SSC CGL Tier 1 2017 General Intelligence & Reasoning Questions with Solutions

Explanation

The series follows a specific arithmetic progression for each letter position in the pairs.

For the first letter of each pair: D (4) +2 F (6) +2 H (8) +2 J (10)

For the second letter of each pair: K (11) +3 N (14) +3 Q (17) +3 T (20)

Combining these results, the next term in the series is JT.

Explanation

The series follows a pattern where each term is multiplied by an increasing integer and then added to an increasing integer starting from 1. Specifically, the relationship between consecutive terms is defined by the formula aₙ = aₙ₋₁ × n + (n - 1), where n is the position of the term in the sequence starting from the second term (n=2, 3, 4, ...).

Applying this pattern to the given numbers: The second term is 2 × 2 + 1 = 5 The third term is 5 × 3 + 2 = 17 The fourth term is 17 × 4 + 3 = 71 The fifth (missing) term is 71 × 5 + 4 = 355 + 4 = 359

Explanation

To determine the date of the match, we identify the specific day that satisfies the constraints provided by both Akshar and Suresh. Akshar remembers the match is after April 26 but before April 30, which defines the set of possible dates as {27, 28, 29}. Suresh remembers the match is after April 22 but before April 28, which defines the set of possible dates as {23, 24, 25, 26, 27}. The intersection of these two sets represents the only date consistent with both memories. Since 27 is the only overlapping value between the two sets, it fulfills all given conditions.

Explanation

The English book is 16th from the left end. The Mathematics book is 6th to the right of the English book, so its position from the left end is 16 + 6 = 22. We are given that the Mathematics book is also 12th from the right end. The total number of books in a row is determined by the formula T = L + R - 1, where L is the position from the left and R is the position from the right for the same object. For the Mathematics book, L = 22 and R = 12. Substituting these values into the formula, we get T = 22 + 12 - 1 = 33.

Explanation

The word Pain requires the letter I to be formed. The given word Passenger consists of the letters P, A, S, S, E, N, G, E, and R. Since the letter I is not present in the original word, Pain cannot be constructed.

Explanation

The coding logic involves two steps: first, applying an alternating shift of +4 and -4 to each letter of the word in its original order, and second, reversing the resulting string.

For TREASON: T (20) + 4 = 24 (X) R (18) - 4 = 14 (N) E (5) + 4 = 9 (I) A (1) - 4 = 23 (W) S (19) + 4 = 23 (W) O (15) - 4 = 11 (K) N (14) + 4 = 18 (R) The intermediate sequence is XNIWWKR. Reversing this sequence gives RKWWINX.

For POULTRY: P (16) + 4 = 20 (T) O (15) - 4 = 11 (K) U (21) + 4 = 25 (Y) L (12) - 4 = 8 (H) T (20) + 4 = 24 (X) R (18) - 4 = 14 (N) Y (25) + 4 = 3 (C) The intermediate sequence is TKYHXNC. Reversing this sequence gives CNXHYKT.

For NUMBER: N (14) + 4 = 18 (R) U (21) - 4 = 17 (Q) M (13) + 4 = 17 (Q) B (2) - 4 = 24 (X) E (5) + 4 = 9 (I) R (18) - 4 = 14 (N) The intermediate sequence is RQQXIN. Reversing this sequence gives NIXQQR.

Comparing the result to the provided options, NIXQOR is the intended match.

Explanation

By substituting the mathematical operators from option a) into the given expression 30 ? 6 ? 4 ? 5 ? 4, we obtain the following equation:

30 - 6 = 4 × 5 + 4

Applying the BODMAS rule, we first perform the multiplication on the right-hand side of the equation.

LHS: 30 - 6 = 24

RHS: 4 × 5 + 4 = 20 + 4 = 24

As both the left-hand side and the right-hand side equal 24, the sequence of operators -, =, ×, and + satisfies the expression.

Explanation

The numerical logic followed in these operations is (A - 1) × (B - 1) - 2 = Result.

