Question 1

In this letter analogy, “BCD is to YXW as FGH is to ______”. Select the group of letters that completes the analogy by using the same mirror image pattern in the alphabet.

Accepted Answer

Introduction / Context: This analogy uses a mirror image pattern in the alphabet, where each letter is paired with another letter such that their positions add up to a constant value. The pair BCD : YXW demonstrates that each letter in BCD is mapped to a letter near the end of the alphabet in a symmetric way. The task is to detect this pattern and then apply it to the sequence FGH in order to select the correct matching group from the options. These questions examine understanding of alphabet symmetry and positional reasoning. Given Data / Assumptions: • First mapping: BCD → YXW. • Second mapping: FGH → ? • Options: UTS, RQP, STU, TUS. • Alphabet positions: A = 1, B = 2, ..., Z = 26. Concept / Approach: In a mirror alphabet pattern, the first letter pairs with a letter such that the sum of their positions is constant, often 27, since 1 + 26 = 27. We check whether B and Y, C and X, D and W follow this rule. If so, we apply the same mirror mapping to F, G, and H. The result should yield a three letter group among the options. The order of letters is preserved, although the mapping itself inverts positions relative to the alphabet centre. Step-by-Step Solution: Step 1: Find positions for BCD and YXW. B = 2, C = 3, D = 4. Y = 25, X = 24, W = 23. Step 2: Add positions for each pair. B (2) + Y (25) = 27. C (3) + X (24) = 27. D (4) + W (23) = 27. Thus, each pair of letters is symmetric about the centre of the alphabet, with sums equal to 27. Step 3: Apply the same mirror rule to FGH. F = 6, G = 7, H = 8. To find the mirror letters, we compute 27 − position. For F: 27 − 6 = 21 → U. For G: 27 − 7 = 20 → T. For H: 27 − 8 = 19 → S. So FGH maps to UTS. Verification / Alternative check: We can verify by repeating the process for the original pair. Using the rule 27 − position, B becomes Y, C becomes X, and D becomes W, which matches the given mapping exactly. Applying the same transformation to UTS should bring us back to FGH if we again sum to 27: U (21) gives 27 − 21 = 6 → F, T (20) gives 7 → G, S (19) gives 8 → H. This confirms that UTS is the correct mirror of FGH under the same scheme. Why Other Options Are Wrong: • RQP: These letters do not match the computed mirror positions of FGH and follow a different ordering pattern. • STU and TUS: Although composed of similar letters, their order does not match the transformation applied to F, G, and H, and they do not preserve position by position mapping. Common Pitfalls: Day to day familiarity with alphabetical order may tempt candidates to choose STU or TUS because they look like simple reversals or near sequences. However, analogies involving mirror images rely on strict correspondences of positions rather than approximate visual shapes. Always convert letters to positions and explicitly check sums or differences to confirm the pattern. Final Answer: The letter group that correctly completes the analogy is UTS.

Question 2

In this number analogy, “66 is to 36 as 99 is to ______”. Select the number that completes the analogy by following the same pattern of taking the product of the digits.

Accepted Answer

Introduction / Context: This analogy links two digit numbers to other numbers using a digit based operation. The pair 66 : 36 suggests that the transformation may be related to the digits themselves rather than the whole number only. One natural idea is to multiply the digits of the two digit number and see if that gives the second number. After identifying the rule in the first pair, we apply the same to 99 and select the correct result from the options. This type of question is common in mental ability tests. Given Data / Assumptions: • First pair: 66 and 36. • Second pair: 99 and an unknown number. • Options: 18, 27, 81, 108. • We consider operations such as product or square of digits for two digit numbers. Concept / Approach: For a two digit number like 66, the digits are 6 and 6. The product 6 * 6 is 36, which exactly matches the second number. This gives a clear rule: the second number is the product of the two digits of the first number. We then apply the same idea to 99, whose digits are 9 and 9. The product 9 * 9 gives the related number. We finally match the result to the options. Step-by-Step Solution: Step 1: Analyse the first pair. The digits of 66 are 6 and 6. Compute the product: 6 * 6 = 36. So the second number 36 is equal to the product of the digits of 66. Step 2: Apply the same rule to 99. Digits of 99 are 9 and 9. Compute the product: 9 * 9 = 81. Step 3: Compare with options. Among 18, 27, 81, and 108, only 81 is the product of 9 and 9. Verification / Alternative check: We can also check other plausible operations. For instance, the sum of digits of 66 is 6 + 6 = 12, not 36. The square of the number 66 is much larger than 36. Therefore, the only simple rule that fits 66 : 36 is digit product. Applying the same logic to 99 gives 81, which fits neatly with the pattern. This coherence across both pairs confirms the rule. Why Other Options Are Wrong: • 18: This is 2 * 9, not related to the digits of 99 directly. • 27: Could be 3³, but it does not arise from 9 and 9 as digits in the given pattern. • 108: This is 12 * 9 or 9 * 12, but no such operation is indicated by the first pair. Common Pitfalls: Many candidates try to connect 66 and 36 by operations on the whole number, such as subtracting 30. However, this does not give a clear way to handle 99. When two digit numbers have repeated digits, you should always consider operations involving those digits, especially multiplication, since repeated digit products often lead to familiar squares like 36 and 81. Final Answer: The number that correctly completes the analogy is 81.

Question 3

In this letter analogy, “DCEF is to QPRS as XWYZ is to ______”. Select the group of letters that completes the analogy by applying the same constant alphabet shift used in the first pair.

