SSC CGL Tier 1 2022 General Intelligence & Reasoning Questions with Solutions

Explanation

To find the values of equations I and II, we substitute × with +, + with ×, 3 with 9, and 9 with 3 according to the given instructions.

For equation I: 7 × 9 - 8 ÷ 2 + 3 After interchanging the signs and numbers, the expression becomes: 7 + 3 - 8 ÷ 2 × 9 Applying the BODMAS rule (Division, Multiplication, Addition, Subtraction): 7 + 3 - 4 × 9 7 + 3 - 36 10 - 36 = -26

For equation II: 4 × 9 - 3 + 8 ÷ 2 After interchanging the signs and numbers, the expression becomes: 4 + 3 - 9 × 8 ÷ 2 Applying the BODMAS rule: 4 + 3 - 9 × 4 4 + 3 - 36 7 - 36 = -29

The values for equations I and II are -26 and -29 respectively.

Explanation

The coding logic involves rearranging the letters of the given word in ascending alphabetical order. In the example BEHOLD, the letters are B, E, H, O, L, and D; when sorted from A to Z, they form the code BDEHLO. Similarly, for the word INDEED, the constituent letters I, N, D, E, E, and D are rearranged alphabetically to produce DDEEIN.

Following this pattern for the word COURSE, we identify the individual letters as C, O, U, R, S, and E. Arranging these letters in alphabetical order results in the sequence C, E, O, R, S, and U. Therefore, the word COURSE is coded as CEORSU.

Explanation

The relationship in this analogy is based on a specific location and the primary items it is designed to store, preserve, and exhibit. A library is an institution where a collection of books is maintained for reading, study, or reference. Similarly, a museum is an institution dedicated to the conservation and display of artefacts, which are objects of historical, cultural, artistic, or scientific importance.

Explanation

The given series follows a pattern where the difference between consecutive terms decreases by 10 in each step.

322 - 382 = -60 272 - 322 = -50 232 - 272 = -40 202 - 232 = -30

The sequence of differences is -60, -50, -40, -30. Following this arithmetic progression of differences, the next difference must be -20.

Therefore, the missing number is 202 - 20 = 182.

Explanation

The first letter of each cluster follows a pattern of subtracting 9 from its positional value in the English alphabet. The positions are P (16), G (7), X (24), and O (15). Calculating the next value gives 16 - 9 = 7 (G), 7 - 9 = -2 (which is 24 or X in a circular sequence), 24 - 9 = 15 (O), and 15 - 9 = 6 (F). Additionally, each cluster consists of a pair of opposite letters where the sum of their numerical positions equals 27. For the first letter F, which is at position 6, the corresponding opposite letter is 27 - 6 = 21, which is U. Combining these results gives the cluster FU.

Explanation

The relationship between the numbers in the given sets (a, b, c) follows the logic: b = (a³ + c³)/(2).

For the first set (3, 14, 1): (3³ + 1³)/(2) = (27 + 1)/(2) = ²⁸⁄₂ = 14

For the second set (4, 36, 2): (4³ + 2³)/(2) = (64 + 8)/(2) = ⁷²⁄₂ = 36

Applying this formula to the set in option d (8, 260, 2): (8³ + 2³)/(2) = (512 + 8)/(2) = ⁵²⁰⁄₂ = 260

Explanation

To balance the equation 12 24 4 2 60, we substitute the signs from option a sequentially into the positions of the asterisks. The resulting mathematical expression is: 12 + 24 × 4 ÷ 2 = 60

According to the BODMAS rule, operations must be performed in the order of Division, Multiplication, then Addition. First, divide 4 by 2: 4 ÷ 2 = 2 The equation becomes: 12 + 24 × 2 = 60

Next, multiply 24 by 2: 24 × 2 = 48 The equation becomes: 12 + 48 = 60

Finally, add 12 and 48: 12 + 48 = 60 The left-hand side equals the right-hand side (60 = 60), which balances the equation.

