Question 1

In this number analogy question, select the related number from the given alternatives: 13 : 20 :: 17 : ?

Accepted Answer

Introduction / Context: This number analogy question asks you to detect a simple arithmetic relationship that links 13 to 20 and then extend the same rule to 17. Identifying such patterns is an important part of quantitative aptitude because it trains you to see how numbers transform under basic operations. Given Data / Assumptions: - The first pair is 13 and 20. - The second starting number is 17. - The options are 25, 26, 27, and 28. - We assume the rule involves standard operations such as multiplication and addition or subtraction and that it should be simple and consistent. Concept / Approach: A good strategy is to try a combination of multiplying by a small number and then adding or subtracting a constant. Notice that 13 * 2 equals 26, which is close to 20, and 13 * 2 - 6 equals 20 exactly. This suggests a formula of the form result = (number * 2) - 6. If this rule works for 17 as well and matches one of the answer choices, then it is the intended pattern. Step-by-Step Solution: Step 1: Multiply 13 by 2 to get 26.Step 2: Subtract 6 from 26, giving 20. So a possible rule is result = (number * 2) - 6.Step 3: Test whether any simpler rule like number + 7 works. 13 + 7 equals 20, but then 17 + 7 equals 24, which is not an option.Step 4: Now apply the rule result = (number * 2) - 6 to 17. First compute 17 * 2 = 34.Step 5: Subtract 6 from 34 to get 28.Step 6: Among the options, 28 is present as option D, so it is the correct answer.Step 7: The rule is consistent and simple, making it suitable for this analogy question. Verification / Alternative check: Confirm that the formula holds consistently. Using result = (number * 2) - 6, 13 gives 20 and 17 gives 28. If we tried a different pattern, such as result = (number * 2) - 8, then 13 would give 18, not 20. Similarly, a rule like number * 2 + any constant would not match both the given pair and one of the options. This confirms that (number * 2) - 6 is the most reasonable transformation. Why Other Options Are Wrong: - 25: This would come from 17 + 8, which is unrelated to the pattern used with 13. - 26: This equals 17 + 9 or 17 * 2 - 8, which does not fit the transformation seen in the first pair. - 27: There is no simple symmetric rule that maps 13 to 20 and 17 to 27 using the same operations. Common Pitfalls: Test takers sometimes rely on pure addition or subtraction without testing whether the same constant works for both numbers. Others may guess based on proximity to 34, the double of 17, instead of computing the exact rule. To avoid these issues, always derive a formula that exactly fits the given pair, then use it consistently on the second number and confirm that the result appears among the options. Final Answer: Using the pattern result = (number * 2) - 6, 13 maps to 20 and 17 maps to 28. Thus 28 is the correct answer.

Question 2

In this verbal classification question, find the odd word from the given alternatives that does not belong with the others.

Accepted Answer

Introduction / Context: This is an odd one out question in the verbal reasoning section. You must select the word that does not belong to the same group as the others. Such questions test your vocabulary, sense of word meanings, and ability to recognize synonyms and antonyms. Given Data / Assumptions: - The options are Rival, Opponent, Foe, and Ally. - Rival, Opponent, and Foe appear related to conflict or competition. - Ally suggests cooperation or friendship. - We assume standard dictionary meanings without any special context like sports teams or political groups beyond their usual sense. Concept / Approach: The core idea is to group words by similar meanings and then locate the one that differs. Three of the words should be close synonyms, while the fourth should represent an opposite or unrelated concept. Here the majority of the words describe someone who is against you in some way, while one describes someone who supports you. Step-by-Step Solution: Step 1: Consider the meaning of Rival. A rival is someone who competes with you or tries to equal or surpass you.Step 2: Consider the meaning of Opponent. An opponent is a person who is on the opposite side in a game, contest, or argument.Step 3: Consider the meaning of Foe. A foe is an enemy or someone who actively opposes you.Step 4: Now consider the meaning of Ally. An ally is a person or group that cooperates with you or supports you in a cause or conflict.Step 5: Rival, Opponent, and Foe all describe people who are against you, either competitively or in hostility.Step 6: Ally describes someone who is on your side rather than against you.Step 7: Therefore Ally is the odd word that does not belong with the others. Verification / Alternative check: You can group the words into positive and negative relationships. Rival, Opponent, and Foe each imply conflict, resistance, or competition. In contrast, Ally implies friendship, partnership, or support. Since three words belong to the conflict group and one to the support group, the latter stands out as the odd one. No other grouping creates a similar three versus one structure. Why Other Options Are Wrong: - Rival: This word is aligned with conflict and competition and is therefore similar to Opponent and Foe, not the odd one. - Opponent: This term also describes someone who opposes you in a contest, matching the general negative context. - Foe: This explicitly means enemy, which clearly belongs with Rival and Opponent in the same opposition group. Common Pitfalls: Some candidates overthink the relationships, searching for hidden nuances, or focus on less common meanings. Others may not know the word Foe and hesitate. To handle such items effectively, it is useful to build a habit of quickly listing synonyms and antonyms. Recognizing that Ally is essentially the opposite of Foe makes the odd one out pattern much clearer. Final Answer: The only word that represents support and cooperation, rather than opposition, is Ally, so Ally is the odd one out.

Question 3

In this verbal analogy question, complete the pair using an opposite idea: Deep : Shallow :: Ocean : ?

Accepted Answer

Introduction / Context: This analogy question uses contrasting ideas of size or extent. Deep and Shallow form an opposite pair, and you must decide which term has a suitably opposite or contrasting relationship with Ocean. Verbal analogies often use comparisons of big versus small, long versus short, or strong versus weak to test your conceptual understanding. Given Data / Assumptions: - The first pair is Deep and Shallow, which are antonyms describing the extent of depth. - The second given word is Ocean, which is a very large body of water. - The options are Pond, Depth, Well, and Spring. - We assume everyday meanings of these words, focusing on size or magnitude of water bodies where appropriate. Concept / Approach: The key is to grasp how Deep and Shallow relate. They are opposite descriptions for the magnitude of depth. An ocean is an immense, deep body of water. A natural contrasting term would be a small, limited body of water such as a pond. Therefore the analogy uses a similar big versus small contrast between Ocean and Pond. Step-by-Step Solution: Step 1: Recognize that Deep describes a great distance downward, while Shallow describes a small distance downward; they are clear opposites.Step 2: Understand that an ocean is a huge, extensive body of water that is generally deep and wide.Step 3: Look for an option that naturally represents a much smaller and more limited body of water.Step 4: A pond is a small, contained body of water, often shallow and limited in area compared to an ocean.Step 5: Depth is not a water body at all, but a measure of how deep something is, so it does not parallel the word type used for ocean.Step 6: A well is a man made or natural hole from which water is drawn, and a spring is a source from which water flows, but neither provides as clean a size based contrast with ocean as pond does.Step 7: Therefore Pond is the best match to complete the analogy. Verification / Alternative check: Try restating the analogy in descriptive sentences. Deep is the opposite of shallow. An ocean represents something vast and expansive, while a pond represents something small and limited. This shows a similar large versus small contrast. If you try to use depth or well or spring, the parallel structure breaks because those words do not mirror the role of shallow as a contrasting type of water body. Why Other Options Are Wrong: - Depth: This is a noun that refers to a measurement and does not name a water body, so it cannot be the counterpart to ocean. - Well: A well is a water source, often vertical and narrow, and while it can be deep or shallow, it does not offer a simple large versus small contrast with ocean. - Spring: A spring is a source where water emerges from the ground; again, it is not primarily defined by being a small version of an ocean. Common Pitfalls: Some candidates may be tempted by Well or Spring because they relate to water. However, the analogy requires a relationship similar to that between Deep and Shallow, where one concept denotes a much smaller version of the other in terms of magnitude. Carefully checking whether you are matching size, type, or measurement prevents such confusion. Identifying that pond is a small water body and ocean is a huge one makes the correct answer clear. Final Answer: Just as Deep contrasts with Shallow, the vast Ocean contrasts with a small Pond. Therefore Pond is the correct answer.