Accepted Answer

Introduction / Context: This analogy uses a constant shift in alphabet positions, similar to a rotation or substitution cipher. The pair “DCEF : QPRS” shows how each letter in the first group is moved forward by the same number of positions to generate the second group. The task is to identify this fixed shift and then apply it to the group XWYZ, choosing the correct resulting sequence from the options. Mastery of alphabet positions and constant shifts is essential to solving such questions. Given Data / Assumptions: • First mapping: DCEF → QPRS. • Second mapping: XWYZ → ? • Options: KJLM, PQRS, STOV, IMGF. • Alphabet positions: A = 1, B = 2, ..., Z = 26, with wrap around when shifting beyond Z. Concept / Approach: We compare each corresponding letter in DCEF and QPRS: D with Q, C with P, E with R, and F with S. By converting these letters to numeric positions, we can check how many positions forward each letter moves. If the difference is the same for all four, this constitutes a constant shift (a rotation). Once we know the shift value, we apply it to each letter of XWYZ, wrapping around the alphabet when necessary, and then match the result to one of the options. Step-by-Step Solution: Step 1: Convert DCEF and QPRS to numeric positions. D = 4, C = 3, E = 5, F = 6. Q = 17, P = 16, R = 18, S = 19. Step 2: Compute the shift for each pair. 4 → 17: shift of +13. 3 → 16: shift of +13. 5 → 18: shift of +13. 6 → 19: shift of +13. Thus, each letter is shifted forward by 13 positions. Step 3: Apply the same shift to XWYZ. X = 24, W = 23, Y = 25, Z = 26. Add 13 to each and wrap around the alphabet by subtracting 26 whenever the sum exceeds 26. X: 24 + 13 = 37, 37 − 26 = 11 → K. W: 23 + 13 = 36, 36 − 26 = 10 → J. Y: 25 + 13 = 38, 38 − 26 = 12 → L. Z: 26 + 13 = 39, 39 − 26 = 13 → M. So XWYZ maps to KJLM. Verification / Alternative check: We can confirm the rule by reversing it. If we subtract 13 from Q, P, R, and S, we should return to D, C, E, and F respectively. Q (17) − 13 = 4 → D, P (16) − 13 = 3 → C, R (18) − 13 = 5 → E, S (19) − 13 = 6 → F. Similarly, subtracting 13 from KJLM should yield XWYZ: K (11) − 13 = −2, which after adding 26 gives 24 → X; J (10) − 13 = −3, plus 26 gives 23 → W; L (12) − 13 = −1, plus 26 gives 25 → Y; M (13) − 13 = 0, plus 26 gives 26 → Z. This confirms the mapping is consistent both forward and backward. Why Other Options Are Wrong: • PQRS: This is the mapping of DCEF itself and does not correspond to the second group XWYZ. • STOV and IMGF: These letter groups do not result from applying a +13 shift to each letter of XWYZ and do not match the consistent rotation pattern identified from the example pair. Common Pitfalls: A common mistake is to try to spot visual sequences like consecutive letters or simple reversals, ignoring the strong evidence from numeric differences. Another pitfall is to forget to wrap around the alphabet when the position goes beyond 26. Always remember that when using constant shifts, positions are effectively taken modulo 26, and subtracting or adding 26 keeps the letters within A to Z. This avoids incorrect mapping when working with letters near the end of the alphabet like X, Y, and Z. Final Answer: The group of letters that correctly completes the analogy is KJLM.

Question 4

In this number analogy, “121 is to 12 as 25 is to ______”. Select the number that completes the analogy by following the same square root plus one pattern used in the first pair.

Accepted Answer

Introduction / Context: This analogy connects each first number with its second number through a operation built on square roots. The pair 121 : 12 suggests that the second number is not simply the square root but slightly larger. Identifying this pattern and applying it to the second first number, 25, will give the correct related number. Recognising standard squares and using small adjustments like plus or minus one is a common technique in aptitude problems. Given Data / Assumptions: • First pair: 121 and 12. • Second pair: 25 and an unknown number. • Options: 5, 6, 7, 8. • Basic square facts: 11² = 121 and 5² = 25. Concept / Approach: First, recognise that 121 is a perfect square. Its square root is 11. The second number in the pair is 12, which is exactly one more than 11. This suggests the pattern: second number = square root of first number plus 1. We then apply this same rule to 25. The square root of 25 is 5, and adding 1 gives 6. Among the options, 6 matches this result. Step-by-Step Solution: Step 1: Express 121 as a square. 121 = 11 * 11 = 11². Step 2: Relate 11 to 12. 12 = 11 + 1, so the second number is the square root plus one. Step 3: Express 25 as a square. 25 = 5 * 5 = 5². Step 4: Apply the same rule to 25. Square root of 25 is 5. Add one: 5 + 1 = 6. Step 5: Match the result with the options; 6 is option B. Verification / Alternative check: Consider alternate rules, such as taking square root minus one. For 121, that would give 10, not 12, so that rule is not valid. Another idea might be to divide the number by 10 or 11, but such operations do not produce a simple pattern that extends to 25 and matches an option. The square root plus one pattern is consistent and uses familiar arithmetic. Additionally, applying this rule to any other perfect square such as 36 would give 6 + 1 = 7, keeping the structure logically stable. Why Other Options Are Wrong: • 5: This is exactly the square root of 25 but does not include the extra one seen in the first pair. • 7 and 8: These are larger than the square root plus one and do not follow the established rule. Common Pitfalls: A very common mistake is to assume that the second number is always just the square root of the first and select 5 for the second pair. This ignores the important detail of the extra one in 121 : 12. Carefully checking how the square root relates to the second number, whether plus or minus one, is crucial for full accuracy in analogy problems built on squares. Final Answer: The number that correctly completes the analogy is 6.

Question 5

In this word analogy, “Calendar is to Dates as Dictionary is to ______”. Choose the word that stands in the same object to item listed relationship for dictionary that dates do for calendar.

Accepted Answer

Introduction / Context: This analogy checks understanding of the relationship between reference tools and the information they organise. The pair “Calendar : Dates” shows that a calendar is a structured tool that displays and organises dates. Similarly, a dictionary is a reference book that organises certain items. The task is to select which of the given options best represents what a dictionary organises, maintaining the same type of relationship. Given Data / Assumptions: • Example pair: Calendar and Dates. • Target pair: Dictionary and ? • Options: Words, Books, Language, Vocabulary. • We assume common uses of these reference sources in everyday and academic contexts. Concept / Approach: A calendar is designed to organise days, weeks, and months, and the key items it displays are dates. A dictionary is designed to organise and list units of language in a systematic order, usually alphabetical. The fundamental units in a dictionary are individual words, each accompanied by definitions, pronunciations, and usage information. Thus the relationship is “reference tool : basic items listed”. For a dictionary, that core element is words. Step-by-Step Solution: Step 1: Clarify the calendar relationship. A calendar structures time into months and days and shows specific dates on which events occur. Step 2: Clarify the role of a dictionary. A dictionary lists words in an organised manner, usually alphabetically, and provides their meanings and other details. Step 3: Examine each option in relation to dictionary. Words: These are the basic entries in a dictionary and are exactly what the dictionary is structured around. Books: A dictionary is itself a type of book; it does not list books inside it as its primary content. Language: A dictionary describes a language, but it does this through entries on individual words rather than listing all languages. Vocabulary: This refers to the collection of words that a person knows, but the immediate, concrete items listed in a dictionary are individual words. Step 4: Conclude that Words is the closest parallel to Dates in the first pair. Verification / Alternative check: We can restate the analogy in the form “tool for reference : fundamental entries in that tool”. A calendar has dates as entries; a dictionary has words as entries. Vocabulary is more abstract and refers to a personal or collective set of words rather than the direct content listing inside the reference book. Therefore, Words mirrors Dates most precisely in this context. Why Other Options Are Wrong: • Books: A dictionary does not mainly list books; it is one book among others. • Language: Too broad; the dictionary is about a language but does not list languages as entries. • Vocabulary: Refers to a person's word knowledge, not to the explicit entries printed in the dictionary. Common Pitfalls: Some candidates may be attracted to Vocabulary because it sounds academic and is related to a dictionary. However, the question focuses on the direct one to one relationship, just as dates are the individual entries on a calendar. Remember to choose the term that names the specific items listed, not the general concept or outcome associated with the book. Final Answer: The word that correctly completes the analogy is Words.

