SSC CGL Tier 1 2023 General Intelligence & Reasoning Questions with Solutions

Explanation

The coding logic involves dividing the ten-letter word into two equal segments of five letters each. The first five letters follow an alternating pattern of adding and subtracting 1, represented as +1, -1, +1, -1, +1. The last five letters follow a similar alternating pattern but with the value 2, represented as +2, -2, +2, -2, +2.

Applying this logic to the word HELICOPTER:

First half: H + 1 = I E - 1 = D L + 1 = M I - 1 = H C + 1 = D

Second half: O + 2 = Q P - 2 = N T + 2 = V E - 2 = C R + 2 = T

Combining both segments results in the coded string IDMHDQNVCT.

Explanation

In the letter-clusters DGJM, NQTW, and TWZC, the numerical position of each letter in the English alphabet increases by a constant difference of 3. For DGJM, the positions are D(4), G(7), J(10), and M(13). For NQTW, the positions are N(14), Q(17), T(20), and W(23). For TWZC, the positions are T(20), W(23), Z(26), and C(3), where the sequence cycles back to the beginning of the alphabet. In contrast, the cluster HIJK consists of letters in consecutive alphabetical order with positions H(8), I(9), J(10), and K(11), representing a constant difference of only 1. Therefore, HIJK does not follow the +3 pattern shared by the others.

Explanation

Conclusion II follows because the statement All jams are desserts implies that the entire set of jams is contained within the set of desserts. In categorical syllogisms, if a class is entirely contained within another, there is a necessary overlap between them, meaning some desserts are jams. Conclusion III follows through the transitive property of the sets described in the statements. Since some fruits are jams and all jams are desserts, those specific fruits that are categorized as jams must also fall under the category of desserts. Thus, the intersection between fruits and desserts is guaranteed to be non-empty.

Explanation

To determine the dictionary order, we compare the letters of each word from left to right. All words begin with the prefix Ci. Comparing the third letter, n in Cinnamon (4) comes before r in Circulate (1), Circuit (2), and Circular (5), and before t in Citrus (3) and Citizen (6). This places Cinnamon (4) as the first word. Among the words starting with the prefix Cir, we examine the sixth letter because the first five letters Circu are common. The letter i in Circuit (2) precedes l in Circulate (1) and Circular (5), so Circuit (2) is second. Between Circular (5) and Circulate (1), both share the prefix Circula. Comparing the eighth letter, r in Circular (5) comes before t in Circulate (1), positioning Circular (5) third and Circulate (1) fourth. Finally, for the words starting with the prefix Cit, we compare the fourth letter. In Citizen (6), the fourth letter is i, while in Citrus (3), it is r. Since i comes before r alphabetically, Citizen (6) is fifth and Citrus (3) is sixth.

Explanation

The mathematical relationship followed by the number pairs (x, y) is y = x(x - 1)². Applying this formula to the given options:

For the pair (7, 252): 7 × (7 - 1)² = 7 × 36 = 252. For the pair (8, 392): 8 × (8 - 1)² = 8 × 49 = 392. For the pair (5, 80): 5 × (5 - 1)² = 5 × 16 = 80.

The pair (6, 216) is the odd one out because it does not follow this operation. While the other pairs use the square of the preceding integer as a multiplier, the second number in this pair is the cube of the first number (6³ = 216). Following the established pattern, the result for the first number 6 should have been 6 × 5² = 150.

Explanation

The coding logic used in this language is a simple Caesar cipher where each letter of the word is shifted forward by one position in the alphabetical sequence (+1 logic).

For the word PENDANT, the transformations are P+1=Q, E+1=F, N+1=O, D+1=E, A+1=B, N+1=O, and T+1=U, resulting in QFOEBOU. Similarly, for LAWFUL, the transformations are L+1=M, A+1=B, W+1=X, F+1=G, U+1=V, and L+1=M, resulting in MBXGVM.

Applying the same +1 shift to the word IMPOSE: I + 1 = J M + 1 = N P + 1 = Q O + 1 = P S + 1 = T E + 1 = F

This sequence of letters forms the code JNQPTF.

Explanation

Mishka and her brother share the same maternal grandmother, who is the mother of their mother. The maternal grandmother's only child is the individual from whom Mishka and her brother are descended in the maternal line. Since there are no other children, this only child must be Mishka's mother.

Explanation

In the given sets (a, b, c), the relationship between the numbers follows the pattern b = a² + 1 and c = 2(a + b).

Applying this logic to the first set (3, 10, 26): 10 = 3² + 1 26 = 2(3 + 10) = 2 × 13

Applying this logic to the second set (4, 17, 42): 17 = 4² + 1 42 = 2(4 + 17) = 2 × 21

In the set (6, 37, 86): 37 = 6² + 1 86 = 2(6 + 37) = 2 × 43

Explanation

The expression Z - B § D § G defines the following genealogical links based on the provided symbols: Z - B means Z is the daughter of B. B § D means B is the father of D. D § G means D is the father of G.

From the first two relations, since B is the father of D and Z is the daughter of B, Z and D are siblings, making Z the sister of D. The third relation states that D is the father of G. Consequently, Z is the sister of G's father. This identifies Z as the father's sister of G.