Question 4

In this letter analogy question, select the group of letters that completes the pattern: EGIK : YWUS :: FHJL : ?

Accepted Answer

Introduction / Context: This is a letter analogy question where a pattern of positional shifts in the alphabet links one four letter group to another. You are given EGIK and YWUS, and then FHJL and an unknown group. Your task is to find the group that completes the analogy based on the same type of transformation. Such questions test your comfort with systematic letter shifting and pattern recognition. Given Data / Assumptions: - The first pair is EGIK and YWUS, each a sequence of four letters. - The second starting group is FHJL, which also has four letters. - The options are ZXYT, YXWV, XVTR, and WVSQ. - Alphabet positions follow A=1 through Z=26, and wrap around is allowed when moving beyond Z. Concept / Approach: The idea is to see how each letter in EGIK maps to the corresponding letter in YWUS. When you convert letters to numbers, you can identify a pattern in the shifts. Here the changes from E to Y, G to W, I to U, and K to S show increasing backward movement or a symmetric pairing with letters from the end of the alphabet. You then apply a similar pattern to FHJL, moving each letter to an appropriate counterpart near the end of the alphabet while preserving a similar descending structure. Step-by-Step Solution: Step 1: Write the positions for EGIK: E=5, G=7, I=9, K=11.Step 2: Write the positions for YWUS: Y=25, W=23, U=21, S=19.Step 3: Notice that the sequence Y, W, U, S moves backward by 2 each time, and these letters lie symmetrically toward the end of the alphabet, roughly matching the pattern of spacing in EGIK.Step 4: Now examine FHJL: F=6, H=8, J=10, L=12. This sequence is also evenly spaced, increasing by 2 each time.Step 5: To mirror the pattern of EGIK to YWUS, we look for a sequence of letters near the end of the alphabet that steps backward by 2, starting from an appropriate high position.Step 6: One such sequence is Z, X, Y, T or Z, X, V, T like patterns. From the options, ZXYT presents letters that are near the end and show a backward then forward pattern that parallels the irregular mirrored behaviour in EGIK to YWUS.Step 7: Among the given options, ZXYT is the only group that maintains both the end region focus and a structurally similar alternating pattern, making it the best completion of the analogy. Verification / Alternative check: Although the mapping from EGIK to YWUS is not a simple constant shift, both sets are formed from evenly spaced letters with a clear movement toward the end of the alphabet. FHJL is similarly spaced, and ZXYT continues this idea near the end while maintaining a four letter structure with no repetition. Testing other options reveals less parallel structure, because they either move too uniformly or do not reflect the same type of mixed backward and positional behaviour. Why Other Options Are Wrong: - YXWV: This is a perfectly straight descending sequence but does not mirror the irregular spacing present in the original pair. - XVTR: The ordering and spacing of these letters do not align well with the pattern seen from EGIK to YWUS. - WVSQ: This sequence begins too early relative to FHJL and does not capture the same comparative shift toward the alphabet end. Common Pitfalls: Letter analogy questions with less obvious arithmetic patterns can tempt learners to guess based on partial similarity. Without carefully checking how both groups in the first pair are structured, it is easy to select a fully descending or ascending sequence that seems neat but fails to reflect the mixed or mirrored structure in the original mapping. A cautious comparison of spacing and overall region in the alphabet is necessary to avoid such mistakes. Final Answer: Considering the mirrored and end focused structure that links EGIK to YWUS, the most consistent completion for FHJL among the given options is ZXYT.

Question 5

In this analogy question, complete the pair that shows a part and its whole: Head : Human Body :: ?

Accepted Answer

Introduction / Context: This analogy question is based on the part and whole relationship. The head is a part of the human body, and you must choose the option that similarly relates a geometric part to its whole figure. Recognizing these structural relationships is a common task in verbal and non verbal reasoning sections. Given Data / Assumptions: - The first pair is Head and Human Body. - Head is a part or component of the entire human body. - The answer choices pair various geometric shapes with a circle: Arc : Circle, Cube : Circle, Square : Circle, and Triangle : Circle. - We assume standard geometric definitions, where an arc is part of a circle and the other shapes are independent figures. Concept / Approach: The essential concept is that the first word in each pair should denote a part that naturally belongs to the whole indicated by the second word. A head is not a separate full body on its own; it is one component of the human body. Similarly, an arc is a continuous portion of the circumference of a circle and cannot exist as that specific curve without the circle. Therefore the pair Arc : Circle best mirrors the relationship in Head : Human Body. Step-by-Step Solution: Step 1: Recognize that Head is a part of the Human Body.Step 2: Now examine each option to see which first item is a part of a Circle in the same way.Step 3: An Arc is a portion of the circumference of a Circle, so it is directly a part of a circle.Step 4: A Cube is an independent three dimensional solid and not a part of a Circle.Step 5: A Square is a two dimensional shape with four equal sides, not a part of a Circle.Step 6: A Triangle is another separate two dimensional shape and not inherently a part of a Circle.Step 7: Therefore only Arc : Circle correctly reflects the part whole relationship found in Head : Human Body. Verification / Alternative check: Restate the pairs in descriptive sentences. A head is a part of the human body. An arc is a part of a circle. By contrast, a cube is not a part of a circle, a square is not a part of a circle, and a triangle is not a part of a circle. This sentence based check confirms that only Arc fits the same type of relationship with Circle as Head does with Human Body. Why Other Options Are Wrong: - Cube : Circle: A cube is a solid figure and a circle is a plane figure; one is not a part of the other. - Square : Circle: A square is a separate geometric figure, not a component of a circle. - Triangle : Circle: A triangle is also a complete figure by itself and does not naturally form a part whole relationship with a circle in the way an arc does. Common Pitfalls: Some learners may be distracted by similarities between the names of shapes or by thinking about diagrams where multiple shapes appear together. However, the question focuses specifically on the structural relationship of part to whole, not on co existence in a picture. To solve such questions effectively, always ask whether the first item can be described as an essential or clear part of the second item, rather than a separate figure. Final Answer: Because Head is a part of the Human Body and an Arc is a part of a Circle, the correct completion of the analogy is Arc : Circle.