Question 6

In this number analogy, “15 is to 225 as 12 is to ______”. Select the number that completes the analogy by applying the same squaring pattern used in the first pair.

Accepted Answer

Introduction / Context: This question uses a straightforward square based pattern. The pair 15 : 225 shows that the second number is the square of the first number. The task is to apply the same pattern to 12 and select the correct result from the options. Recognising when a number is the square of another is an essential skill in quantitative aptitude, especially in analogy and series questions. Given Data / Assumptions: • First pair: 15 and 225. • Second pair: 12 and an unknown number. • Options: 144, 122, 112, 222. • Basic fact: 15² = 225. Concept / Approach: Check whether the second number in the first pair is the square of the first. Since 15 * 15 = 225, the pattern is clear: second number = first number squared. We then apply the same operation to the second first number, 12. So the required second number should be 12². After computing 12², we match the result with the options and choose the one that fits exactly. Step-by-Step Solution: Step 1: Confirm the relationship in the first pair. Compute 15²: 15 * 15 = 225. So the second number is the square of the first. Step 2: Apply the same rule to 12. Compute 12²: 12 * 12 = 144. Step 3: Compare 144 with the options. Option A is 144, which matches the computed square exactly. Verification / Alternative check: We can rule out other types of operations quickly. For example, multiplying 15 by 10 gives 150, not 225. Adding a constant would not match 225 exactly either. Because 225 is a familiar square, identifying it as 15² is straightforward. Similarly, 144 is a well known square of 12. This symmetry strongly supports the square pattern as the intended logic for this analogy. Why Other Options Are Wrong: • 122 and 112: These are not perfect squares of integer values close to 12 and have no clear link to 12 in a simple square based rule. • 222: Only superficially resembles 225 in digits, but does not represent the square of 12 or any similar pattern. Common Pitfalls: Occasionally students misread 225 and assume some addition based pattern, for example adding 210 to 15. Such a rule is not meaningful and does not generalise to 12. To avoid this, always test whether a number is a perfect square when numbers like 225 and 144 appear. Recognising these squares saves time and improves accuracy on many evaluation questions. Final Answer: The number that correctly completes the analogy is 144.

Question 7

In this physical quantity analogy, “Luminous intensity is to Candela as Pressure is to ______”. Select the SI unit that stands in the same physical quantity to SI unit relationship for pressure that candela does for luminous intensity.

Accepted Answer

Introduction / Context: This analogy tests knowledge of SI units and their corresponding physical quantities. The pair “Luminous intensity : Candela” connects a physical quantity with its SI base unit. To complete the analogy, we must choose the SI unit that corresponds to pressure in the same way. Such questions are common in basic physics and general science sections of competitive exams and reinforce familiarity with standard units. Given Data / Assumptions: • Physical quantity: Luminous intensity. • SI unit: Candela (symbol cd). • Another quantity: Pressure. • Options for possible units: Radian, Newton, Pascal, Joule. • We assume standard SI definitions: Newton for force, Pascal for pressure, Joule for energy, and radian as a unit of plane angle. Concept / Approach: The relationship is clearly “physical quantity : its SI unit”. Luminous intensity is measured in candela. For the second pair, we need the SI unit in which pressure is measured. In the International System of Units, pressure is defined as force per unit area and its derived SI unit is Pascal (Pa), which equals one Newton per square metre. Therefore the correct completion of the analogy is Pressure : Pascal. Step-by-Step Solution: Step 1: Restate the first pair. Luminous intensity, one of the base physical quantities, is measured in candela. Step 2: Identify the nature of pressure. Pressure is defined as force acting per unit area. Step 3: Recall the SI unit of pressure. Since pressure = force / area and the SI unit of force is Newton while the SI unit of area is square metre, the SI unit of pressure is Newton per square metre. This combined unit is given the special name Pascal (Pa). Step 4: Match with the options. Radian measures angles, Newton measures force, Pascal measures pressure, and Joule measures energy or work. Thus, Pascal is the correct SI unit for pressure. Verification / Alternative check: Verify by checking each candidate unit against its standard physical quantity. Radian is used for angular measure, such as the angle around a circle. Newton is used for force (mass times acceleration). Joule is used for energy, for example in mechanics and thermodynamics. Only Pascal is reserved for pressure, defined as one Newton per square metre. This confirms that Pascal is the unique choice that fits the analogy structure. Why Other Options Are Wrong: • Radian: Unit of plane angle; unrelated to pressure. • Newton: Unit of force, not pressure; pressure uses Newton in combination with area in the numerator. • Joule: Unit of energy or work, not force per area. Common Pitfalls: A common error is to choose Newton because pressure involves force. However, Newton alone measures force, not force per unit area. Remember that pressure is a derived quantity, and its correct SI name is Pascal. Keeping a small list of key SI units in memory, like metre, kilogram, second, ampere, kelvin, mole, candela, and some derived units such as Newton and Pascal, greatly helps with these questions. Final Answer: The SI unit that correctly completes the analogy is Pascal.

Question 8

In the following letter analogy, APPARENT is related to RENTAPPA by a specific rearrangement of letters. Following the same pattern, MUSCULAR is related to which of the following options?