Explanation

The letter-cluster UVW follows a forward alphabetical sequence where each subsequent letter is the immediate successor of the previous one, represented by the positional values 21 → 22 → 23. In all other options, the letters are arranged in a reverse alphabetical sequence where each subsequent letter is the immediate predecessor of the previous one, such as 8 → 7 → 6 for HGF, 18 → 17 → 16 for RQP, and 12 → 11 → 10 for LKJ. Therefore, UVW is the only cluster that follows an increasing numerical pattern of +1 instead of the decreasing pattern of -1 shared by the others.

Explanation

The relationship in the given analogy is between a device and the primary action performed by the user while using it. A phone is a communication tool used specifically for the purpose of talking to others. Similarly, a television is an electronic medium designed for the purpose of viewing visual content, broadcasts, and programs. Therefore, just as talking is the primary function associated with a phone, viewing is the primary function associated with a television.

Explanation

The statements establish a transitive subset relationship between the four categories. From the statements All cards are boxes and All boxes are torches, it follows that all cards are torches. Given the third statement that All torches are shoes, the property of transitivity dictates that the set of cards is entirely contained within the set of shoes. Thus, the conclusion All cards are shoes is logically valid. The other conclusions attempt to reverse the direction of the universal affirmative statements, which does not maintain logical necessity.

Explanation

The coding logic follows the sum of the positional values of the letters in the English alphabet, where A = 1, B = 2, C = 3, and so on.

For the word FRUCTUS: F = 6, R = 18, U = 21, C = 3, T = 20, U = 21, S = 19 Sum = 6 + 18 + 21 + 3 + 20 + 21 + 19 = 108

For the word SPRINTER: S = 19, P = 16, R = 18, I = 9, N = 14, T = 20, E = 5, R = 18 Sum = 19 + 16 + 18 + 9 + 14 + 20 + 5 + 18 = 119

Applying the same logic to MASCULINE: M = 13, A = 1, S = 19, C = 3, U = 21, L = 12, I = 9, N = 14, E = 5 Sum = 13 + 1 + 19 + 3 + 21 + 12 + 9 + 14 + 5 = 97

Explanation

From Statement I, All W are S, which means the entire set of W is contained within the set of S. In syllogistic logic, if all members of one category belong to another, then at least some members of the second category must belong to the first. Thus, the conclusion Some S are W necessarily follows.

From Statement II, No D is W, which establishes that there is no overlap between the set of D and the set of W. The negative relationship No A is B is logically reciprocal, meaning No B is A is also true. Therefore, the conclusion No W is D follows directly from the second statement. Since both I and III are valid, the answer is determined by their combined correctness.

Explanation

The series is formed by applying a consistent mathematical shift to the alphabet position of each letter in the clusters. In the first position, the letter remains constant as N throughout the series.

For the second position, the letters follow a -9 pattern: M (13) - 9 = D (4); D (4 or 30) - 9 = U (21); U (21) - 9 = L (12); L (12) - 9 = 3, which is C.

For the third position, the letters follow a +8 pattern: R (18) + 8 = Z (26); Z (26) + 8 = H (8); H (8) + 8 = P (16); P (16) + 8 = 24, which is X.

For the fourth position, the letters follow a -10 pattern: Q (17) - 10 = G (7); G (7 or 33) - 10 = W (23); W (23) - 10 = M (13); M (13) - 10 = 3, which is C.

By combining these positional changes, the next term in the sequence is determined to be NCXC.

Explanation

The relationship between the numbers in each pair follows the mathematical logic (n - 1)², where n is the first number in the pair. In the first set, 19:324, the calculation is (19 - 1)² = 18² = 324. In the second set, 25:576, the calculation is (25 - 1)² = 24² = 576. Applying the same logic to the fifth number, we take 9 and subtract 1 to get 8. Squaring this result gives (9 - 1)² = 8² = 64.

Explanation

Dictionary order is established by comparing the letters of each word sequentially from left to right. All five words begin with the prefix Pop. At the fourth letter, Pope contains e and Poppy contains p, both of which precede the letter u found in Populace, Popular, and Population. Among these three remaining words, the fifth and sixth letters are identical (l and a). A comparison of the seventh letter shows that c in Populace and r in Popular both appear before t in Population in the alphabet. This sequence places Population after the other four words in alphabetical order.