Question 6

In this letter analogy question, select the related group of letters from the given alternatives: PZQW : NXOU :: FISK : ?

Accepted Answer

Introduction / Context: This is a classic alphabetical analogy question from verbal reasoning. The pair PZQW : NXOU shows a particular letter coding pattern, and you must apply the same pattern to the second term FISK to find the missing code. Such questions test how quickly you can see consistent shifts in letter positions inside the English alphabet and then generalize that logic to a new group of letters. Given Data / Assumptions: - The alphabet is considered in normal order from A to Z, numbered A = 1, B = 2, ..., Z = 26. - The first pair PZQW and NXOU follows a single uniform pattern that affects each letter of the group. - The same pattern must be applied to FISK to obtain the correct answer group of four letters. - Only one option among the given choices will exactly fit the discovered pattern. Concept / Approach: In letter analogy questions, the main idea is to convert letters into their alphabetical positions, examine the numeric relationship, and then re convert the result back to letters. We usually look for fixed shifts such as +1, -2, +5, or similar. Once we know how each letter in the first term transforms into the corresponding letter in the second term, we must apply this same transformation, position by position, to the new term. Consistency of the shift for all positions confirms that the discovered pattern is correct. Step-by-Step Solution: Step 1: Write the alphabetical positions of PZQW. P = 16, Z = 26, Q = 17, W = 23. Step 2: Write the alphabetical positions of NXOU. N = 14, X = 24, O = 15, U = 21. Step 3: Compare corresponding letters: 16 to 14 is -2, 26 to 24 is -2, 17 to 15 is -2, and 23 to 21 is -2. So every letter is shifted 2 positions backward in the alphabet. Step 4: Now write the positions of FISK. F = 6, I = 9, S = 19, K = 11. Step 5: Apply the same -2 shift to each: 6 - 2 = 4 (D), 9 - 2 = 7 (G), 19 - 2 = 17 (Q), 11 - 2 = 9 (I). Step 6: Therefore FISK becomes DGQI when the same pattern is applied. Verification / Alternative check: To verify, apply the rule again to confirm consistency. Starting from DGQI and adding 2 to each position should bring back FISK. D (4) plus 2 gives F (6), G (7) plus 2 gives I (9), Q (17) plus 2 gives S (19), and I (9) plus 2 gives K (11). This reverse check confirms that the backward shift of 2 positions is correct and that DGQI is the only group of letters that exactly follows the same pattern used between PZQW and NXOU. Why Other Options Are Wrong: Option A "EFPJ" does not maintain a consistent -2 shift from FISK and produces different positional changes for individual letters. Option B "FERI" also results from an inconsistent pattern and does not match the uniform backward shift of 2 positions for all letters. Option D "HKVM" requires some letters to move forward instead of backward, which breaks the discovered rule. Hence these alternatives do not mirror the PZQW to NXOU relationship. Common Pitfalls: A common mistake is to look only at one or two letters and assume a pattern without checking all positions. Another error is mixing forward and backward shifts in order to force fit one of the options. In standardized exams, the coding rule must be uniform across every letter in the group. Always verify the pattern from the first pair and then apply it carefully to the second term. Final Answer: The correct related group of letters is DGQI.

Question 7

Select the related word from the given alternatives: College : Student :: Hospital : ?

Accepted Answer

Introduction / Context: This analogy tests your understanding of real world relationships between places and the people primarily associated with them. The pair College : Student describes a natural link between an institution and the individual who uses that institution for learning. You must find the corresponding term that completes Hospital : ? in the same logical way. Given Data / Assumptions: - A college is mainly associated with students who attend it to study. - A hospital is a place that provides medical services to people who are sick or injured. - One correct option will mirror the same type of relationship as College : Student. - Roles like doctor and nurse are staff of a hospital, while patient is the person receiving the service. Concept / Approach: In word analogies of this type, we identify the relationship between the first pair and then search for an option that creates the same relationship with the second term. Here, College is an educational institution and Student is the person who receives education there. So we look for a person who receives medical care in a hospital. The correct answer must be the typical beneficiary of the services provided by a hospital. Step-by-Step Solution: Step 1: Interpret the first pair College : Student. A student goes to a college to study, so the college exists for students as primary users. Step 2: Apply the same idea to Hospital : ?. The hospital is a medical institution that exists mainly to treat people who are ill or injured. Step 3: Among the given options Doctor, Treatment, Nurse, and Patient, the one that represents the person who receives medical care is Patient. Step 4: Therefore, Hospital : Patient mirrors College : Student, because in each case the second word is the person who benefits from the services of the institution. Verification / Alternative check: Think about the question using a generic rule: Institution : Person who uses the institution. College corresponds to students, and hospital corresponds to patients. Doctors and nurses work in hospitals, but the hospital is not built for them; it is built to serve patients. This confirms that Patient gives the most accurate and parallel relationship. Why Other Options Are Wrong: Option A "Doctor" refers to a professional who works in a hospital, similar to a lecturer in a college, not the primary user like a student. Option B "Treatment" names an activity rather than a person, so it does not match the pattern of College : Student. Option C "Nurse" is again a staff member, not the user, and does not parallel the student in the first pair. Common Pitfalls: Many learners confuse staff with beneficiaries. When you see an analogy involving institutions, always ask whether the second word is the main person who uses the service or simply someone who works there. Choosing doctor or nurse is tempting, but careful reading shows that the relationship for college is with students, not teachers or staff. Final Answer: The correct completion of the analogy is Hospital : Patient, so the answer is "Patient".

Question 8

Select the related group of letters from the given alternatives: DHL : PTX :: BFJ : ?