Accepted Answer

Introduction / Context: This question is a classic letter analogy from verbal and non verbal reasoning. You are given one pair of related words and then asked to apply exactly the same pattern or rule to a new word. Here, the relationship between APPARENT and RENTAPPA must be understood and then used to find how MUSCULAR should be transformed. Such problems test pattern recognition, attention to detail and comfort with manipulating sequences of letters. Given Data / Assumptions: - First word pair in the analogy: APPARENT and RENTAPPA. - Second word that must undergo a similar transformation: MUSCULAR. - All answer options are rearrangements of the letters of MUSCULAR. - We assume that no letters are added or removed, only rearranged, just as in the example pair. Concept / Approach: To solve this, observe how APPARENT becomes RENTAPPA. Count the letters. APPARENT has eight letters. The first four letters are APPA and the last four letters are RENT. In the transformed word RENTAPPA, the last four letters come to the front and the first four letters move to the end. So the rule is: split the eight letter word into two equal halves and swap the halves. We now apply this same half swapping rule to MUSCULAR, which is also an eight letter word. Step-by-Step Solution: Step 1: Write APPARENT as two halves: APPA and RENT. Step 2: Swap the halves to get RENTAPPA, confirming the pattern in the example pair. Step 3: Write MUSCULAR and split into two halves. The first four letters are MUSC and the last four letters are ULAR. Step 4: Apply the same rule: bring the last half ULAR to the front and send the first half MUSC to the end, giving ULARMUSC. Step 5: Compare ULARMUSC with the given options and select the exactly matching option. Verification / Alternative check: Check that no letters are lost or duplicated. MUSCULAR contains M, U, S, C, U, L, A, R. The rearranged form ULARMUSC still contains exactly the same multiset of letters and the length is unchanged. Also verify that the same half swapping rule applies cleanly because the length is even. This confirms that ULARMUSC is a consistent and unique application of the given pattern. Why Other Options Are Wrong: Option A ULAMMUSC changes the number of letter M and does not preserve the original letter pattern. Option C UMAMLUSC rearranges the letters in a way that does not correspond to a simple half swap. Option D ULARMUCS changes the final order and is not a direct last half plus first half construction. Therefore these distractors do not correctly mirror the APPARENT to RENTAPPA transformation. Common Pitfalls: Learners sometimes try to look for simple reversal or alternating letter patterns instead of splitting the word exactly in the middle. Another frequent mistake is to miscount the letters and split them unevenly, which leads to an incorrect transformation. It is also easy to overlook duplicate letters and accidentally change their count when mentally rearranging. Writing the letters down clearly and marking the halves avoids these errors. Final Answer: The correct transformed form of MUSCULAR, using the same half swapping pattern as APPARENT to RENTAPPA, is ULARMUSC.

Question 9

In the following coded letter analogy, PEON is related to QRHS by a specific reversal and letter shift. Using the same rule, JOCK is related to which of the following options?

Accepted Answer

Introduction / Context: This question involves a coded letter analogy where one word is converted into another using a pattern based on letter positions in the English alphabet. You must decode how PEON becomes QRHS and then apply the same transformation to the word JOCK. Such questions are common in aptitude tests and evaluate a candidate's ability to handle abstract coding and decoding of words. Given Data / Assumptions: - Given pair: PEON and QRHS. - Target base word: JOCK. - All answer options are four letter strings matching the length of JOCK. - The same rule used on PEON must be used on JOCK to maintain a valid analogy. Concept / Approach: We first convert letters to their numerical positions in the alphabet. Then we look for a positional or rearrangement pattern between PEON and QRHS. Direct letter by letter shifting appears irregular. A useful idea is to check whether the original word has been reversed before a uniform shift is applied. If we reverse PEON, we get NOEP. Now we can examine what happens when each letter of NOEP is shifted forward by a fixed number of positions. Step-by-Step Solution: Step 1: Write PEON and reverse it to get NOEP. Step 2: Convert letters to positions: N is 14, O is 15, E is 5, P is 16. Step 3: Add 3 to each position: 14 becomes 17 (Q), 15 becomes 18 (R), 5 becomes 8 (H), 16 becomes 19 (S), giving QRHS. Step 4: Confirm that reversing then adding 3 explains the given pair PEON : QRHS. Step 5: Apply the same procedure to JOCK. Reverse JOCK to get KCOJ. Step 6: Convert K, C, O, J to numbers: 11, 3, 15, 10, then add 3 to each to get 14 (N), 6 (F), 18 (R), 13 (M), forming NFRM. Step 7: Match NFRM with the options and select it. Verification / Alternative check: Re check that PEON to QRHS indeed follows the rule reversed word plus three positions. NOEP shifted by three gives QRHS exactly. Doing the same with KCOJ gives NFRM, and this output appears exactly as option A. No other option follows the same two step rule consistently, which confirms the correctness of the answer. Why Other Options Are Wrong: Option B NFMR, option C NEFM and option D NFMM all use some of the same letters but in different orders or with different shifts. They might look similar at a glance, but they do not come from reversing JOCK and adding three to each letter. Since the analogy must mirror the given mapping exactly, these alternatives are invalid. Common Pitfalls: A common mistake is to attempt a direct shift on PEON without noticing that the letters have been reversed before shifting. Another pitfall is inconsistent shifting, such as adding different values to different letters, which breaks the uniform pattern needed in analogies. Always confirm whether reordering steps like reversal are involved before looking for numerical shifts. Final Answer: Using the reverse then plus three coding rule, the correct coded form of JOCK is NFRM.

Question 10

In the following number analogy, 34 is related to 81 through an exponential relationship. Using the same pattern, 23 is related to which number?

Accepted Answer

Introduction / Context: This analogy question tests numerical pattern recognition. You are given that 34 is related to 81 and you must identify how 23 will be related to another number using the same rule. The challenge is to notice that the digits in each pair can be interpreted as base and exponent to form a power. Such problems appear frequently in quantitative aptitude and reasoning sections of exams. Given Data / Assumptions: - First pair: 34 and 81. - Second starting number: 23. - All answer options are positive integers. - The same mathematical pattern must connect 23 to the correct answer that connects 34 to 81. Concept / Approach: Look at 34 and 81. A very strong hint is that 81 is a well known power, namely 3 raised to the power 4. The number 34 consists of the digits 3 and 4. This suggests we interpret 34 not as thirty four but as a compact way of writing 3 as base and 4 as exponent. That is, 34 corresponds to 3^4 which equals 81. Once we see this, we can apply exactly the same logic to 23 by treating it as 2^3. Step-by-Step Solution: Step 1: Interpret 34 as 3^4, where 3 is the first digit and 4 is the second digit. Step 2: Compute 3^4 = 3 * 3 * 3 * 3 = 81, which matches the given pair. Step 3: Apply the same idea to 23, treating it as 2^3, where 2 is the base and 3 is the exponent. Step 4: Calculate 2^3 = 2 * 2 * 2 = 8. Step 5: Compare the result 8 with the options and choose option A. Verification / Alternative check: Check quickly whether any other simple interpretation of 34 could produce 81. Common operations like 3 + 4, 3 * 4, or 34 + a constant do not yield 81. The only natural and neat explanation is using exponentiation. Similarly, 2^3 is unambiguously equal to 8, and no other choice fits this very specific pattern. This confirms that the relationship is based on base exponent structure and that 8 is correct. Why Other Options Are Wrong: Option B 16 might come from 4^2 or squaring, but that does not mirror the 3^4 pattern. Option C 4 would correspond to 2^2, again inconsistent. Option D 12 could arise from addition or multiplication, but it cannot be derived using the same exponent rule used in the first pair. Therefore these answers fail to respect the base exponent idea that underlies the analogy. Common Pitfalls: Students sometimes focus only on addition, subtraction or multiplication of digits and completely miss exponentiation as a possibility. Another error is to reverse the base and exponent and try 4^3 instead of 3^4 for the first pair, which gives 64 and does not match 81. Always confirm which interpretation exactly reproduces the given mapping before applying it to the second case. Final Answer: Using the pattern base^exponent, 34 corresponds to 3^4 = 81, so 23 corresponds to 2^3 = 8.