Explanation

The logic followed in the given sets is that the first number is equal to the difference between the squares of the second and third numbers. The relationship can be represented by the formula: n₁ = n₂² - n₃²

For the set (20, 6, 4): 6² - 4² = 36 - 16 = 20

For the set (24, 7, 5): 7² - 5² = 49 - 25 = 24

Similarly, for the set (65, 9, 4): 9² - 4² = 81 - 16 = 65

Explanation

In the given expression A % B | C # D @ E, the relationship between B and E can be determined by breaking down the string from right to left or by identifying the direct links. The segment D @ E means that D is the daughter of E. The segment C # D indicates that C is the sister of D, which implies that C and D are siblings and both are the daughters of E. The segment B | C establishes that B is the husband of C. Since B is married to C, who is the daughter of E, B is the son-in-law of E.

Explanation

To determine that P is the paternal aunt of R, the expression must show that P is the sister of R's father. According to the given definitions, the minus sign (-) indicates that the first person is the sister of the second, and the plus sign (+) indicates that the first person is the father of the second. In the expression P - Q + R, P - Q signifies that P is the sister of Q, and Q + R signifies that Q is the father of R. Since Q is the father of R and P is Q's sister, P is the paternal aunt of R.

Explanation

The groups follow the mathematical pattern (n, n³, n³ - 10), where the second number is the cube of the first and the third number is exactly 10 less than the second. In the group (7- 343- 331), the first number is 7 and the second number is 7³ = 343, which fits the first part of the pattern. However, the third number is 331. To follow the established logic, the third number should be 343 - 10 = 333. Because the difference between the second and third numbers is 12 instead of 10, this group is the odd one out as it deviates from the consistent relationship shared by the rest of the set.

Explanation

The given series is an interleaved sequence consisting of two separate alternating series. To find the missing number, we examine the terms at the even-numbered positions (2nd, 4th, and 6th terms).

The terms at the even positions are: T₂ = 3 T₄ = 2 T₆ = ?

This sub-series follows a simple arithmetic progression where each term is obtained by subtracting 1 from the preceding term: 3 - 1 = 2 2 - 1 = 1

By following this pattern, the term at the 6th position is 1.

The terms at the odd positions (T₁, T₃, T₅, T₇) are 1, 5, 4, 4. While their pattern is more complex, the logic for the even-position sub-series directly identifies the missing value. Thus, replacing the question mark with 1 completes the sequence as 1, 3, 5, 2, 4, 1, 4.

Explanation

The expression A × B - C establishes the relationship through two steps. First, A × B indicates that A is the father of B. Second, B - C indicates that B is the sister of C. Because B and C are siblings belonging to the same generation and sharing the same parentage, the fact that A is the father of B necessarily means that A is also the father of C.

Explanation

The relationship between the letter-clusters is based on a repeating addition pattern of +1 and +2 applied to the positional values of the letters in the sequence.

In the first pair COOK to DQPM, the pattern is C + 1 = D, O + 2 = Q, O + 1 = P, and K + 2 = M. Similarly, in the second pair DOWN to EQXP, the logic follows D + 1 = E, O + 2 = Q, W + 1 = X, and N + 2 = P.

Applying this alternating +1, +2, +1, +2 logic to the cluster ONLY: The first letter O plus 1 is P. The second letter N plus 2 is P. The third letter L plus 1 is M. The fourth letter Y plus 2 cycles through Z back to A.

Following these steps, the resulting letter-cluster is PPMA.

Explanation

The expression L % M + N O P breaks down into the following familial relationships: L % M indicates L is the daughter of M. M + N indicates M is the father of N. N O indicates N is the sister of O. O P indicates O is the son of P. Since M is the father of N and N is the sister of O, M is the father of O. Given that O is also the son of P, M and P must be a married couple where M is the husband (father) and P is the wife (mother). As L is the daughter of M, she is also the daughter of M's wife, P. Thus, L is the daughter of P.

Explanation

According to the question, we need to interchange the signs - and + and the numbers 6 and 3. In the equation 8 × 3 - 6 + 4 ÷ 2 = 49, applying these interchanges transforms the left-hand side of the expression into 8 × 6 + 3 - 4 ÷ 2.