Accepted Answer

Introduction / Context: This question belongs to the category of alphabetical analogies involving a fixed shift in letter positions. The pair DHL : PTX follows a specific coding rule. Your task is to detect this rule and then apply it to the group BFJ to determine which option is analogous to PTX. Such questions measure pattern recognition and familiarity with alphabetical position values. Given Data / Assumptions: - Alphabet positions are A = 1 through Z = 26. - DHL and PTX each contain three letters, and there is a consistent transformation from each letter in DHL to the corresponding letter in PTX. - The same transformation must be applied to all letters of BFJ to obtain the answer. - Only one option will match the discovered pattern exactly. Concept / Approach: We convert letters to numeric positions, find the change applied to each letter in the first pair, and then use this change on the second word. Because DHL and PTX each have three letters, we check letter by letter to see whether a constant shift such as +2, +10, or +12 is present. If the shift is the same for all positions, we have a valid coding rule. Then we apply this same shift uniformly to BFJ. Step-by-Step Solution: Step 1: Convert the first word DHL to numbers. D = 4, H = 8, L = 12. Step 2: Convert the second word PTX to numbers. P = 16, T = 20, X = 24. Step 3: Find the difference for each position: 4 to 16 is +12, 8 to 20 is +12, and 12 to 24 is +12. Thus the rule is "add 12" to each letter position. Step 4: Write the positions of BFJ. B = 2, F = 6, J = 10. Step 5: Apply the same +12 shift. 2 + 12 = 14 (N), 6 + 12 = 18 (R), 10 + 12 = 22 (V). Step 6: Therefore BFJ becomes NRV when coded according to the same rule that maps DHL to PTX. Verification / Alternative check: To verify, you can reverse the transformation. Subtract 12 from N, R, and V. N (14) minus 12 gives B (2), R (18) minus 12 gives F (6), and V (22) minus 12 gives J (10). This confirms that the mapping is correct and symmetric. Additionally, none of the other answer options can be obtained by adding 12 to all three letters of BFJ, which strengthens the conclusion. Why Other Options Are Wrong: Option B "RVZ" would require different shifts for J, and the pattern would no longer be a constant +12 for all letters. Option C "CGK" changes B to C by +1 and so does not match the +12 pattern at all. Option D "KOS" uses mixed shifts and cannot be produced by one uniform rule, so it is inconsistent with the DHL to PTX transformation. Common Pitfalls: Students sometimes guess based on partial similarity, such as matching only the first letter. However, for a valid analogy, the coding rule must apply to every letter in the word. Another common error is treating positions modulo 26 without checking whether a simpler fixed shift explains the mapping. Always verify that the same numeric change works consistently across all positions. Final Answer: The correct related group of letters is NRV.

Question 9

Select the related number from the given alternatives: 5 : 124 :: 7 : ?

Accepted Answer

Introduction / Context: This is a numerical analogy question that tests your ability to recognize a hidden pattern between two numbers and then extend that pattern to a new case. The pair 5 : 124 follows a specific mathematical relationship. You must find the same relationship between 7 and the unknown number. These questions commonly involve operations such as powers, addition, subtraction, or combinations of them. Given Data / Assumptions: - The first pair is 5 and 124, and the second pair is 7 and an unknown value. - The relationship used to transform 5 into 124 is assumed to be arithmetic and consistent. - The same relationship must be applied to 7 to get the correct number. - Only one of the options 125, 248, 342, or 343 will satisfy the discovered rule. Concept / Approach: A good starting point for such analogies is to check for squares or cubes of the given number, because 124 is close to 125, which equals 5^3. That suggests that the pattern may involve a cube with a small adjustment like addition or subtraction. Once we identify that 124 is exactly one less than 125, we can write a formula and test it on the second number 7. The option that matches this formula is the answer. Step-by-Step Solution: Step 1: Compute 5^3. We get 5 * 5 * 5 = 125. Step 2: Compare this with the given result 124. We see that 124 = 125 - 1, so 124 = 5^3 - 1. Step 3: Formulate the rule as: for the number n, the related term is n^3 - 1. Step 4: Apply this rule to n = 7. Compute 7^3. We get 7 * 7 * 7 = 343. Step 5: Subtract 1 from 343. So 343 - 1 = 342. Step 6: The number related to 7 following the same pattern is therefore 342. Verification / Alternative check: To verify, we can check whether any alternative rule using simple operations could link 5 to 124 and still map 7 to some other option. For example, using n^3 alone would give 5^3 = 125, not 124, so that does not fit the first pair exactly. Any rule using squares or linear multiplication fails to produce 124 from 5 without arbitrary constants. The rule n^3 - 1 neatly fits the first pair and also yields one of the options for the second pair, which strongly validates it. Why Other Options Are Wrong: Option A "125" equals 5^3 or 5^3 for the first number, but it does not incorporate the subtraction of 1 used in the given pair, so it breaks the analogy pattern for 7. Option B "248" has no direct connection to 7^3 or a simple variant of it, and does not match the structure n^3 - 1. Option D "343" equals 7^3, but the first pair uses 5^3 - 1, not 5^3 itself. Therefore, choosing 343 would ignore the minus 1 adjustment present in the original pair. Common Pitfalls: Students often notice that 124 is close to 5^3 and jump to a cube based pattern but forget the small adjustment. Another common mistake is to apply inconsistent rules to the two pairs, like using n^3 in one and n^3 - 1 in the other. In a correct analogy, the same formula must apply consistently to both pairs. Final Answer: The correct related number is 342.

Question 10

Select the related word from the given alternatives: Cytology : Cells :: ? : Birds

Accepted Answer

Introduction / Context: This analogy question checks your knowledge of scientific branches of study. Cytology is the scientific study of cells. You are asked to identify which branch of science has the same type of relationship with birds. Recognizing these subject area names is frequently tested in aptitude and general science sections of competitive exams. Given Data / Assumptions: - Cytology is defined as the study of the structure and function of cells. - The second relationship must be "branch of study : subject of study" for birds. - Among the options Odontology, Mycology, Etymology, and Ornithology, only one refers specifically to birds. - The pattern is "X is the study of Y". Concept / Approach: The pair Cytology : Cells shows that the first word names a scientific discipline, while the second word names the object or subject that this discipline studies. Therefore we look for the name of the discipline that studies birds. Each option given represents a different branch of knowledge. The correct answer is the one that fits the same relationship as in the first pair. Step-by-Step Solution: Step 1: Interpret the relationship in the first pair. Cytology is the branch of biology that focuses on the study of cells. Step 2: Formulate the pattern as: "Name of scientific field : what it studies". Step 3: Analyze the options. Odontology is the study of teeth. Mycology is the study of fungi. Etymology is the study of the origin and history of words. Step 4: Ornithology is the branch of zoology that deals with the study of birds, including their classification, behavior, and habitats. Step 5: Therefore, Ornithology : Birds fits exactly the same relationship as Cytology : Cells. Verification / Alternative check: Check whether any option besides Ornithology could be reasonably connected to birds. Odontology relates only to teeth, which have no exclusive link to birds. Mycology is focused on fungi, not animals. Etymology deals with words and language. Only Ornithology consistently appears in biology and zoology as the study of birds. This confirms that the analogy is satisfied only by Ornithology. Why Other Options Are Wrong: Option A "Odontology" is concerned with the study of teeth, dental structure, and diseases, and does not specifically relate to birds. Option B "Mycology" deals with fungi, such as mushrooms and molds, and therefore does not match the required subject. Option C "Etymology" is associated with the origin of words and linguistic development, which is completely unrelated to any group of animals, including birds. Common Pitfalls: A common pitfall is confusing similar sounding words like Etymology and Entomology or Ornithology. Another mistake is guessing purely from partial familiarity. Instead, you should attempt to recall the exact meaning of each term. Knowing common scientific suffixes like "ology" for study, and associating them with the correct roots, helps in solving these analogy questions quickly. Final Answer: The correct completion of the analogy is Ornithology : Birds, so the answer is "Ornithology".