Question 11

In the following analogy, Foot is to Man as Hoof is to which of the following options?

Accepted Answer

Introduction / Context: This is a simple verbal analogy based on body parts and the living beings they belong to. Foot is a part of the human body, specifically a lower limb extremity in a man. The question asks you to extend the same relationship to identify which animal commonly has a hoof. Such analogy questions check basic general knowledge and the ability to see category membership and part whole relations. Given Data / Assumptions: - First pair: Foot and Man, where foot is a body part of a man. - Second term given: Hoof. - Options list various words including animals and other related ideas. - We assume that the second pair should also show a body part to organism relationship of the same type. Concept / Approach: In the first pair, the relationship is body part to its owner. A foot belongs to a human being. We must now find which option represents an animal for which hoof is the correct standard foot structure. Hooves are characteristic of certain mammals, especially horses, cows, deer and similar ungulates. Among the options given, Horse is the typical and most widely known hoofed animal in common aptitude questions. Step-by-Step Solution: Step 1: Identify the relationship in the first pair as body part of a human being. Step 2: Note that hoof is also a body part but belongs to some specific animals, not humans. Step 3: Examine the options. Leg is another body part, not an animal. Dog is an animal but it has paws, not hooves. Horse is a classic hoofed animal. Shoe is an item worn on a foot or hoof, not the animal itself. Step 4: Select Horse as the animal for which hoof is the characteristic foot structure, forming the pair Hoof : Horse. Verification / Alternative check: Check consistency: Foot : Man is part to owner. Hoof : Horse is part to owner in the same pattern. None of the other options produce a consistent and usual biological pairing. Therefore Horse uniquely matches the intended relationship. Why Other Options Are Wrong: Option A Leg is a body part rather than the organism. The analogy would become body part to body part, which is not consistent. Option B Dog is a valid animal but dogs have paws rather than hooves. Option D Shoe is an object used by humans or even horses, but it is not an animal and therefore breaks the structure of the analogy completely. Common Pitfalls: Sometimes examinees choose Dog simply because it is a familiar animal without recalling the correct anatomical term for its foot. Others may be distracted by Shoe, since shoes are worn on feet and hooves, but this changes the relationship from part to owner into part to object, which is not parallel. Always identify the exact relationship in the first pair and keep it identical in the second. Final Answer: Foot is a body part belonging to a man, and in the same way a hoof is a characteristic body part of a Horse.

Question 12

In the following letter analogy, ACEG is related to ZXVT using opposite positions in the alphabet. Using the same pattern, IKMO is related to which of the following options?

Accepted Answer

Introduction / Context: This analogy tests how well you understand positional relationships of letters within the English alphabet. The pair ACEG : ZXVT uses a specific pattern based on letters that are opposite or complementary when counted from the start and end of the alphabet. You must discover this rule and then apply it to the second set of letters IKMO to find the correct related sequence. Given Data / Assumptions: - First letter group: ACEG. - Related group: ZXVT. - Second base group: IKMO. - All answer options are four letter strings, just like the groups in the analogy. - We assume that each letter in ACEG is mapped individually to a new letter to form ZXVT, and the same type of mapping must be used on IKMO. Concept / Approach: Write down positions of letters A to Z as 1 to 26. For complementary or opposite letters, the sum of their positions is often constant. For ACEG and ZXVT, notice that A (1) with Z (26) gives 27, C (3) with X (24) gives 27, E (5) with V (22) gives 27 and G (7) with T (20) gives 27. So each letter is replaced by the letter whose position index adds up to 27. This is a symmetric mapping around the middle of the alphabet. We apply the same 27 rule to IKMO. Step-by-Step Solution: Step 1: Confirm the pattern on ACEG. Map A to Z, C to X, E to V and G to T and verify that each pair sums to 27. Step 2: Convert I, K, M and O to positions: I is 9, K is 11, M is 13 and O is 15. Step 3: Find the complementary letter for each by calculating 27 minus the position. For I, 27 - 9 = 18, which is R. For K, 27 - 11 = 16, which is P. For M, 27 - 13 = 14, which is N. For O, 27 - 15 = 12, which is L. Step 4: Write the mapped sequence in order as RPNL. Step 5: Compare RPNL with the options and select the exact match. Verification / Alternative check: Quickly verify that R and I are complementary (9 + 18 = 27), P and K are complementary (11 + 16 = 27), N and M (13 + 14 = 27) and L and O (15 + 12 = 27). This confirms that the same mapping has been applied. None of the other options maintain this consistent complementary relation for all four letters, so the pattern is unique. Why Other Options Are Wrong: Options A, B and D do not give complementary pairs for each letter of IKMO. Some letters may accidentally fit the 27 rule, but the complete four letter group does not satisfy the pattern throughout. Since a valid analogy requires the same rule to hold for each position, these options must be rejected. Common Pitfalls: A common error is to search for simple forward or backward shifts by a fixed number instead of checking sums of positions. Another mistake is to identify the complementary rule for some letters but fail to apply it consistently to all positions. Writing down the alphabet with numerical positions helps prevent such slips. Final Answer: Using the complementary letter rule where positions add up to 27, IKMO maps to RPNL.

Question 13

In this number analogy, 68 is related to 130 using a two step arithmetic rule. Applying the same rule, 222 is related to which of the following numbers?