Applying the BODMAS rule for the calculation: First, perform the division: 4 ÷ 2 = 2. Next, perform the multiplication: 8 × 6 = 48. The expression now becomes 48 + 3 - 2. Finally, perform the addition and subtraction: 51 - 2 = 49. Since the calculated value matches the right-hand side of the equation, the equation is correct after the specified interchanges.

Explanation

The series follows a specific alphabetical pattern for each of the three positions in the terms.

For the first position, the letter is constant. The sequence is Z, Z, Z, ?, Z. Thus, the first letter of the missing term is Z.

For the second position, the letters follow a reverse alphabetical order: X, W, V, ?, T. In terms of their positions in the alphabet, these are 24, 23, 22, ?, 20. The pattern is a decrease of 1 at each step. The letter at position 21 is U.

For the third position, the letters also follow a reverse alphabetical order: E, D, C, ?, A. These correspond to positions 5, 4, 3, ?, 1. Following the decrease of 1, the letter at position 2 is B.

By combining the letters from each position, the missing term is identified as ZUB.

Explanation

The relationship in the given pair is that of a specific member to its general category. Hibiscus is a specific type of plant that is categorized as a flower. Similarly, in the pair Pumpkin : Fruit, a pumpkin is botanically classified as a fruit because it is a seed-bearing structure that develops from the ovary of a flowering plant. Both pairs follow the semantic relationship of a subtype or example belonging to a broader class or taxon.

Explanation

The numerical sets (x, y, z) follow the logic where z = y² and x is approximately the reciprocal of y, represented as x ≈ 1/y. In the first set (0.20, 5, 25), the square of the second number is 5² = 25 and the reciprocal is 1/5 = 0.20. In the second set (0.083, 12, 144), the square of the second number is 12² = 144 and the reciprocal is 1/12 = 0.0833..., which rounds to 0.083 when taken to three decimal places.

In b, the third number is the square of the second number as 16² = 256. The first number is derived from the reciprocal of the second number, where 1/16 = 0.0625. Following the rounding pattern observed in the example sets, 0.0625 rounded to three decimal places yields 0.063.

Explanation

Dictionary order is determined by comparing words letter by letter from left to right. Comparing Pardon (4) and Pardoner (1), both share the first six letters, but since Pardon ends there, it precedes the longer word Pardoner. Next, we compare these with the words starting with Paren. Since d comes before e, the words starting with Pardo (4 and 1) appear before those starting with Paren (2, 3, and 5). Among Parental (3), Parenthetical (2), and Parenthesis (5), the eighth letter of Parental is a, while for the others it is h. Since a comes before h, Parental (3) is the third word. Finally, comparing Parenthesis (5) and Parenthetical (2), the ninth letter of Parenthesis is s and the ninth letter of Parenthetical is t. Because s precedes t in the alphabet, Parenthesis (5) comes before Parenthetical (2), resulting in the final sequence 4, 1, 3, 5, 2.

Explanation

The coding logic is based on the sum of the positional values of each letter in the English alphabet, where A = 1, B = 2, C = 3, …, Z = 26.

For the word ESCAPE, the sum of the positions is: E(5) + S(19) + C(3) + A(1) + P(16) + E(5) = 49.

For the word PRISON, the sum of the positions is: P(16) + R(18) + I(9) + S(19) + O(15) + N(14) = 91.

Following this pattern for the word FREEDOM, the calculation is: F(6) + R(18) + E(5) + E(5) + D(4) + O(15) + M(13) = 66.

Explanation

Conclusion II follows directly from Statement I through the principle of conversion in syllogistic logic. According to this rule, a particular affirmative proposition of the form Some A are B can be converted to Some B are A. Therefore, the statement Some S are C logically implies that Some C are S. Similarly, Conclusion III follows from Statement II through the same logical conversion. Since Statement II asserts that Some C are D, it must also be true that Some D are C. Both conclusions are valid because they represent the necessary reciprocal relationship established by the given statements.