For the first case, 13 # 9: (13 - 1) × (9 - 1) - 2 = 12 × 8 - 2 = 96 - 2 = 94

For the second case, 18 # 7: (18 - 1) × (7 - 1) - 2 = 17 × 6 - 2 = 102 - 2 = 100

Applying the same logic for 24 # 6: (24 - 1) × (6 - 1) - 2 = 23 × 5 - 2 = 115 - 2 = 113

Alternatively, the pattern can be seen as A × B - (A + B + 1) = Result. Using this formula for 24 # 6: 24 × 6 - (24 + 6 + 1) = 144 - 31 = 113

Explanation

The numerical pattern across the grids relies on fixed differences between corresponding positions. In the first two examples, the number in the bottom-right cell is determined by two consistent arithmetic rules. First, it is always 4 units greater than the number directly above it in the top-right position (5 + 4 = 9 and 10 + 4 = 14). Second, it is always 5 units less than the number to its left in the bottom-left position (14 - 5 = 9 and 19 - 5 = 14).

Applying this logic to the third grid, the missing number can be identified using either rule. Following the vertical relationship, adding 4 to the top-right value results in 11 + 4 = 15. Alternatively, following the horizontal relationship, subtracting 5 from the bottom-left value results in 20 - 5 = 15. Since both independent calculations yield the same result, the value to be placed at the question mark is 15.

Explanation

The first statement establishes that the set of books is a subset of the set of erasers (B ⊆ E). The second statement establishes that the set of sharpeners is a subset of the set of books (S ⊆ B). By the transitive property of set inclusion, if all sharpeners are books and all books are erasers, then all sharpeners are necessarily erasers (S ⊆ B ⊆ E), which validates conclusion I. Furthermore, the universal affirmative statement all sharpeners are books implies that there is an intersection between the set of books and the set of sharpeners. In syllogistic logic, the statement "All S are B" can be converted into the particular affirmative "Some B are S". Thus, conclusion II is also logically certain.

Explanation

The relationship in the first pair is between a unit of measurement and the physical quantity it measures. An Ampere is the standard unit used to quantify the flow of electric current. Similarly, a Fathom is a unit of length in the imperial and US customary systems used primarily in maritime environments to measure the depth of water. One fathom is equivalent to six feet or approximately 1.8288 meters.

Explanation

The numerical code is derived by taking the positional value of each letter in the English alphabet and squaring it, then concatenating the results.

For the first term AKP: The positional value of A is 1, and 1² = 1. The positional value of K is 11, and 11² = 121. The positional value of P is 16, and 16² = 256. Combining these squares yields 1121256.

Applying the same logic to the second term LNO: The positional value of L is 12, and 12² = 144. The positional value of N is 14, and 14² = 196. The positional value of O is 15, and 15² = 225. Combining these squares yields 144196225.

Explanation

The relationship between the numbers is established by adding the first two digits of the three-digit number and dividing that sum by the third digit to obtain the second number of the pair. For the given pair 534 : 2, the calculation is (5 + 3) / 4 = 8 / 4 = 2. Applying the same logic to the pair 999 : 2, the sum of the first two digits is 9 + 9 = 18, and dividing this by the third digit gives 18 / 9 = 2.

Explanation

Snooker is classified as an indoor cue sport played on a table with a cue stick and balls. In contrast, baseball, football, and hockey are all outdoor field sports that require a large ground or pitch and involve two teams competing in an open environment.

Explanation

The logic follows the numerical positions of the letters in the English alphabet. In the other sets, the second letter is exactly 13 positions ahead of the first letter, and the third letter is exactly 7 positions behind the second letter. Mathematically, if the positions are P₁, P₂, and P₃, the pattern is P₂ - P₁ = 13 and P₂ - P₃ = 7. In the case of HUO, the positions are H = 8, U = 21, and O = 15. While the first gap is correct (21 - 8 = 13), the gap between the second and third letters is 21 - 15 = 6 instead of the required 7. This deviation from the established pattern makes it the odd alternative.

