept / Approach: One useful strategy in two-letter analogies is to check whether the letters are reversed and then shifted by a fixed number of positions. When we examine "TC" and "EV", we can see that if we first reverse TC to get CT and then move each letter forward by 2 positions, we obtain EV. We will verify this and then apply the same two-step operation to the pair NS. Step-by-Step Solution: Step 1: Start with TC. Reverse the order of the letters to get CT. Step 2: Convert C and T to their alphabet positions. C is 3 and T is 20. Step 3: Add 2 to each position. For C (3), 3 + 2 = 5, which is E. For T (20), 20 + 2 = 22, which is V. Step 4: Thus, CT becomes EV, confirming that the rule is: reverse the pair, then shift both letters two positions forward. Step 5: Apply the same steps to NS. Reverse NS to get SN. Step 6: S is the 19th letter. 19 + 2 = 21, which is U. N is the 14th letter. 14 + 2 = 16, which is P. Step 7: Therefore, SN becomes UP, and the correct corresponding pair for NS is UP. Verification / Alternative check: We can quickly check other options to ensure no other pair follows the same transformation. For NS, any correct option must be obtained by reversing NS to SN and then shifting each letter two steps ahead. Only U and P satisfy this condition. Pairs like QT, LK, PU and RV do not match the exact letters obtained in this process. Therefore, UP is uniquely consistent with the discovered rule, confirming the answer. Why Other Options Are Wrong: QT would require different shifts or a different ordering that does not align with the reverse-and-shift pattern used for TC. LK is not derived from NS by reversing and then shifting forward by two positions, so it breaks the analogy. PU has the correct letters but in the wrong order, indicating that the full pattern, including reversal, is not satisfied. RV introduces letters that require larger or unequal shifts and does not follow the simple two-step transformation identified. Common Pitfalls: A common error is to observe only the shift in positions without noticing the reversal of letters. Another pitfall is to choose options that contain similar letters but ignore their precise order and exact positional changes. For success in such questions, always examine both the order and the numerical shifts carefully. Final Answer: Using the rule "reverse the pair and then shift each letter two positions forward", NS corresponds to UP.

Question 16

In this letter analogy question, DR is related to KK, so you must select the pair of letters that stands in the same relationship to LN from the given alternatives.

Accepted Answer

Introduction / Context: This is a slightly different letter analogy that involves a numeric relationship between pairs of letters. The pair "DR : KK" is formed by applying a specific rule to the positions of D and R. Your task is to identify the same rule and use it to convert the pair "LN" into another pair from the given options. Recognising patterns in sums and differences of alphabet positions is crucial here. Given Data / Assumptions: - First pair: DR becomes KK. - Second pair to complete: LN becomes ?. - Alphabet positions: A = 1, B = 2, ..., Z = 26. - Options: QH, SH, SG, GR and MM. - The same numeric relationship must link both letters of each input pair to the corresponding output pair. Concept / Approach: The pattern used here involves both the sum of the positions of the letters in each pair and a fixed increase applied to the first letter. For DR, D is the 4th letter and R is the 18th letter. Their sum is 22. The output KK has both letters K, and K is the 11th letter. Two Ks together also sum to 22 (11 + 11). Additionally, the first letter in the output, K, is 7 more than the first input letter D. We will confirm this and then apply the same logic to LN. Step-by-Step Solution: Step 1: Convert D and R to numbers. D is 4 and R is 18. Their sum is 4 + 18 = 22. Step 2: The output KK corresponds to 11 and 11. Their sum is 11 + 11 = 22, so the total is preserved. Step 3: Notice that the first output letter K (11) is 7 more than the first input letter D (4). So 4 + 7 = 11. Step 4: To keep the total sum the same, the second output letter is automatically determined. It must be 22 minus 11, which is also 11, giving KK. Step 5: Apply the same idea to LN. L is 12 and N is 14. Their sum is 12 + 14 = 26. Step 6: Increase the first letter L by 7 positions. 12 + 7 = 19, which is S. Step 7: To keep the sum 26, the second letter must have position 26 minus 19 = 7, which is G. Step 8: Therefore, LN becomes SG under the same transformation. Verification / Alternative check: We can verify by checking the total sums again. For LN (12 and 14), the total is 26. For SG, S is 19 and G is 7, and 19 + 7 = 26. The sum is preserved just like in DR and KK. Also, S is exactly 7 positions ahead of L, matching the increase observed from D to K in the first pair. No other option satisfies both the sum-preservation and the +7 increment for the first letter simultaneously, so SG is the unique correct answer. Why Other Options Are Wrong: QH corresponds to 17 and 8. Their sum is 25, not 26, so it fails the sum-preservation rule. SH is 19 and 8, giving a sum of 27, which again does not match 26. GR is 7 and 18, with a sum of 25, and G is not 7 steps ahead of L, so it breaks both parts of the pattern. MM would give 13 and 13, whose sum is 26, but 13 is only 1 step ahead of L, not 7, so the increment condition is violated. Common Pitfalls: Students often look only for direct shifts such as adding or subtracting a fixed number to each letter independently. In this question, the pattern depends on a combination of two ideas: shifting the first letter by a fixed amount and preserving the total sum of positions. Ignoring either condition leads to wrong answers. Always examine both the individual letter changes and the behaviour of the pair as a whole. Final Answer: Using the same pattern that converts DR into KK, the pair LN is converted into SG.