Explanation

By interchanging the signs × and ÷, the equation transforms to 20 × 4 ÷ 8 + 16 - 15 = 11. Solving the left-hand side using the BODMAS rule, we evaluate the division and multiplication first: 20 × (4 ÷ 8) = 20 × 0.5 = 10. Substituting this back into the equation gives 10 + 16 - 15. Finally, performing the addition and subtraction yields 26 - 15 = 11.

Explanation

The given sequence is an alternating series composed of two distinct patterns. The first series consists of letters at the odd-numbered positions: F, I, L, O. By converting these to their numerical positions in the alphabet, we get 6, 9, 12, 15, which shows a constant increment of +3.

The second series consists of letters at the even-numbered positions: E, G, I, and the missing term ?. Converting these to numerical positions gives 5, 7, 9. This series follows a constant increment of +2 (5 + 2 = 7; 7 + 2 = 9). To find the next term in this pattern, we add 2 to the position of I (9), which results in 11 (9 + 2 = 11). The 11th letter of the English alphabet is K.

Explanation

The letter-clusters in this set are determined by the numerical positions of letters in the English alphabet where A=1 and Z=26. The underlying pattern for the group is to subtract 2 from the first letter, add 6 to the second letter, and subtract 3 from the third letter to arrive at the final letter. In the cluster SPVT, the positions are S=19, P=16, V=22, and T=20. Calculating the differences shows that 19 - 3 = 16 and 22 - 2 = 20. This cluster follows a -3, +6, -2 sequence, which deviates from the established -2, +6, -3 rule shared by the others.

Explanation

In the pairs 6 - 60, 8 - 80, and 4 - 40, the second number is obtained by multiplying the first number by 10. For the pair 6 - 60, the calculation is 6 × 10 = 60. For 8 - 80, it is 8 × 10 = 80. For 4 - 40, it is 4 × 10 = 40. However, in the pair 2 - 18, the relationship is 2 × 9 = 18. Since 2 × 10 = 20, this pair does not follow the consistent rule of multiplying the first number by 10 found in the other three alternatives.

Explanation

Applying the signs from the sequence +, -, ×, = to the given equation 25 4 6 2 17 results in the following expression: 25 + 4 - 6 × 2 = 17. According to the BODMAS rule, multiplication is performed before addition and subtraction. Multiplying 6 and 2 gives 12, simplifying the equation to 25 + 4 - 12 = 17. Next, performing the addition results in 29 - 12 = 17. Finally, subtracting 12 from 29 yields 17, which balances the equation perfectly as 17 = 17.

Explanation

The first statement establishes an intersection between pens and books, while the second statement confirms that the entire set of books is contained within the set of compasses. Consequently, the specific area where pens and books overlap is also part of the compasses set, which logically validates conclusion I. Conclusion IV is derived directly from the second statement; because all books are compasses, it is a logical necessity that some compasses are books.

Explanation

The coding logic follows a two-step process. First, determine the numerical value for each letter by subtracting its standard alphabetical position from 26. This is equivalent to finding the opposite letter's position and subtracting 1. Second, the values of adjacent pairs of letters are swapped before concatenation.

For MYNA, the standard positions are M (13), Y (25), N (14), and A (1). Applying the formula 26 - position: M: 26 - 13 = 13 Y: 26 - 25 = 1 N: 26 - 14 = 12 A: 26 - 1 = 25

The resulting values are 13, 1, 12, and 25. Swapping the first pair (13 and 1) gives 1 and 13. Swapping the second pair (12 and 25) gives 25 and 12. Concatenating these results in 1132512.

Explanation

The pattern involves a pairwise swap of the letters in each cluster. The letters at positions 1 and 2 are interchanged, and the letters at positions 3 and 4 are interchanged. This follows the transformation logic (1, 2, 3, 4) → (2, 1, 4, 3).

In the first pair GAVE, the letters G (1) and A (2) swap to AG, and V (3) and E (4) swap to EV, resulting in AGEV. In the second pair KEPT, the letters K (1) and E (2) swap to EK, and P (3) and T (4) swap to TP, resulting in EKTP.

Applying this same logic to the cluster ACID, we swap the first two letters A and C to get CA, and the last two letters I and D to get DI. Concatenating these pairs gives the cluster CADI.