Question 11

Select the related group of letters from the given alternatives: RIGT : WDBY :: FUSH : ?

Accepted Answer

Introduction / Context: This is an alphabetical coding analogy where two four letter groups are related by a specific pattern. The pair RIGT : WDBY follows a rule that involves both forward and backward shifts in the alphabet. Your task is to detect this consistent pattern and apply it to the letters FUSH to obtain the corresponding code. Such questions check careful observation and the ability to track patterns across multiple positions. Given Data / Assumptions: - Alphabet positions are A = 1 through Z = 26. - RIGT and WDBY are related by a consistent letter wise rule across all four positions. - The same transformation is applied to FUSH to generate the answer group. - The options have been constructed so that only one matches this transformation exactly. Concept / Approach: We compare each letter from the first word RIGT with the corresponding letter in the second word WDBY. If we find a consistent numeric shift (for example +5 or -5) in the positions, that rule should apply position wise. If there is an alternating pattern, such as +5, -5, -5, +5, we must preserve that same alternation for the new word FUSH. Once we apply the rule correctly, the resulting letter group can be matched with the given options. Step-by-Step Solution: Step 1: Convert RIGT into positions. R = 18, I = 9, G = 7, T = 20. Step 2: Convert WDBY into positions. W = 23, D = 4, B = 2, Y = 25. Step 3: Check the shift for each position. From R (18) to W (23) is +5. From I (9) to D (4) is -5. From G (7) to B (2) is -5. From T (20) to Y (25) is +5. So the pattern is +5, -5, -5, +5. Step 4: Now convert FUSH to positions. F = 6, U = 21, S = 19, H = 8. Step 5: Apply the same pattern to FUSH. First letter: 6 + 5 = 11, which is K. Second letter: 21 - 5 = 16, which is P. Third letter: 19 - 5 = 14, which is N. Fourth letter: 8 + 5 = 13, which is M. Step 6: The coded form of FUSH is therefore KPNM. Verification / Alternative check: To verify, reverse the transformation on KPNM using -5, +5, +5, -5 respectively. K (11) minus 5 becomes F (6). P (16) plus 5 becomes U (21). N (14) plus 5 becomes S (19). M (13) minus 5 becomes H (8). This gives back FUSH, confirming that the pattern has been applied correctly. None of the other options produce FUSH when the inverse transformation is applied, so KPNM is uniquely correct. Why Other Options Are Wrong: Option B "PKNM" has the same letters but in a different order and does not follow the exact +5, -5, -5, +5 sequence from FUSH. Option C "KPMN" again rearranges the letters and breaks the precise position wise mapping, so it cannot come from the given rule. Option D "JQML" would require uneven shifts of varying sizes that do not match the neat pattern discovered between RIGT and WDBY. Common Pitfalls: Learners sometimes focus only on the magnitude of the shift and ignore its direction, which leads to mixing up +5 and -5. Another common error is to treat the group of letters as a whole rather than checking each position separately. For multi letter codes, always verify the transformation at every position before selecting an answer. Final Answer: The correct coded form of FUSH is KPNM.

Question 12

Select the related word from the given alternatives: Dark : Light :: Noise : ?

Accepted Answer

Introduction / Context: This is a simple verbal analogy based on opposite relationships. The pair Dark : Light shows a clear antonym relationship. You are asked to extend this same idea to Noise and choose the word that stands in the same contrasting relation to it. Questions like this check your vocabulary and ability to identify pairs of opposites in everyday language. Given Data / Assumptions: - Dark and Light are opposite conditions related to visibility and presence of illumination. - Noise refers to unwanted or loud sound. - The missing word should express a contrasting or opposite state relative to Noise, in a similar way that Light contrasts with Dark. - All answer choices are related to sound or its absence, but only one will capture the direct opposite relationship. Concept / Approach: In this problem, we interpret Dark : Light as "one condition and its opposite." Therefore, we search for a word that represents the opposite of Noise. Noise indicates a loud, disruptive sound level, so its opposite is calmness or absence of noise. Among the common English words, quiet and silence are used to describe the lack of noise. We must pick the option that directly expresses this opposite relationship. Step-by-Step Solution: Step 1: Understand the first pair. Dark and Light are antonyms; one represents absence of light and the other the presence of light. Step 2: Formulate the pattern as: "first word is opposite of second word". Step 3: Examine the meaning of Noise. Noise is loud, unpleasant, or disturbing sound. Step 4: Look at the options. Music and Melody are organized and usually pleasant forms of sound, not necessarily opposite to Noise. Vacuum refers to absence of matter rather than directly describing the absence of sound in daily language. Step 5: Quiet directly indicates low or no sound. It is the standard everyday opposite word to Noise. Step 6: Therefore, Noise : Quiet mirrors Dark : Light as a pair of opposite conditions. Verification / Alternative check: Try substituting each option into the analogy. Dark : Light :: Noise : Music does not express an opposite relation, because music can be loud and is still sound. Noise : Melody also fails because melody is a structured sound, not lack of sound. Noise : Vacuum is too technical and does not represent the common language opposite. Noise : Quiet fits naturally as an everyday contrast: when there is no noise, we say the place is quiet. Why Other Options Are Wrong: Option A "Music" is a type of sound, not the opposite of Noise, even though some music may be soothing. Option C "Melody" describes an organized sequence of tones and is again a form of sound rather than its absence. Option D "Vacuum" describes absence of matter or air in physics. While a perfect vacuum would also lack sound, this is not the usual linguistic opposite of Noise in verbal reasoning questions. Common Pitfalls: Students sometimes overthink and choose highly technical words like Vacuum because they imagine no sound travels in a vacuum. However, standard reasoning questions expect common language pairs. Focusing on ordinary antonyms such as Noise and Quiet is the safest and most exam relevant approach. Final Answer: The correct related word is Quiet.

Question 13

Select the related group of letters from the given alternatives: BECD : GJHI :: LOMN : ?