Question 17

In this numerical analogy question, 5 is related to 100, so you must select the number that stands in the same relation to 6 from the given alternatives.

Accepted Answer

Introduction / Context: This question is a numerical analogy where a specific mathematical operation relates the first number to the second. The pair "5 : 100" suggests that the answer might involve powers or products rather than simple addition or subtraction. Your task is to detect the exact rule used to obtain 100 from 5 and then apply the same rule to the number 6 to find the missing term. Given Data / Assumptions: - First pair of numbers: 5 and 100. - Second pair to be completed: 6 and ?. - Options: 180, 150, 160, 170 and 144. - Standard arithmetic operations and basic algebraic expressions such as n^2, n^3 or combinations are considered. Concept / Approach: We suspect that a combined power and product rule may link 5 and 100. Clearly, 5^2 = 25 and 5^3 = 125, neither equals 100 alone. However, if we multiply 5^2 by (5 minus 1), that is 25 * 4, we obtain 100. This leads to a compact expression n^3 - n^2 = n^2 * (n - 1). We can verify this expression for n = 5 and then apply the same for n = 6 to determine the second term. Step-by-Step Solution: Step 1: Write an expression that turns 5 into 100. One suitable formula is n^3 - n^2. Step 2: Substitute n = 5. Compute 5^3 = 125 and 5^2 = 25. Then 5^3 - 5^2 = 125 - 25 = 100, matching the given pair. Step 3: Recognise that this simplifies to n^2 * (n - 1), since n^3 - n^2 = n^2 * (n - 1). Step 4: Apply the same rule to n = 6. Compute 6^3 = 216 and 6^2 = 36. Then 6^3 - 6^2 = 216 - 36. Step 5: 216 - 36 = 180. Step 6: Therefore, 6 is related to 180 in the same way that 5 is related to 100. Verification / Alternative check: We can verify by checking whether any simpler rules fit equally well. Doubling 5 or using 5 * 20 gives 100, but applying the same fixed factor to 6 would give 120, which is not in the options. Similarly, 5^2 * 4 = 100 uses a factor (n - 1) when n = 5. For n = 6, this would be 6^2 * 5 = 36 * 5 = 180, which agrees with our n^3 - n^2 formula. Among the options provided, only 180 matches this result, confirming the correctness of the rule. Why Other Options Are Wrong: 150 cannot be expressed as 6^3 - 6^2 or 6^2 * (6 - 1), so it does not follow the same pattern. 160 also fails to match the derived expression and thus breaks the analogy. 170 is an arbitrary nearby number with no clear relation to 6 via the rule n^3 - n^2. 144 might be attractive as 12^2, but the original mapping from 5 to 100 did not use a pure square alone, so 144 is inconsistent with the rule. Common Pitfalls: Some candidates may try simple multiplication or addition first and then pick an option that seems reasonably close. However, numerical analogies in exams often depend on structured expressions like n^2 * (n - 1) or combinations of powers. Another pitfall is stopping after testing only one plausible formula without confirming that it fits both the given pair and the options uniformly. Final Answer: Following the same rule that maps 5 to 100, the number 6 is mapped to 180.

Question 18

In this analogy question on basic geometry, Rectangle is related to Four, so you must select the figure and number pair that stands in the same relation from the given alternatives.