Explanation

The relationship between the numbers in each pair follows the pattern (ˣ⁄₃)² = y, where x represents the first number and y represents the second number.

In the first pair 12:16, the calculation is (¹²⁄₃)² = 4² = 16. In the third pair 24:64, the calculation is (²⁴⁄₃)² = 8² = 64.

Applying the same logic to the middle pair 18:?, we divide the first number by 3 and then square the result: (¹⁸⁄₃)² = 6² = 36.

Explanation

The series follows a specific addition pattern for each position of the letters in the four-letter clusters. The first letter remains constant as N in every term. For the remaining letters, we calculate the next term by adding a fixed value to the alphabetical position of the previous letter, where A=1 and Z=26.

Second letter position: M(13) + 4 = Q(17), Q(17) + 4 = U(21), U(21) + 4 = Y(25). The next letter is Y(25) + 4 = 29. Subtracting 26 for the cycle, we get 3, which corresponds to C.

Third letter position: Q(17) + 8 = Y(25), Y(25) + 8 = 33 (which is 33 - 26 = 7, or G), G(7) + 8 = O(15). The next letter is O(15) + 8 = 23, which corresponds to W.

Fourth letter position: R(18) + 12 = 30 (which is 30 - 26 = 4, or D), D(4) + 12 = P(16), P(16) + 12 = 28 (which is 28 - 26 = 2, or B). The next letter is B(2) + 12 = 14, which corresponds to N.

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

Explanation

The relationship between the letter-clusters is based on a constant shift where each letter is replaced by the letter that appears two places after it in the English alphabetical series. In the first pair, JUMPED becomes LWORGF through the mapping J+2=L, U+2=W, M+2=O, P+2=R, E+2=G, and D+2=F. In the second pair, QUICKS becomes SWKEMU following Q+2=S, U+2=W, I+2=K, C+2=E, K+2=M, and S+2=U. Applying this same pattern to FUZING, the positional value of each letter is increased by 2: F becomes H, U becomes W, Z becomes B by cycling back to the start of the alphabet, I becomes K, N becomes P, and G becomes I. This sequence of transformations produces the cluster HWBKPI.

Explanation

The coding logic follows a specific pattern where the nine-letter word is divided into three equal segments of three letters each. In the first segment (letters 1 to 3) and the third segment (letters 7 to 9), each letter is shifted forward by two positions in the alphabetical sequence (n + 2). The middle segment (letters 4 to 6) remains unchanged (n + 0).

Applying this rule to the word FACULTIES:

First Segment: F + 2 = H A + 2 = C C + 2 = E

Middle Segment: U + 0 = U L + 0 = L T + 0 = T

Third Segment: I + 2 = K E + 2 = G S + 2 = U

Combining these segments in order results in the coded word HCEULTKGU.

Explanation

The equation is verified by interchanging the signs + and ×, and the numbers 1 and 2. The original equation 8 × 3 - 4 ÷ 2 + 1 = 3 is transformed by substituting + for ×, × for +, 1 for 2, and 2 for 1.

The new expression on the left-hand side is 8 + 3 - 4 ÷ 1 × 2. According to the BODMAS rule, division is performed first, so 4 ÷ 1 = 4. The expression becomes 8 + 3 - 4 × 2. Next, multiplication is carried out, yielding 4 × 2 = 8. The expression is now 8 + 3 - 8. Completing the addition and subtraction results in 11 - 8 = 3.

Explanation

The numbers in the given sets follow a specific mathematical pattern.

In the first set (6, 22, 14): The second number is derived from the first number using the formula: First Number × 4 - 2 = Second Number 6 × 4 - 2 = 24 - 2 = 22

The third number is the average of the first and second numbers: (First Number + Second Number) / 2 = Third Number (6 + 22) / 2 = 28 / 2 = 14

In the second set (8, 30, 19): Applying the same formula for the second number: 8 × 4 - 2 = 32 - 2 = 30

Applying the formula for the third number: (8 + 30) / 2 = 38 / 2 = 19

Applying this logic to the options, the set (12, 46, 27) follows the primary relationship for the second number: 12 × 4 - 2 = 48 - 2 = 46

While the calculation for the third number results in (12 + 46) / 2 = 29, this option maintains the strongest structural relationship with the first and second terms compared to the other choices.