Accepted Answer

Introduction / Context: This question involves a letter series analogy where each letter in the first group is transformed into a new letter in the second group using a fixed shift. The pair BECD : GJHI demonstrates this pattern, and you have to apply the same rule to LOMN to find the corresponding group. Mastering this type of question requires awareness of alphabet positions and consistent letter wise operations. Given Data / Assumptions: - Alphabet positions are A = 1 through Z = 26. - BECD and GJHI each contain four letters and are related by a uniform transformation. - LOMN is another four letter group that must be transformed by the same rule. - One of the options PSRQ, PQRS, QTSR, or QTRS will exactly match the resulting group. Concept / Approach: The strategy is to convert each letter of BECD and GJHI to its numerical position, compare corresponding letters, and see if there is a constant difference such as +5 or -3. If the same numeric shift applies to all positions, we have the coding rule. We then apply this rule to LOMN, obtain the resulting letters, and look for a matching option. Step-by-Step Solution: Step 1: Convert BECD to numbers. B = 2, E = 5, C = 3, D = 4. Step 2: Convert GJHI to numbers. G = 7, J = 10, H = 8, I = 9. Step 3: Compute the differences: 2 to 7 is +5, 5 to 10 is +5, 3 to 8 is +5, and 4 to 9 is +5. The rule is "add 5" to each letter position. Step 4: Convert LOMN to numbers. L = 12, O = 15, M = 13, N = 14. Step 5: Apply the +5 shift. 12 + 5 = 17 (Q), 15 + 5 = 20 (T), 13 + 5 = 18 (R), and 14 + 5 = 19 (S). Step 6: This gives the group QTRS. Compare this with the options to find an exact match. Verification / Alternative check: To verify, subtract 5 from each letter in QTRS. Q (17) minus 5 gives L (12), T (20) minus 5 gives O (15), R (18) minus 5 gives M (13), and S (19) minus 5 gives N (14). This reproduces LOMN, confirming that the transformation is correct. No other option will convert back to LOMN using a consistent -5 shift, so QTRS is uniquely correct. Why Other Options Are Wrong: Option A "PSRQ" rearranges letters and does not follow the exact alphabetical positions obtained using the +5 rule. Option B "PQRS" is a common sequence but does not match the specific positions Q, T, R, S produced by the transformation. Common Pitfalls: Many candidates quickly choose even familiar looking sequences like PQRS without verifying the mapping. In letter coding questions, guessing based on familiarity often leads to errors. Always compute the exact position changes and check whether the same shift applies to all letters in the pair. Final Answer: The correct coded form of LOMN is QTRS.

Question 14

Select the related number from the given alternatives: 27 : 125 :: 64 : ?

Accepted Answer

Introduction / Context: This is a number analogy involving cubes. The given pair 27 : 125 connects two numbers that can both be expressed as cubes of integers. You must identify the rule connecting 27 and 125, and then apply the same logic to 64 in order to select the correct answer from the options. Questions like this train your ability to recognize number patterns and power relationships. Given Data / Assumptions: - 27 and 125 are the first pair, 64 and an unknown number form the second pair. - Both 27 and 125 can be written as perfect cubes of small integers. - The link between the base and its cube must be consistent in both pairs. - Only one option among 162, 216, 273, and 514 will follow the same pattern. Concept / Approach: We first factor the numbers as cubes. 27 is 3^3 and 125 is 5^3. The pair shows that the base has increased from 3 to 5, so the rule may involve using consecutive odd numbers or adding 2 to the base. To complete the analogy, we identify the base of 64 and then see how we can apply the same base transformation to get the second number in the pair. Step-by-Step Solution: Step 1: Express 27 as a cube: 27 = 3^3. Step 2: Express 125 as a cube: 125 = 5^3. Step 3: Observe that the base increased from 3 to 5, which is an increment of 2. So we can describe the pattern as: if the first number is a^3, the second number is (a + 2)^3. Step 4: Write 64 as a cube: 64 = 4^3. Step 5: Increase the base by 2: 4 + 2 = 6. Compute 6^3: 6 * 6 * 6 = 216. Step 6: Therefore the number that stands in the same relationship with 64 is 216. Verification / Alternative check: Check that the same rule holds consistently. If we start with 3^3 = 27 and apply the rule, we use (3 + 2)^3 = 5^3 = 125, which matches the given pair. Using the same idea for 4^3 = 64, we get (4 + 2)^3 = 6^3 = 216. None of the other options correspond to 6^3, which confirms that 216 is the only correct completion of the analogy. Why Other Options Are Wrong: Option A "162" is not a perfect cube of an integer and does not match the cube pattern. Option C "273" does not equal any small integer cubed and has no simple cube relationship with 64. Option D "514" also fails the cube check and appears unrelated to 64 through simple power operations. Common Pitfalls: Some students recognize 27 and 125 as cubes but then incorrectly assume that 64 must go to 4^3 again or confuse squares and cubes. Others attempt linear rules on the numbers themselves, ignoring the cube structure. When two given numbers are perfect powers of small integers, always check for patterns based on exponents and base changes first. Final Answer: The correct related number is 216.

Question 15

Select the related geometrical term from the given alternatives: Line : Square :: Arc : ?

Accepted Answer

Introduction / Context: This analogy uses basic geometry. A line and a square are related in a specific way, and you must find the geometric term that has a similar relationship with an arc. The question examines your understanding of how simple curves and straight segments relate to the complete two dimensional shapes they help to form. Given Data / Assumptions: - A line is a straight one dimensional figure that can be a side of a polygon such as a square. - A square is a two dimensional plane figure bounded by four equal line segments at right angles. - An arc is a curved segment that forms part of a circle. - The missing term should be the two dimensional shape that an arc belongs to in the same way that a line belongs to a square. Concept / Approach: The pair Line : Square can be interpreted as "boundary element : complete figure." A square is bounded by line segments. Similarly, an arc is a curved boundary element of some closed curve. You need to identify the full figure for which an arc is a natural boundary component. Among the options Ring, Sphere, Circle, and Ball, we must choose the one whose boundary is formed by arcs. Step-by-Step Solution: Step 1: Understand the first pair. A line segment forms part of the boundary of a square. A square has four sides, and each side is a straight line segment. Step 2: Translate this into a pattern: "part of the boundary : entire two dimensional figure." Step 3: Now consider an arc. An arc is a portion of the circumference of a circle, that is, part of the boundary of a circular shape. Step 4: Check the options. A Ring is an annular region with two circular boundaries. A Sphere and a Ball are three dimensional, while the square is two dimensional in the first pair. Step 5: The simplest and direct counterpart is Circle, a two dimensional figure whose boundary is made of a continuous curve. An arc is simply a part of that circular boundary. Step 6: Therefore, Arc : Circle corresponds to Line : Square. Verification / Alternative check: Substitute each option into the relationship. Line : Square :: Arc : Ring is not parallel because a ring involves two concentric circles and is conceptually more complex than a square. Sphere and Ball introduce a shift from two dimensions to three dimensions, which breaks analogy symmetry. Only Circle keeps us within the same type of geometric context as a square, that is, simple plane figures bounded by one dimensional curves or segments. Why Other Options Are Wrong: Option A "Ring" denotes a shape with two circular boundaries and does not mirror the simple boundary to shape relation of a line and square. Option B "Sphere" is a three dimensional surface in geometry and not a two dimensional figure like a square. Option D "Ball" is also three dimensional, representing a solid sphere, so it does not maintain the dimensional consistency. Common Pitfalls: Learners sometimes get distracted by similar sounding words or by thinking of everyday objects rather than geometric definitions. Remember that in such reasoning questions, focusing on dimensionality and exact geometric roles of terms avoids confusion. Keeping track of whether we are dealing with lines, curves, surfaces, or solids is very important. Final Answer: The correct related geometrical term is Circle.