Accepted Answer

Introduction / Context: This question is a number analogy where a specific arithmetic rule connects each pair of numbers. You are told that 68 corresponds to 130 and must determine which number should be paired with 222 using the same transformation. Such questions are common in quantitative aptitude tests and help examiners see whether a student can extract a hidden rule from one example and then generalise it correctly. Given Data / Assumptions: - First pair: 68 and 130. - Second given number: 222. - The options are candidate results of applying the same rule to 222. - We assume a single consistent arithmetic pattern, such as scaling and shifting, applies to both pairs. Concept / Approach: A good starting point is to check simple linear transformations. Notice that if we multiply 68 by 2 we obtain 136. If we then subtract 6, we get 130. So one neat pattern is: result = 2 * number - 6. This works exactly for the given pair 68 : 130. The next step is to verify this rule by applying it to 222 and seeing which option matches. Step-by-Step Solution: Step 1: Test doubling: 2 * 68 = 136. Step 2: Subtract 6 from 136: 136 - 6 = 130, which matches the given related number. Step 3: Conclude that the rule is f(n) = 2 * n - 6. Step 4: Apply the same rule to 222. Compute 2 * 222 = 444. Step 5: Subtract 6 from 444: 444 - 6 = 438. Step 6: Compare 438 with the answer options and select it as the correct related number. Verification / Alternative check: Test whether any other simple operation on 68, like adding a fixed constant or squaring, gives 130 in a neat way. Adding a constant would require 62, and there is no reason to prefer that over 2n minus a constant when the doubling pattern works so cleanly. Also, when the same rule is applied to 222, we obtain 438 which lies in a reasonable range and is explicitly present among the options. This double then subtract rule is simple, consistent and reproducible. Why Other Options Are Wrong: Option B 430, option C 444 and option D 450 cannot be obtained by the rule 2n minus 6. For instance, 2 * 222 is 444, so 444 would correspond to subtracting zero. That would break the pattern used to generate 130 from 68. Similarly, 430 or 450 would require arbitrary constants that do not match the first pair. Because a single uniform rule must apply to both pairs, these alternatives must be rejected. Common Pitfalls: A frequent mistake is to focus on the digits and attempt slow digit wise manipulations rather than treating the number as a whole. Others may try complicated operations such as mixing squares and cubes without noticing that a very simple linear rule fits perfectly. Always start with testing small, neat transformations like doubling, halving, adding or subtracting constants before considering more complex patterns. Final Answer: Using the rule result = 2 * number - 6, 68 maps to 130 and 222 maps to 438.

Question 14

Rabi Crop is related to Oat in the same way that Kharif Crop is related to which of the following crops?

Accepted Answer

Introduction / Context: This analogy question is based on basic agricultural knowledge, particularly cropping seasons. Rabi and Kharif are two major crop seasons in countries like India. The pair Rabi Crop and Oat indicates that oat is an example of a Rabi crop. You must identify which option is a typical Kharif crop that completes the analogy with Kharif Crop in the same way. Given Data / Assumptions: - First pair: Rabi Crop and Oat, meaning oat is a representative Rabi season crop. - Second term: Kharif Crop, which relates to the rainy or monsoon season crop. - Options include Mustard, Wheat, Barley and Paddy. - We assume only one option is a standard, widely known Kharif crop in basic general knowledge contexts. Concept / Approach: Rabi crops are generally sown in winter and harvested in spring. Common examples include wheat, barley, oats and mustard. Kharif crops are sown with the onset of monsoon and harvested in autumn. Typical Kharif crops include paddy (rice), maize and cotton. Since Oat is a well known Rabi crop, we need a similarly standard example of a Kharif crop from the options given. Step-by-Step Solution: Step 1: Confirm that Oat is indeed cultivated as a Rabi crop in many regions. Step 2: Recall standard Rabi crops such as wheat, barley, mustard and oat. Step 3: Recall standard Kharif crops such as paddy, maize, sorghum and cotton. Step 4: Examine the options: Mustard, Wheat and Barley all belong to the Rabi group, while Paddy is a classic Kharif crop that depends on monsoon rains and flooded fields. Step 5: Select Paddy as the crop that stands in the same type of relationship with Kharif Crop as Oat does with Rabi Crop. Verification / Alternative check: Verify that each option correctly matches its season. Mustard and Wheat are winter crops sown after the monsoon. Barley is again a Rabi season crop. Only Paddy is primarily a monsoon season crop, directly linked to Kharif. Hence the analogy Rabi Crop : Oat :: Kharif Crop : Paddy is consistent and unique. Why Other Options Are Wrong: Mustard, Wheat and Barley are all Rabi crops, so pairing any of them with Kharif Crop would mix seasons and break the structure of the analogy. The question must connect Kharif to one of its own representative crops, not to another Rabi crop, therefore these options are incorrect. Common Pitfalls: Many learners remember lists of crops but confuse which belong to Rabi and which to Kharif. It is easy to pick a familiar crop like Wheat without checking its season. A good habit is to keep a small mental map: Rabi equals winter crops like wheat and barley, Kharif equals monsoon crops like paddy and maize. This quickly resolves such analogy questions. Final Answer: Rabi Crop is related to Oat, and in a similar way Kharif Crop is related to the classic monsoon crop Paddy.

Question 15

In the following letter code analogy, CM is related to P by a positional rule in the alphabet. Using the same rule, PM is related to which of the following single letters?

Accepted Answer

Introduction / Context: This question involves converting a pair of letters into a single letter using their positions in the English alphabet. You are told that CM maps to P, and you must then determine what PM maps to using the same rule. These types of analogies check your comfort with letter position arithmetic and pattern recognition under a coded format. Given Data / Assumptions: - First input pair: CM. - First output: P. - Second input pair: PM. - Options are letters F, E, D and C. - We assume a simple numerical relationship based on alphabetical positions rather than arbitrary assignment. Concept / Approach: Assign numerical positions to letters: A is 1, B is 2, ..., Z is 26. For CM, C has position 3 and M has position 13. Notice that the sum 3 + 13 equals 16, and the 16th letter of the alphabet is P. Therefore, CM is mapped to P by adding the positions of the two letters and converting the sum back to a letter. We apply the same rule to PM. Step-by-Step Solution: Step 1: Convert C and M to their positions, 3 and 13. Step 2: Add these positions: 3 + 13 = 16. Step 3: Identify the 16th letter of the alphabet, which is P. This confirms the rule for the first mapping. Step 4: Now process PM. P has position 16 and M has position 13. Step 5: Add 16 and 13 to get 29. Step 6: Because the alphabet has 26 letters, we convert 29 back into a valid position by subtracting 26. So 29 minus 26 equals 3. Step 7: The 3rd letter of the alphabet is C, so PM maps to C. Verification / Alternative check: Check that the same modular logic works for CM. The sum 3 + 13 is 16, which does not exceed 26, so no wraparound is needed and P is directly valid. For PM, wraparound is required because 29 is greater than 26. Taking 29 minus 26 to get 3 is a standard modular arithmetic step when working with letter positions. The resulting letter C appears exactly among the options and matches the rule consistently. Why Other Options Are Wrong: Options F, E and D correspond to positions 6, 5 and 4. None of these values equals 3, which is the reduced position we obtain from 16 + 13. Selecting any of them would break the sum based mapping that works perfectly for CM. Therefore they cannot be correct under a single consistent rule. Common Pitfalls: One common mistake is forgetting to wrap around after 26, leading candidates to pick 29 as if it were a valid letter position. Another is trying to use different operations for the second pair, like subtraction instead of addition, which violates the requirement of a uniform rule. Always apply the same numeric rule and remember that letter positions cycle after 26. Final Answer: CM maps to P by adding the letter positions, so PM maps to position 3 and therefore to the letter C.