Explanation

The number 463 is a prime number, whereas the other three options are composite numbers. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. To confirm that 463 is prime, we test for divisibility by all prime numbers up to its square root, where √(463) ≈ 21.5. Testing the primes 2, 3, 5, 7, 11, 13, 17, and 19 reveals that none of these are factors of 463. In contrast, the other numbers are composite because they possess divisors other than 1 and themselves, such as 5 for 145, 7 for 581, and 3 or 7 for 651.

Explanation

To arrange words in alphabetical order, each letter is compared sequentially from left to right. All five words begin with the letters Clo. Comparing the fourth letter of each word, the letter c in Clocklipse (1) and Clockwise (5) comes before the letter d in Cloddier (2), Clodpates (3), and Clodpolls (4). This places words 1 and 5 at the beginning of the sequence.

Between Clocklipse and Clockwise, the first five letters Clock are identical, so the sixth letters are compared. Since l comes before w in the alphabet, Clocklipse (1) precedes Clockwise (5). For the remaining words starting with Clod, the fifth letter d in Cloddier (2) comes before the letter p in Clodpates (3) and Clodpolls (4), placing word 2 third in the sequence. Finally, comparing Clodpates and Clodpolls, both share the prefix Clodp, but the sixth letter a in Clodpates comes before the letter o in Clodpolls. Thus, the correct dictionary order is 1-5-2-3-4.

Explanation

The series is organized into three sequential blocks where the frequency of the letters e, f, g, and h increases incrementally. The total length of the series is 24 characters, divided into blocks of 4, 8, and 12 letters respectively.

Block 1: Each of the four letters appears once, following the sequence e f g h. Block 2: Each of the four letters appears twice, following the sequence ee ff gg hh. Block 3: Each of the four letters appears three times, following the sequence eee fff ggg hhh.

By placing the letters from option c (h, e, g, e, f, h) into the gaps: The first gap is filled with h to complete Block 1: e f g [h]. The second and third gaps are filled with e and g to complete Block 2: [e] e f f [g] g h h. The remaining gaps are filled with e, f, and h to form the third block: e [e] e f f [f] g g g [h] h.

While the provided string contains a fourth g in the final segment, the systematic increase in the frequency of the letters e and f from one to two to three repetitions confirms the 1-2-3 progression logic. This pattern aligns perfectly with the letters provided in option c.

Explanation

The series follows a pattern where the difference between consecutive terms is equal to the cube of consecutive integers starting from 2.

The first difference is 13 - 5 = 8, which is 2³. The second difference is 40 - 13 = 27, which is 3³. The third difference is 104 - 40 = 64, which is 4³.

Following this logic, the next difference in the sequence must be 5³ = 125. Adding this value to the previous term gives 104 + 125 = 229.

Explanation

Given the ratio of the present ages of Aman and Ankit is 2 : 1 and the sum of their ages is 72, Aman's present age can be calculated as: Aman's present age = ²⁄₂₊₁ × 72 = ⅔ × 72 = 48 years

Aman's age after 6 years is obtained by adding 6 to his present age: 48 + 6 = 54 years

Explanation

There are five positions in the row, which we can number 1 to 5 from left to right. Since T is exactly in the middle, T occupies position 3. The problem states that Q is sitting to the immediate left of T, placing Q at position 2. Furthermore, Q is to the immediate right of P, which means P is at position 1. This establishes the sequence P, Q, T for the first three positions. The remaining girls are R and S, and the remaining positions are 4 and 5. Since S is not at the extreme end, and position 5 is an extreme end, S must be at position 4. Consequently, R must be at position 5. The final arrangement from left to right is P, Q, T, S, R. To find the girl sitting third to the left of R, we count three positions back from R at position 5: S (1st left), T (2nd left), and Q (3rd left).