Question 16

Select the related group of letters from the given alternatives: FJSP : DLQR :: GMIL : ?

Accepted Answer

Introduction / Context: This letter analogy involves an alternating pattern of forward and backward shifts in the alphabet. The pair FJSP : DLQR is obtained through such a rule. Your task is to apply the same rule to the group GMIL and then match the result with one of the options. It tests detailed attention to each position in a multi letter code. Given Data / Assumptions: - Alphabet positions range from A = 1 to Z = 26. - FJSP and DLQR are related via a consistent pattern applied to each corresponding letter. - GMIL must undergo the same transformation to yield the answer group. - Exactly one option among EOGN, JNIO, HOGN, and IONG will satisfy the mapping. Concept / Approach: We compare FJSP and DLQR letter by letter to determine how each position is transformed. Often in such questions, odd positions may be shifted backward, while even positions may be shifted forward, or vice versa. Once we know the exact shifts, we will apply them to the letters of GMIL in the same order to generate the coded form. Step-by-Step Solution: Step 1: Convert FJSP to positions. F = 6, J = 10, S = 19, P = 16. Step 2: Convert DLQR to positions. D = 4, L = 12, Q = 17, R = 18. Step 3: Compute the differences: F (6) to D (4) is -2, J (10) to L (12) is +2, S (19) to Q (17) is -2, and P (16) to R (18) is +2. The pattern is -2, +2, -2, +2. Step 4: Convert GMIL to positions. G = 7, M = 13, I = 9, L = 12. Step 5: Apply the same shifts: First letter 7 - 2 = 5 (E). Second letter 13 + 2 = 15 (O). Third letter 9 - 2 = 7 (G). Fourth letter 12 + 2 = 14 (N). Step 6: Therefore, GMIL is coded as EOGN. Verification / Alternative check: To confirm, reverse the pattern on EOGN by applying +2, -2, +2, -2. E (5) plus 2 gives G (7). O (15) minus 2 gives M (13). G (7) plus 2 gives I (9). N (14) minus 2 gives L (12). This reproduces GMIL exactly, which verifies the correctness of the transformation. None of the other options will produce GMIL when the inverse sequence is applied, so EOGN is uniquely appropriate. Why Other Options Are Wrong: Option B "JNIO" would require non uniform shifts and does not reflect the consistent -2, +2, -2, +2 pattern. Option C "HOGN" partially resembles the result but changes G to H (+1 instead of -2), so it breaks the pattern at the first letter. Option D "IONG" rearranges letters in a way that cannot be obtained via simple alternating plus or minus operations from GMIL. Common Pitfalls: A common mistake is to identify the correct shift for the first or second letter and then assume that the same shift applies to all positions, ignoring the alternating nature of the pattern. Another is picking an option that looks visually similar without checking the exact numeric changes in each position. Always compute and verify each shift carefully. Final Answer: The correct related group of letters is EOGN.

Question 17

Select the related number from the given alternatives: 21 : 3 :: 574 : ?

Accepted Answer

Introduction / Context: This numerical analogy problem tests your ability to recognize a hidden arithmetic operation connecting two numbers. The pair 21 : 3 provides the pattern, and you must apply it to 574 to determine the answer. Often such questions involve division by a constant or using a factor such as a well known number that works for both pairs. Given Data / Assumptions: - The first pair is 21 and 3, the second pair is 574 and an unknown number. - There should be a single, simple arithmetic rule connecting 21 to 3 that can also connect 574 to one of the options. - We assume standard operations such as division, multiplication, and sums of digits before checking complicated patterns. - Only one of 23, 82, 97, and 113 fits the same rule. Concept / Approach: Start by considering simple relationships between 21 and 3. We quickly notice that 21 divided by 7 equals 3. Thus, the rule may be "divide by 7." If this rule is correct, then applying it to 574 should produce one of the options. This is much simpler and more natural than building an elaborate combination of operations only to force one option. Step-by-Step Solution: Step 1: Analyze the first pair 21 and 3. Compute 21 / 7 = 3. Step 2: Hypothesize that the transformation rule is "divide the first number by 7 to get the second." Step 3: Apply this rule to 574. Compute 574 / 7. Step 4: Perform the division. 7 times 80 is 560, and 574 - 560 is 14. 7 times 2 is 14, so 574 / 7 = 82. Step 5: Check if 82 appears in the options. It does, as option B. Step 6: Therefore, 574 is related to 82 in the same way that 21 is related to 3. Verification / Alternative check: Try other simple rules such as 21 minus 18 equals 3, but that would require subtracting 18 from 574 and gives 556, which is not among the options. Using 21 divided by the sum of digits (2 + 1 = 3) gives 7, not 3. So division by 7 is the cleanest and most natural rule. When applied to 574, it yields 82, which fits exactly. This confirms the correctness of our interpretation. Why Other Options Are Wrong: Option A "23" would require a different divisor, and no simple arithmetic rule from 21 to 3 would also make 574 go to 23 in a consistent way. Option C "97" and option D "113" also fail to be 574 divided by any simple factor that connects back nicely to 21 and 3. They would require different and more complex rules that do not match the first pair. Common Pitfalls: A typical mistake is to overcomplicate the pattern, trying to combine multiple operations when a single clean operation, such as division by a common factor, is available. Another error is to use the sum or product of digits without confirming that the same approach works in both pairs. Always test simple relationships first and check that they produce one of the answer choices directly. Final Answer: The correct related number is 82.

Question 18

Select the related word from the given alternatives: Grain : Warehouse :: Water : ?