Question 16

From the following list of trees, identify the one that does not belong to the same botanical group as the others.

Accepted Answer

Introduction / Context: This question is an odd one out problem based on basic botany and types of trees. You are given four tree names and must select the one that does not share the same key characteristics as the other three. Such problems test classification skills, general science awareness and the ability to recognise patterns of similarity and difference. Given Data / Assumptions: - The tree names given are Banyan, Pine, Spruce and Fir. - Three of these belong to a similar botanical category, while one belongs to a different category. - We assume familiarity with broad groups such as coniferous evergreen trees and broad leaved deciduous trees. Concept / Approach: Pine, Spruce and Fir are all coniferous trees. They have needle like leaves, produce cones and are generally evergreen. In contrast, Banyan is a broad leaved deciduous or semi evergreen tree from the fig family. It has large flat leaves, aerial roots and does not bear cones like conifers. Therefore, Banyan differs from the other three in leaf type, reproduction and general morphology. Step-by-Step Solution: Step 1: Recall that Pine is a well known conifer with needle like leaves and cones. Step 2: Recognise that Spruce is another conifer, similar in appearance to Pine, also bearing cones. Step 3: Note that Fir is again a coniferous evergreen tree, often used as a Christmas tree in many regions. Step 4: Consider Banyan, which has broad leaves, a massive spreading canopy and aerial prop roots, and belongs to the fig family. Step 5: Conclude that Banyan is the only non conifer among the options and is therefore the odd one out. Verification / Alternative check: Verify the key feature: Pine, Spruce and Fir all produce woody cones and have needle like leaves. Banyan does not fit this description. It produces figs and has a very different growth habit. In classification terms, the three conifers belong to a different group of gymnosperms, whereas Banyan is an angiosperm with a contrasting structure. This confirms that Banyan is the unique member in the list. Why Other Options Are Wrong: Choosing Pine, Spruce or Fir as the odd one out would be incorrect because each of them shares the coniferous evergreen characteristics with the other two. None of these three stands apart in the same way Banyan does. The question is designed so that the majority category is conifers and the single different tree is a broad leaved non conifer. Common Pitfalls: Students sometimes focus only on superficial familiarity, for example, picking Pine because it is the most commonly mentioned tree. Others may not recall the precise botanical grouping and simply guess. Remembering that conifers bear cones and have needle like leaves helps to quickly isolate which trees are similar and which are not. Final Answer: The only tree that is not a conifer among the four is Banyan, so it is the odd one out.

Question 17

In the following vocabulary based analogy, Pernicious is related to Lethal as Indict is related to which of the following words?

Accepted Answer

Introduction / Context: This analogy focuses on English vocabulary and synonym relationships. Pernicious is strongly related to the meaning of Lethal, both describing something that causes serious harm or death. The question now asks you to identify which word stands in a similar relationship to Indict. This type of problem checks your grasp of nuanced word meanings and your ability to match them correctly. Given Data / Assumptions: - First pair: Pernicious and Lethal, which are closely related in meaning. - Second base word: Indict, which is a verb used in legal contexts. - Options: Insolent, Impudent, Spoil and Accuse. - We assume the analogy is based on synonymy or very close meaning, not on opposite meanings. Concept / Approach: Pernicious describes something harmful, destructive or potentially deadly. Lethal similarly means deadly or fatal. So the first pair is built around synonymy. Indict is a legal term that means to formally charge someone with a crime. Therefore, the correct related word should be another verb that captures the idea of formally accusing or charging. Among the options, Accuse is closest in meaning to Indict. Step-by-Step Solution: Step 1: Confirm the first pair. Pernicious means harmful in a serious way, and Lethal means deadly. Both refer to severe harm, showing a synonym relationship. Step 2: Understand the word Indict. In legal usage, to indict someone is to formally charge that person with an offence, often via a grand jury in some legal systems. Step 3: Examine the options. Insolent means showing rude or disrespectful behaviour. Impudent is similar, referring to shamelessly bold or rude conduct. Spoil means to damage, ruin or overindulge. Step 4: Note that Accuse means to state or claim that somebody has committed a wrongdoing or crime, which is conceptually very close to Indict. Step 5: Therefore, Indict is to Accuse as Pernicious is to Lethal, and option D is correct. Verification / Alternative check: Check whether any option can stand as a true synonym of Indict in a sentence. Replacing Indict with Insolent or Impudent produces nonsense grammatically and semantically. Spoil also changes the core meaning entirely. Only Accuse fits naturally in contexts where Indict is used, reinforcing that the relationship is one of near synonymy. Why Other Options Are Wrong: Insolent and Impudent refer to rudeness or shameless boldness, which are personality traits, not legal actions. Spoil refers to damaging or indulging, again unrelated to formally charging someone with an offence. Because the question is built on a synonym relationship, these words are not acceptable substitutes for Indict. Common Pitfalls: Learners sometimes get distracted by word sound rather than meaning. For example, they may pick Spoil because it also has a negative tone. A better strategy is always to briefly recall the dictionary style meaning of each word before deciding. In vocabulary analogies, meaning match is more important than emotional tone. Final Answer: Pernicious and Lethal are near synonyms, and in the same way Indict is most closely related to Accuse.

Question 18

In the following letter analogy, FG is related to UT using complementary positions in the alphabet. Applying the same pattern, HI is related to which pair of letters?