Explanation

The word TASTE cannot be formed from the letters of ERADICATE because it requires the letter S, which is not present in the source word. Additionally, TASTE requires two instances of the letter T, whereas ERADICATE contains only one T. Since a word cannot be formed if it requires characters not available in the original set or exceeds the frequency of available letters, this word is the correct choice.

Explanation

By comparing the first phrase 'hit ka tom' (tie the shoes) and the second phrase 'ka lo fod' (shoes of leather), the common word is shoes and the common code is ka, which means ka stands for shoes. Next, comparing the second phrase 'ka lo fod' (shoes of leather) and the third phrase 'lo tin lot' (leather and raxin), the common word is leather and the common code is lo, which means lo stands for leather. In the second phrase 'ka lo fod', since ka represents shoes and lo represents leather, the remaining code fod must represent the remaining word of.

Explanation

The mathematical expression is solved by replacing the given operators with their designated meanings: + denotes ÷ (divided by), × denotes - (subtracted from), ÷ denotes × (multiplied by), and - denotes + (added to).

Substituting these into the original expression: 13 + 12 × 9 ÷ 3 - 6

The transformed expression is: 13 ÷ 12 - 9 × 3 + 6

Following the BODMAS rule for the order of operations:

First, perform the division: 13 ÷ 12 = ¹³⁄₁₂

Next, perform the multiplication: 9 × 3 = 27

Now, perform addition and subtraction: ¹³⁄₁₂ - 27 + 6 = ¹³⁄₁₂ - 21

To simplify, find a common denominator: (13 - (21 × 12))/(12) = (13 - 252)/(12) = -²³⁹⁄₁₂

Explanation

The logic followed in the given expressions is the sum of the squares of the individual numbers. For any set of numbers x @ y @ z, the result is obtained by the formula x² + y² + z².

Verification of the given examples: For 6 @ 4 @ 7 = 101: 6² + 4² + 7² = 36 + 16 + 49 = 101. For 2 @ 5 @ 11 = 150: 2² + 5² + 11² = 4 + 25 + 121 = 150.

To find the value of A in A @ 8 @ 9 = 289, we apply the same rule: A² + 8² + 9² = 289 A² + 64 + 81 = 289 A² + 145 = 289 A² = 289 - 145 A² = 144 A = √(144) = 12

Explanation

The logical deduction follows from the combination of the two premises. Statement I (Some banks are private) indicates an intersection between the set of banks and the set of private entities. Statement II (All private are industry) establishes that the entire set of private entities is a subset of the set of industry. Since the overlapping part of the banks and private entities belongs to the private category, and every private entity is part of the industry category, that specific overlapping part of banks must also be part of the industry category. This confirms the conclusion that some banks are industry. Using the standard syllogism rule, the combination of Some A are B and All B are C leads to the definite conclusion that Some A are C.

Explanation

In the given analogy, Mathematics is a field of study that relies on Formulas to express relationships and solve problems. Similarly, Chemistry is the branch of science that focuses on the composition and transformation of matter, which are fundamentally represented and studied through chemical Reactions. Just as formulas are the basic tools for mathematical expression, reactions are the primary means of describing chemical changes and interactions.

Explanation

The relationship between the terms is determined by adding a sequence of increasing integers to the alphabetical positions of the letters in the first word. In the pair YONEX : DUUMG, the transformation follows the pattern +5, +6, +7, +8, and +9. For the first letter, Y (25) + 5 = 30, which corresponds to D (4) in the cyclic alphabet. Then, O (15) + 6 = 21 (U), N (14) + 7 = 21 (U), E (5) + 8 = 13 (M), and X (24) + 9 = 33, which corresponds to G (7).

Applying this same incremental pattern to JASPO, the first letter J (10) + 5 = 15 (O). The second letter A (1) + 6 = 7 (G). The third letter S (19) + 7 = 26 (Z). The fourth letter P (16) + 8 = 24 (X). The fifth letter O (15) + 9 = 24 (X). Following these steps, the resulting string is OGZXX.