Accepted Answer

Introduction / Context: This is a simple geometry-based analogy question. The pair "Rectangle : Four" connects a shape to the number of its sides. Your task is to identify which of the given pairs follows exactly the same type of relationship between a geometric figure and the count of its sides. Knowledge of basic plane shapes is sufficient to answer this question correctly. Given Data / Assumptions: - A rectangle is a quadrilateral with four sides. - A triangle has three sides. - A square is also a quadrilateral with four equal sides. - A general polygon can have many sides, typically more than or equal to three. - A circle does not have straight sides; it is defined by a continuous curve. - The options link each figure to a suggested number of sides: Square : Seven, Polygon : Two, Circle : Six, Triangle : Three and Hexagon : Five. Concept / Approach: The relationship between Rectangle and Four is "name of the figure : correct number of sides." We need another pair where the right-hand number correctly states the number of sides of the figure on the left. We will check each option against standard geometric facts and select the one that accurately matches. At the same time, we must ensure that the relationship type is identical to the original pair, focusing strictly on the count of sides. Step-by-Step Solution: Step 1: Confirm the base relationship. A rectangle has four sides, so "Rectangle : Four" is figure to correct number of sides. Step 2: Examine "Square : Seven". A square has four sides, not seven, so the number is wrong. Step 3: Examine "Polygon : Two". A polygon must have at least three sides, so two is not a valid count. Step 4: Examine "Circle : Six". A circle has no straight sides; instead, it forms a continuous curved boundary, so six is not an accurate side count. Step 5: Examine "Triangle : Three". A triangle has three straight sides, so this pair is correctly matched. Step 6: Examine "Hexagon : Five". A regular hexagon has six sides, so five is incorrect. Step 7: Only "Triangle : Three" parallels "Rectangle : Four" by giving the correct number of sides for the figure. Verification / Alternative check: To further verify, list standard side counts: triangle (3), quadrilateral including rectangle and square (4), pentagon (5), hexagon (6) and so on. Comparing these with the numeric values in each option shows that every pair except "Triangle : Three" contains a deliberate mismatch. Therefore, "Triangle : Three" is the unique pair that preserves the same relationship as "Rectangle : Four". Why Other Options Are Wrong: Square : Seven is incorrect because a square is a four-sided figure, not a seven-sided one. Polygon : Two is invalid since no polygon can have only two sides; at least three sides are required to form a closed polygonal shape. Circle : Six is wrong because a circle is not defined by straight sides at all, so associating it with six sides is conceptually incorrect. Hexagon : Five is wrong because a hexagon has six sides, not five. Common Pitfalls: Some test takers may misremember the number of sides of a hexagon or become distracted by the word polygon. Others may think that since a circle can be approximated by many small line segments, it might be linked to a larger number such as six. However, exam questions rely on standard textbook definitions, where the side counts mentioned are exact and not approximations. Final Answer: The pair that correctly mirrors "Rectangle : Four" is Triangle : Three.

Question 19

In this number analogy question, 13 is related to 17, so you must select the pair of numbers that stands in the same relationship from the given alternatives.