Accepted Answer

Introduction / Context: This analogy uses complementary letter positions in the English alphabet. You are told that FG corresponds to UT and must determine the pair that corresponds to HI under the same rule. Recognising complements or mirror positions is a standard theme in logical reasoning questions involving letter series and analogies. Given Data / Assumptions: - First pair of letters: FG. - Related pair: UT. - Second base pair: HI. - Options: HI, GH, SR and ED. - We assume a consistent mapping from each letter to another symbol based on position, not arbitrary replacement. Concept / Approach: Assign numbers to letters: A is 1, B is 2, ..., Z is 26. For complementary letters, a common pattern is that their positions sum to a constant, often 27 or 26. Here, F is 6 and G is 7, while U is 21 and T is 20. Notice that 6 + 21 = 27 and 7 + 20 = 27. So each original letter is mapped to a letter whose index adds up to 27 with it. This is the complement rule around the centre of the alphabet. We now apply this same rule to H and I. Step-by-Step Solution: Step 1: Confirm the pattern for FG to UT. F is 6 and U is 21, so 6 + 21 = 27. G is 7 and T is 20, so 7 + 20 = 27. Step 2: Conclude that each letter is replaced by the letter with position 27 minus its own position. Step 3: Convert H and I to positions. H is 8 and I is 9. Step 4: Find the substitute for H: 27 - 8 = 19, which is S. Step 5: Find the substitute for I: 27 - 9 = 18, which is R. Step 6: Combine the results to get SR. Step 7: Compare SR with the answer options and select option C. Verification / Alternative check: Verify consistency by checking the sum for the new pair. H plus S is 8 + 19 = 27 and I plus R is 9 + 18 = 27, which matches the pattern from the example. No other option pair yields this complement relationship for both letters. Therefore, SR is the only valid mapped pair for HI under the given rule. Why Other Options Are Wrong: Option A HI simply repeats the original letters and ignores the complement mapping. Option B GH swaps the first pair but does not use the complement rule. Option D ED consists of letters whose positions do not sum to 27 when paired with H and I. These options fail to preserve the fundamental complement relationship identified in the first pair. Common Pitfalls: Some learners try simple forward or backward shifting rather than inspecting sums of positions. Others may correctly identify the pattern but apply it only to the first letter, producing partially correct but unsupported answers. To avoid errors, always check that the identified rule works for every letter in the given examples and in the target pair as well. Final Answer: Using the complement rule where letter positions add up to 27, HI maps to the pair SR.

Question 19

In the following analogy, a missing pair of letters must be found: ? is to LM as QR is to WX. Which pair of letters correctly completes the analogy?

Accepted Answer

Introduction / Context: This question gives you a letter pair analogy with one pair missing. You are shown that QR is related to WX, and you must find the pair that relates to LM in the same way. Such problems test your ability to identify fixed positional shifts of letters across the alphabet and then apply that pattern consistently. Given Data / Assumptions: - Known second pair: QR and WX. - Unknown first pair: ? and LM. - Options: CD, EF, FG and TU. - We assume that each letter in QR is shifted by a fixed amount to produce WX and that the same shift is used from the missing pair to LM. Concept / Approach: Convert letters into positions in the alphabet. Q is 17, R is 18, W is 23 and X is 24. Moving from Q to W is a shift of +6 (17 to 23) and from R to X is also +6 (18 to 24). Therefore the pattern is that both letters are shifted six steps forward. To create an analogy, the unknown pair must be such that applying a +6 shift to each of its letters results in L and M respectively. Step-by-Step Solution: Step 1: Confirm the shift from QR to WX: 17 to 23 and 18 to 24 show a consistent +6. Step 2: Let the unknown pair be AB, representing some letters X and Y, where X shifted by +6 becomes L and Y shifted by +6 becomes M. Step 3: Convert L and M to positions: L is 12 and M is 13. Step 4: Subtract 6 from each: 12 - 6 = 6 and 13 - 6 = 7. Step 5: The 6th and 7th letters of the alphabet are F and G. Step 6: Thus the missing pair must be FG, because FG shifted forward by 6 positions becomes LM. Verification / Alternative check: Check the forward shift: F (6) plus 6 is 12 which is L, and G (7) plus 6 is 13 which is M. This exactly replicates the pattern seen from Q to W and from R to X. No other given option pair, when shifted by +6, results in LM for both letters. This consistency verifies the correctness of FG. Why Other Options Are Wrong: Option A CD has letters in positions 3 and 4. When each is increased by 6, they become 9 (I) and 10 (J), not L and M. Option B EF in positions 5 and 6 would map to positions 11 (K) and 12 (L), giving KL instead of LM. Option D TU would map to Z and beyond the alphabet, requiring wraparound and breaking the neat pattern. None of these produce LM under a simple +6 shift. Common Pitfalls: A typical mistake is to attempt matching LM directly to QR and WX without checking for the precise shift value. Another error is to ignore that the same numerical difference must apply to both letters in each pair. Writing out letter positions and systematically computing the shift steeply reduces guesswork and errors. Final Answer: The only pair which, when each letter is shifted six places forward, produces LM is FG.

Question 20

In the following number analogy, 4 is related to 44 using a specific multiplication rule. Using the same rule, which number should be related to 77?

Accepted Answer

Introduction / Context: This number analogy problem checks your ability to detect a simple arithmetic relationship between two numbers. You are told that 4 is related to 44, and must find what number corresponds to 77 under the same rule. Recognising common patterns such as multiplication by a constant is key to solving such questions quickly in aptitude exams. Given Data / Assumptions: - Known pair: 4 and 44. - Second known number: 77. - Options for the missing number: 3, 6, 7 and 5. - We assume a single consistent arithmetic rule is responsible for the mapping. Concept / Approach: Observe that 44 is 4 multiplied by 11. That is, 4 * 11 = 44. This suggests a pattern where each base number is multiplied by 11 to get the second number in the pair. If that is correct, then we must find the number which, when multiplied by 11, gives 77. Step-by-Step Solution: Step 1: Confirm the pattern for the first pair: 4 * 11 = 44. Step 2: Formulate the rule as related number = base number * 11. Step 3: Apply this rule in reverse to 77 by dividing 77 by 11. Step 4: Compute 77 / 11 = 7. Step 5: Check that 7 appears among the given options. Step 6: Conclude that 7 is the base number that relates to 77 in the same way 4 relates to 44. Verification / Alternative check: Verify that no other simple pattern fits as neatly. For example, adding a fixed constant to 4 to obtain 44 would require 40, while to obtain 77 from the same constant would give 37, which does not match any option. The multiplication by 11 pattern is widely recognised and works consistently across both pairs, which confirms it as the intended rule. Why Other Options Are Wrong: Option A 3 would give 3 * 11 = 33, not 77. Option B 6 would give 66, and option D 5 would give 55. None of these results match 77, so they cannot be correct under the identified rule. Therefore they fail the consistency requirement of number analogies. Common Pitfalls: Some candidates overcomplicate simple problems by looking for digit manipulation, such as repeating digits or concatenation, instead of testing basic multiplication. Another mistake is to try multiple inconsistent rules for different pairs, which is not allowed in a valid analogy. Always confirm the same operation works for all pairs involved before finalising your answer. Final Answer: Since 4 relates to 44 by the rule 4 * 11, the number that relates to 77 must satisfy n * 11 = 77, giving n = 7.

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