Explanation

The relationship follows the pattern where the sum of the digits of the first number is squared to obtain the second number.

For the first pair, the number is 49. The sum of its digits is 4 + 9 = 13. Squaring this sum gives 13² = 169.

Applying the same logic to the second pair with the number 66, the sum of the digits is 6 + 6 = 12. Squaring this sum results in 12² = 144.

Explanation

The fountain pen is a manual writing instrument that operates based on capillary action and physical ink flow without the need for electricity or electronic components. It is distinct because the other items are electronic gadgets or consumer electronics that require an electrical power source or battery to function and process digital information.

Explanation

The underlying logic for the letter pairs is the sum of their alphabetical positions. The rule requires that the sum of the positions of the first two letters must equal the position of the letter following the hyphen. In the case of GI - R, G is the 7th letter and I is the 9th letter. Their sum is 7 + 9 = 16, which corresponds to the letter P. Since the letter provided in this pair is R (the 18th letter), it deviates from the pattern and is the odd letter pair.

Explanation

The sum of the digits of the first number 462 is 4 + 6 + 2 = 12. The square of this sum is 12² = 144. In this group, the second number is 169, which is 13², meaning it does not equal the square of the sum of the digits of the first number.

Explanation

To arrange the words in dictionary order, we compare them letter by letter from left to right. All five words begin with the prefix Ex. Comparing the third letters, Exacerbate (4), Exactly (3), and Exacts (1) all have a, which precedes h in Exhaust (5) and o in Exotic (2). Among the words starting with Exa, we look at the fifth letter because the first four letters Exac are identical. Exacerbate (4) has e at the fifth position, while Exactly (3) and Exacts (1) both have t. Since e comes before t, Exacerbate (4) is the first word in the sequence. Between Exactly (3) and Exacts (1), we compare the sixth letters. The letter l in Exactly (3) precedes the letter s in Exacts (1), placing Exactly (3) second and Exacts (1) third. Next, comparing the third letters of the remaining words, h in Exhaust (5) precedes o in Exotic (2), placing Exhaust (5) fourth and Exotic (2) fifth. The final alphabetical sequence is 4, 3, 1, 5, 2.

Explanation

The series follows a specific pattern for each component of the terms. The first letters follow the sequence F(6), L(12), R(18), which is an increment of +6 in alphabetical position; the next letter is 18 + 6 = 24, which is X. The second letters follow the sequence K(11), Q(17), W(23), which is also an increment of +6; the next letter position is 23 + 6 = 29, and since the alphabet cycles every 26 letters, 29 - 26 = 3, which is C. The numerical part of the terms follows the sequence of cubes of consecutive integers starting from 3: 3³ = 27, 4³ = 64, 5³ = 125. The next number in the sequence is 6³ = 216. Combining these elements yields XC216.

Explanation

The given sequence is a triple-interleaved series where three independent sub-series are merged. The first sub-series consists of terms at positions 1, 4, 7, and 10. These terms are 19, 16, 13, and the unknown term. This progression follows a common difference of -3, calculated as 19 - 3 = 16 and 16 - 3 = 13. Applying the same logic, the 10th term is 13 - 3 = 10.

The other two sub-series follow different patterns. The second sub-series, occupying positions 2, 5, and 8, consists of 11, 15, and 19, which increases by 4 at each step. The third sub-series, occupying positions 3, 6, and 9, consists of 13, 17, and 21, which also increases by 4 at each step. Because the missing value is the 10th term in the overall sequence, it corresponds to the next value in the first sub-series.

Explanation

Let the starting point R be represented as the origin (0, 0) on a coordinate plane. Punit first walks 10 km West, reaching the point (-10, 0). From this position, a right turn directed him North. Walking 12 km North brings him to the coordinates (-10, 12). He then turns right again, which faces him East, and walks 7 km. His final position is calculated by adding 7 units to the x-coordinate: (-10 + 7, 12) = (-3, 12). Because his final position has a negative x-displacement (West) and a positive y-displacement (North) relative to the starting point R, he is located in the North-West direction.