Accepted Answer

Introduction / Context: This is a number analogy that tests basic knowledge of prime numbers and their patterns. The pair "13 : 17" connects two special numbers that both happen to be prime and separated by a fixed difference. Your task is to find a similar pair among the options that maintains the same type of relationship. Given Data / Assumptions: - First pair: 13 and 17. - Candidate pairs: 17 : 24, 19 : 23, 19 : 27, 21 : 23 and 15 : 21. - Prime numbers are integers greater than 1 that have no positive divisors other than 1 and themselves. - We assume that the analogy is based on simple properties like primality and numerical difference. Concept / Approach: We first look at what is special about 13 and 17. Both are prime numbers, and their difference is 17 minus 13, which equals 4. Thus, 13 and 17 form a pair of prime numbers with a difference of 4. We now scan the option pairs to find another pair where both numbers are prime and the difference between them is also 4. Step-by-Step Solution: Step 1: Confirm that 13 and 17 are prime. Neither has factors other than 1 and itself. Step 2: Compute their difference. 17 - 13 = 4. Step 3: Examine each option pair and check for both primality and a difference of 4. Step 4: For 17 : 24, 17 is prime but 24 is composite, and the difference is 7. Step 5: For 19 : 23, both 19 and 23 are prime, and 23 - 19 = 4, matching both criteria. Step 6: For 19 : 27, 27 is composite and the difference is 8. Step 7: For 21 : 23, 21 is composite and the difference is 2. Step 8: For 15 : 21, both numbers are composite and do not satisfy the prime requirement. Step 9: Conclude that only 19 : 23 matches the pattern of prime numbers separated by 4. Verification / Alternative check: We can list nearby prime numbers to confirm the pattern: 11, 13, 17, 19, 23 and 29. Looking at these, we see that some consecutive primes differ by 2, some by 4 or more. The pair 13 and 17 is a prime pair with a difference of 4, and similarly, 19 and 23 form the next such pair in this sequence. No other option reproduces the same combination of properties. This confirms that 19 : 23 is the correct analogy. Why Other Options Are Wrong: 17 : 24 fails because 24 is not a prime number and the difference is 7, not 4. 19 : 27 fails because 27 is composite and the difference is 8, so the pair does not mirror the original pattern. 21 : 23 has one composite and one prime number with a smaller difference of 2, so it does not match the structure of the first pair. 15 : 21 consists of two composite numbers and therefore does not follow the prime-number theme at all. Common Pitfalls: A common error is to focus only on the difference and ignore whether the numbers are prime. For example, one might be tempted by any pair with a difference of 4 even if one of the numbers is composite. It is important to identify all key properties of the first pair, not just one. Another pitfall is misidentifying prime numbers, so candidates should be comfortable checking divisibility for numbers up to at least 30. Final Answer: The pair that mirrors the relationship of prime numbers differing by four is 19 : 23.

Question 20

In this analogy question about professions and workplaces, Scientist is related to Laboratory, so you must select the place that stands in the same relation to Astronomer from the given alternatives.

Accepted Answer

Introduction / Context: This is a profession-and-workplace analogy. The pair "Scientist : Laboratory" links a profession with the place where that professional typically performs experimental or research work. Your task is to determine which location is similarly related to an astronomer, who studies celestial objects such as stars, planets and galaxies. Given Data / Assumptions: - A scientist generally conducts experiments and research in a laboratory. - An astronomer specialises in studying celestial bodies and cosmic phenomena. - Options: Garage, Battlefield, Observatory, Hospital and Library. - We assume standard professional contexts, not unusual or metaphorical meanings. Concept / Approach: The underlying relationship is "professional : typical primary workplace." A laboratory is the main work environment for many scientists. For an astronomer, the equivalent specialised workplace is the observatory, where telescopes and other instruments are installed for systematic observation of the sky. While astronomers may also work in offices or universities, the observatory is the most precise answer that parallels the laboratory in the original pair. Step-by-Step Solution: Step 1: Interpret the first pair. Scientists carry out experiments and research in laboratories, so the relationship is profession to main work environment. Step 2: Identify the core working environment of an astronomer. Astronomers observe stars, planets and other celestial objects, often using large telescopes and specialised equipment. Step 3: Such instruments are typically housed in an observatory, which is specifically designed for astronomical observations. Step 4: Review the options. A garage is used for vehicle repair or storage, a battlefield is associated with soldiers, a hospital is linked with doctors and nurses, and a library is associated with reading and research but not specifically astronomy. Step 5: Only an observatory clearly serves as the dedicated professional environment for astronomers, just as a laboratory does for scientists. Verification / Alternative check: We can verify by forming similar descriptive sentences. "A scientist works in a laboratory" and "An astronomer works in an observatory" are both clear and accurate. If we try similar sentences with other options such as "An astronomer works in a battlefield" or "An astronomer works in a garage", they become obviously incorrect. This confirms that the observatory is the correct workplace corresponding to the astronomer in the analogy. Why Other Options Are Wrong: Garage is associated with mechanics who repair vehicles, not with astronomical observation. Battlefield is related to soldiers and military operations, not scientific sky observation. Hospital is primarily associated with medical professionals like doctors and nurses, not astronomers. Library is a place for reading and research in general, but it is not the specific professional workplace for practical astronomical observation, unlike an observatory. Common Pitfalls: Some candidates might be tempted by the word library because astronomers and scientists both read and research. However, libraries are support environments common to many professions. The analogy demands a specialised workplace, just as a laboratory is specialised for scientists. Another pitfall is not focusing on the profession at all and instead making a guess based on familiarity of words. Final Answer: The workplace that correctly completes the analogy is Observatory, giving the pair "Astronomer : Observatory".

Analogy Questions