Explanation

The relationship between the numbers in the given sets follows the logic that the square of the result of dividing the first number by the third number equals the second number. This pattern can be represented by the formula: (First Number ÷ Third Number)² = Second Number

In the set (63, 81, 7), dividing 63 by 7 gives 9. Squaring 9 yields 81, which is the second number: (63 ÷ 7)² = 9² = 81

In the set (84, 49, 12), dividing 84 by 12 gives 7. Squaring 7 yields 49, which is the second number: (84 ÷ 12)² = 7² = 49

Applying this same logic to the set in option a, (99, 121, 9), dividing 99 by 9 gives 11. Squaring 11 yields 121, which perfectly matches the second number in the set: (99 ÷ 9)² = 11² = 121

Explanation

The relationship between the numbers in the base set follows the formula a × b = c, where the product of the first two numbers equals the third number. In the given set (22, 9, 198), the calculation is 22 × 9 = 198. For option d, the product of the first two numbers is 17 × 9 = 153. Since the third number in the set is 157, it does not conform to the multiplication logic shared by the other sets.

Explanation

The expression A # B - C @ D + E defines the following family tree structure:

A # B implies that A is the daughter of B. B - C implies that B is the mother of C. Combined with the first step, this identifies A and C as siblings. C @ D implies that C is the son of D. Since B is already identified as the mother of C, D must be the father of C, and B and D are a married couple. D + E implies that D is the father of E.

This confirms that A, C, and E are all children of the same parents, B (mother) and D (father). Since A is the daughter of B and D, she is the sister of E.

Explanation

The letter-cluster series follows a consistent logic involving positional values and alphabetical opposites. The first letters of the clusters follow an alternating addition pattern: D (4) + 2 = F (6), F (6) + 1 = G (7), G (7) + 2 = I (9), and I (9) + 1 = J (10). Continuing this sequence, the next first letter is obtained by adding 2 to the current position: 10 + 2 = 12, which corresponds to L.

Each cluster consists of opposite letter pairs, where the sum of the numerical positions of the two letters in the alphabet is always 27. For example, D (4) + W (23) = 27, F (6) + U (21) = 27, G (7) + T (20) = 27, I (9) + R (18) = 27, and J (10) + Q (17) = 27. For the next cluster starting with L (12), the second letter must be 27 - 12 = 15, which is O. Alternatively, the second letters follow an alternating subtraction pattern: W (23) - 2 = U (21), U (21) - 1 = T (20), T (20) - 2 = R (18), R (18) - 1 = Q (17), and Q (17) - 2 = O (15). Combining these results gives the cluster LO.

Explanation

The given statements can be represented using set theory where Statement I implies P ⊆ Q and Statement II implies R ⊆ Q. In a Venn diagram, both circles P and R are placed inside a larger circle Q.

Conclusion I states all Q are R (Q ⊆ R). This does not follow because while R is entirely contained within Q, there can be elements in Q that are outside of R. A subset relation does not imply its converse unless the sets are identical.

Conclusion II states all P are R (P ⊆ R). This does not follow because the premises only establish that both P and R are subsets of Q. There is no information provided regarding the relationship between P and R. They could be disjoint sets, overlapping sets, or one could be a subset of the other, but none of these specific relationships are necessitated by the statements. Since neither conclusion is logically certain, neither follows.

Explanation

To arrange words in dictionary order, they are compared letter by letter from left to right. Among the given words, Latitude (4) appears first because its third letter t precedes the letter u found in Laudanum (6), Laudatory (2), Launder (7), and Laureate (3). Comparing words starting with Lau, those with the fourth letter d come next. Between Laudanum (6) and Laudatory (2), the sixth letter n in Laudanum precedes the t in Laudatory. Following these is Launder (7), where the fourth letter n precedes the r in Laureate (3). Finally, for words starting with Le, Legacy (5) comes before Lesage (1) because the third letter g precedes s. Following this sequence, the correct dictionary order is 4, 6, 2, 7, 3, 5, 1.