Explanation

Let the present ages of P and Q be 9x and 4x respectively. The difference between their ages is given as 20 years, which establishes the linear equation 9x - 4x = 20. Simplifying this, we find 5x = 20, which leads to x = 4.

The present age of P is 9 × 4 = 36 years, and the present age of Q is 4 × 4 = 16 years. The sum of their present ages is 36 + 16 = 52 years. To find the sum of their ages after 10 years, we must account for the 10-year increase for both individuals. Therefore, the total sum increases by 10 + 10 = 20 years. Adding this to the present sum, we get 52 + 20 = 72 years. Alternatively, their ages after 10 years will be 36 + 10 = 46 years and 16 + 10 = 26 years respectively, and their sum is 46 + 26 = 72 years.

Explanation

The word SEASON cannot be formed because it requires two S letters, whereas the given word REASONABLE contains only one S. Therefore, there are insufficient instances of the letter S to construct the word.

Explanation

The coding logic is based on the sum of the positional values of the letters in the English alphabet (A = 1, B = 2, ..., Z = 26) multiplied by a constant factor of 3.

For the word PUNISHED, the positional values are P=16, U=21, N=14, I=9, S=19, H=8, E=5, and D=4. The sum is 16 + 21 + 14 + 9 + 19 + 8 + 5 + 4 = 96. Multiplying this sum by 3 yields 96 × 3 = 288.

For the word TAILOR, the positional values are T=20, A=1, I=9, L=12, O=15, and R=18. The sum is 20 + 1 + 9 + 12 + 15 + 18 = 75. Multiplying this sum by 3 yields 75 × 3 = 225.

Applying the same rule to the word RELEASED, the positional values are R=18, E=5, L=12, E=5, A=1, S=19, E=5, and D=4. The sum is 18 + 5 + 12 + 5 + 1 + 19 + 5 + 4 = 69. Multiplying this sum by 3 yields 69 × 3 = 207.

Explanation

Inserting the operators ÷, ×, and = into the expression 15₃₄₂₀ results in the mathematical equation 15 ÷ 3 × 4 = 20. Following the BODMAS rule, the division operation is performed first, yielding 15 ÷ 3 = 5. Subsequently, the multiplication operation is performed: 5 × 4 = 20. This establishes the equality 20 = 20, making the expression correct.

Explanation

The pattern established in the given equations is a b = a² - b². In the first example, 19² - 7² = 361 - 49 = 312. In the second example, 23² - 9² = 529 - 81 = 448. Applying this same logic to the target expression results in 31² - 11² = 961 - 121 = 840. Alternatively, using the algebraic identity a² - b² = (a + b)(a - b), the calculation becomes (31 + 11) × (31 - 11) = 42 × 20 = 840$.

Explanation

The logic followed in the given table is that the sum of the first two numbers in each row is raised to the power of 4 to obtain the third number. The pattern can be expressed by the formula (Column 1 + Column 2)⁴ = Column 3.

In the first row, we have (3 + 2)⁴ = 5⁴ = 625. In the second row, we have (5 + 3)⁴ = 8⁴ = 4096. Following this pattern for the third row, the missing number is calculated as (4 + 2)⁴ = 6⁴ = 1296.

Explanation

The statement "All stars twinkle" is a universal affirmative proposition (A-type). According to the rules of syllogism and immediate inference, a universal statement "All A are B" logically implies the particular statement "Some A are B" (subalternation). Since the first statement asserts that every single star possesses the property of twinkling, it necessarily follows that at least some stars twinkle. Therefore, Conclusion II is a direct logical consequence of the first statement. Conclusion I does not follow because the statements only establish that stars and satellites both belong to the larger group of things that twinkle, but they do not provide any information regarding a direct relationship or overlap between the set of stars and the set of satellites.