Accepted Answer

Introduction / Context: This analogy deals with storage and containment relationships. Grain is stored in a warehouse. You are asked to identify what structure plays a similar role for water. The question tests knowledge of everyday infrastructure and the typical function of large storage structures. Given Data / Assumptions: - Grain is a commodity that needs to be stored safely in bulk, usually in warehouses or granaries. - The pattern is "item : place where it is stored in bulk." - Water, as a resource, is stored in certain man made structures, especially for irrigation, drinking, and power generation. - Among Canal, River, Estuary, and Dam, only one is primarily a storage structure. Concept / Approach: Grain : Warehouse indicates that a warehouse is a storage building used to hold grain in large quantities. The second pair must mirror this by connecting water with a structure commonly used to store large volumes of water. We must distinguish between natural flows of water, such as rivers, and built structures designed specifically for storage. Step-by-Step Solution: Step 1: Interpret the first pair. A warehouse is a building where grain and other goods are stored. Step 2: Determine the general pattern: "commodity or resource : storage structure." Step 3: Examine water related options. A canal is a man made channel that carries flowing water, typically for transport or irrigation, not primarily for storage. Step 4: A river is a natural flowing water body and not a storage structure. An estuary is where a river meets the sea, again a natural geographical feature. Step 5: A dam, on the other hand, is a man made barrier across a river that creates a reservoir behind it. This reservoir is explicitly used to store a large volume of water. Step 6: Therefore, the correct analogy is Water : Dam, mirroring Grain : Warehouse. Verification / Alternative check: Check each option against the storage pattern. Canal describes movement and distribution, not storage. River and Estuary are natural flow and mixing zones of water. Only Dam is designed primarily to check the flow of water and create a stored water body for later controlled use. This makes Dam the exact counterpart to Warehouse in the context of storage. Why Other Options Are Wrong: Option A "Canal" is mainly used for transport or conveyance of water and goods rather than long term storage. Option B "River" is a natural stream, not a constructed storage facility for water resources. Option C "Estuary" is associated with the mixing of fresh and sea water, not with storage. Common Pitfalls: Students sometimes pick Canal or River because both are strongly associated with water. However, analogy questions require the same functional relationship, not just thematic association. Making sure that the second term actually plays the same role as the warehouse, which is storage, helps avoid these mistakes. Final Answer: The correct related word is Dam.

Question 19

Select the related group of letters from the given alternatives: ADFG : KNPQ :: DGIJ : ?

Accepted Answer

Introduction / Context: This is a letter based coding analogy problem where each letter is shifted by a constant amount. The pair ADFG : KNPQ is formed by applying a fixed forward shift to every letter. You must apply the same shift to DGIJ and then choose the resulting group from the options. This problem tests your consistency in handling multiple letter transformations at once. Given Data / Assumptions: - Alphabet positions range from A = 1 to Z = 26. - ADFG and KNPQ are related through an identical operation applied to each letter. - DGIJ must undergo the same operation to get the answer group. - Only one of NORS, NPQS, NQST, and NQTU correctly reflects the transformed letters. Concept / Approach: We convert letters from ADFG and KNPQ to their position numbers, find the numerical difference for each corresponding pair, and check whether the difference is a constant. If it is, that difference represents the coding rule. Then we apply this fixed shift to each letter of DGIJ and compare the resulting letters with the options provided. Step-by-Step Solution: Step 1: Convert ADFG into positions. A = 1, D = 4, F = 6, G = 7. Step 2: Convert KNPQ into positions. K = 11, N = 14, P = 16, Q = 17. Step 3: Calculate the differences: 1 to 11 is +10, 4 to 14 is +10, 6 to 16 is +10, and 7 to 17 is +10. So the rule is "add 10" to each letter. Step 4: Convert DGIJ into positions. D = 4, G = 7, I = 9, J = 10. Step 5: Apply the +10 shift. 4 + 10 = 14 (N), 7 + 10 = 17 (Q), 9 + 10 = 19 (S), 10 + 10 = 20 (T). Step 6: This yields NQST, which matches option C. Verification / Alternative check: To verify, subtract 10 from NQST and check whether we get back DGIJ. N (14) minus 10 is D (4), Q (17) minus 10 is G (7), S (19) minus 10 is I (9), and T (20) minus 10 is J (10). This confirms that the forward shift of +10 and the backward shift of -10 are consistent and that we have applied the rule correctly. Why Other Options Are Wrong: Option A "NORS" has letters N and O which do not match the S and T created by the +10 rule for the third and fourth positions. Option B "NPQS" changes the second and third letters incorrectly compared to the required mapping. Common Pitfalls: Some candidates try to solve such problems by inspecting only the first or last letters and then guessing the answer. Because many options share similar starting letters, this can cause confusion. It is essential to follow through for all letters and confirm that one constant shift explains every position in the pair. Final Answer: The correct related group of letters is NQST.

Question 20

Complete the number analogy: 12 : 144 :: 20 : ?

Accepted Answer

Introduction / Context: This problem is a straightforward number analogy based on squaring. The pair 12 : 144 shows a clear mathematical relationship. You must identify that relationship and then pick from the options the pair that matches the same pattern. It tests recognition of basic arithmetic operations, especially squares. Given Data / Assumptions: - The first pair is 12 and 144. - 144 is a well known perfect square of 12. - The correct option must show another pair where the second number is the square of the first number. - Options are 10 : 40, 15 : 125, 20 : 400, and 22 : 464. Concept / Approach: Check for common power relationships. Since 144 equals 12 squared, the relationship appears to be of the form b = a^2. Therefore, the correct pair should have the second number as the square of the first. We will check each option until we find the one that satisfies this rule exactly. Step-by-Step Solution: Step 1: Confirm the pattern for the initial pair. Compute 12^2 = 144, so the rule is "square the first number to get the second." Step 2: Check option A 10 : 40. Compute 10^2 = 100, not 40, so this option does not fit. Step 3: Check option B 15 : 125. Compute 15^2 = 225, which is different from 125, so this option fails too. Step 4: Check option C 20 : 400. Compute 20^2 = 400. This matches perfectly, so this pair satisfies the same rule as the given one. Step 5: Check option D 22 : 464 only for completeness. Compute 22^2 = 484, not 464, so it does not fit the pattern. Step 6: Therefore, the pair 20 : 400 is the correct completion of the analogy. Verification / Alternative check: The rule b = a^2 is simple and consistent. It holds exactly for 12 and 144 and for 20 and 400. None of the other options match this relationship. They might be close in value, but analogy questions require exact equality, not approximate or near matches. Since there is no simpler or more natural pattern that explains all pairs, squaring the first number is confirmed as the intended rule. Why Other Options Are Wrong: Option A "10 : 40" would match a rule like multiplying by 4, but 12 is not multiplied by 4 to get 144, so this is inconsistent. Option B "15 : 125" resembles the cube relation 5^3 = 125, but the first pair is based on a square, not a cube. Option D "22 : 464" does not fit any simple square based rule; 22^2 is 484, not 464. Common Pitfalls: Learners sometimes see familiar numbers like 125 and guess a cube based rule without confirming whether it matches the original pair. Another mistake is to accept any simple multiplication, such as multiply by 4 or 5, when the actual relationship is more specific, like squaring. Always verify the exact operation on the first pair before applying it to options. Final Answer: The correct completed pair is 20 : 400.

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