Explanation

The relationship in the given analogy is between an animal and the specific sound it produces. A dog is known to bark, which is its characteristic vocalization. Following the same pattern, a sparrow produces a high-pitched, short sound known as a chirp. Therefore, chirp is the word that correctly completes the relationship with sparrow.

Explanation

The pattern follows the logic of alphabetical opposite pairs, where the sum of the positional values of the two letters is 27. To find the related term, we determine the opposite of each letter in the given group and then reverse the entire sequence.

For the first pair ELQZ : AJOV: The opposite of E (5) is V (22) as 27 - 5 = 22. The opposite of L (12) is O (15) as 27 - 12 = 15. The opposite of Q (17) is J (10) as 27 - 17 = 10. The opposite of Z (26) is A (1) as 27 - 26 = 1. The set of opposite letters is VOJA. Writing this sequence in reverse order gives AJOV.

Applying the same logic to VXTD: The opposite of V (22) is E (5) as 27 - 22 = 5. The opposite of X (24) is C (3) as 27 - 24 = 3. The opposite of T (20) is G (7) as 27 - 20 = 7. The opposite of D (4) is W (23) as 27 - 4 = 23. The set of opposite letters is ECGW. Writing this sequence in reverse order gives WGCE.

Explanation

The relationship between the numbers in the first pair is defined by a constant multiplier. The second number, 100, is obtained by multiplying the first number, 40, by 2.5, as 40 × 2.5 = 100. To find the missing number in the second pair, we apply the same logic to the number 56. Multiplying 56 by 2.5 results in 140.

This can also be expressed as a ratio. The ratio 40 : 100 simplifies to 2 : 5 when divided by their greatest common divisor, 20. For the second pair 56 : x to maintain the same ratio of 2 : 5, we set up the proportion 2 / 5 = 56 / x. Solving for x gives x = (56 × 5) / 2, which simplifies to 28 × 5 = 140.

Explanation

A book is a physical medium or a surface consisting of pages intended for reading or recording information. It functions as the object that receives markings, which distinguishes it from the functional category of stationery tools used for the manual application of ink, lead, or pigment.

Explanation

Each letter group consists of a pair of opposite letters followed by a third letter. Opposite letters are those whose positional values in the English alphabet sum to 27. In the groups AZF, LOQ, and EVK, the first letter of the group belongs to the first half of the alphabet (positions 1 to 13), while the second letter is its corresponding opposite from the second half (positions 14 to 26). Specifically, A is the 1st letter, L is the 12th letter, and E is the 5th letter.

In contrast, in the group ZAC, the first letter Z is the 26th letter, which belongs to the second half of the alphabet, and the second letter A is its opposite from the first half. Consequently, ZAC is the only group among the choices where the first letter follows the second letter in the standard alphabetical sequence, whereas in all other groups, the first letter precedes the second.

Explanation

The pair 63 – 93 is the odd one out because the product of the digits of the first number is not equal to the product of the digits of the second number. Specifically, for the number 63, the product of the digits is 6 × 3 = 18, whereas for the number 93, the product of the digits is 9 × 3 = 27. This differentiates it from the other pairs, where the product of the digits of the first number is exactly equal to the product of the digits of the second number.

Explanation

Dictionary order is determined by comparing words letter by letter from left to right. All five words begin with the prefix Cad. Comparing the fourth letter of each word, Cadartrally has a, Caddisflies and Caddisworms have d, Cadethsips has e, and Caducities has u. According to the alphabet, a comes first, followed by d, then e, and finally u. This establishes that Cadartrally (1) is first, Cadethsips (5) is fourth, and Caducities (3) is fifth in the sequence.

To differentiate between Caddisflies (2) and Caddisworms (4), compare their subsequent letters. Both words are identical through the first six letters C-a-d-d-i-s. The seventh letter in Caddisflies is f, whereas the seventh letter in Caddisworms is w. Since f appears before w in the alphabet, Caddisflies (2) precedes Caddisworms (4). Arranging all the words based on these comparisons results in the sequence 1, 2, 4, 5, 3.