Explanation

The relationship between the numbers in these pairs follows the formula y = 6x, where x is the first value and y is the second value. In the pair (84,672), the second number is calculated as 84 × 8 = 672. This pair utilizes a multiplier of 8, whereas the established pattern for the set involves a constant multiplier of 6.

Explanation

The letter-cluster BXE is the odd one out because the first and second letters do not form an alphabetical opposite pair. In the consistent pattern followed by the other clusters, the sum of the numerical positions of the first and second letters is 27 (reverse pairs), and the third letter is 3 positions ahead of the first letter (L1 + 3 = L3). For B (2) and X (24), the sum is 2 + 24 = 26, failing the opposite pair requirement where the second letter should be Y (25). Although the third letter E (5) correctly follows the 2 + 3 = 5 logic, the deviation in the first two letters distinguishes BXE from the group.

Explanation

The logic followed in the given numerical pairs is based on the ratio 6:5 or multiplying the first number by 1.2 to obtain the second number. In the first pair, 175 × ⁶⁄₅ = 35 × 6 = 210. In the second pair, 310 × ⁶⁄₅ = 62 × 6 = 372. Applying the same mathematical operation to the fifth number, we get 295 × ⁶⁄₅ = 59 × 6 = 354.

Explanation

The logic follows a constant addition of +4 to the positional value of each letter in the English alphabet. In the first pair CNY:GRC, the transformations are C(3) + 4 = G(7), N(14) + 4 = R(18), and Y(25) + 4 = C(3) (by cycling back after Z). In the second pair FRL:JVP, the letters follow the same pattern: F(6) + 4 = J(10), R(18) + 4 = V(22), and L(12) + 4 = P(16).

Applying this rule to the third pair ITK:?, we calculate the values for each letter: I(9) + 4 = 13, which corresponds to M. T(20) + 4 = 24, which corresponds to X. K(11) + 4 = 15, which corresponds to O.

The resulting letter-cluster is MXO.

Explanation

The pattern followed in the letter-clusters is that each letter in the first cluster is shifted forward by 7 positions in the English alphabetical order to obtain the corresponding letter in the second cluster. For the first pair, QIN to XPU, the logic is Q (17) + 7 = X (24), I (9) + 7 = P (16), and N (14) + 7 = U (21).

Following the same logic for the third pair, DSY to KZF, we have D (4) + 7 = K (11), S (19) + 7 = Z (26), and Y (25) + 7 = 32. Since there are only 26 letters, 32 - 26 = 6, which corresponds to F.

Applying this +7 constant addition to the fifth letter-cluster ALM: A (1) + 7 = 8, which is H L (12) + 7 = 19, which is S M (13) + 7 = 20, which is T

Explanation

The letter series follows a repeating pattern of the five-letter sequence CEXUP. By dividing the series into groups of five, we can identify the missing letters:

Group 1: C _ _ U P Group 2: _ E X _ P Group 3: C _ X U _ Group 4: _ E _ U P

Comparing each group to the base pattern CEXUP: In the first group (C _ _ U P), the missing letters are E and X (C E X U P). In the second group (_ E X _ P), the missing letters are C and U (C E X U P). However, looking at the provided string C_UP_EX_PC_XU_E_UP and the letters in option (b) EXCUEPCX, let us re-examine the placement:

The complete sequence is formed by repeating CEXUP four times: C E X U P | C E X U P | C E X U P | C E X U P

Mapping this to the given blanks in the series C _ _ U P _ E X _ P C _ X U _ _ E _ U P: 1st and 2nd blanks: E, X (C E X U P) 3rd blank: C (C E X) 4th blank: U (U P C) 5th blank: E (C E X) 6th and 7th blanks: P, C (X U P C E) 8th blank: X (E X U P)

The sequential letters are E, X, C, U, E, P, C, X.

Explanation

The relationship between the numbers in the given sets follows the logic (First Number × Second Number) × 2 = Third Number. In the first set (9, 18, 324), multiplying the first and second numbers gives 9 × 18 = 162, and doubling this product yields 162 × 2 = 324. Similarly, in the second set (14, 11, 308), the product is 14 × 11 = 154, and doubling it results in 154 × 2 = 308. Applying this same rule to the set (7, 12, 168), we calculate 7 × 12 = 84, and then 84 × 2 = 168.

Explanation

The pattern applied in these number analogies is (2n - 1)², where n is the first number of the pair. For the first pair 2:9, substituting n = 2 gives (2 × 2 - 1)² = 3² = 9. In the second pair 6:121, substituting n = 6 gives (2 × 6 - 1)² = 11² = 121. Following the same logic for the number 5, the calculation is (2 × 5 - 1)² = 9² = 81.

Explanation

The logic followed in the given sets (8, 13, 21) and (13, 18, 31) is that the sum of the first two numbers equals the third number, and the absolute difference between the first two numbers is exactly 5. Mathematically, for a set (A, B, C), these conditions are A + B = C and |A - B| = 5. In the first given set, 8 + 13 = 21 and 13 - 8 = 5. In the second given set, 13 + 18 = 31 and 18 - 13 = 5. In the set (11, 16, 29), while the difference between the first two numbers is 16 - 11 = 5, their sum is 11 + 16 = 27. Because the third number in this set is 29 rather than 27, it does not satisfy the A + B = C relationship.

Explanation

The coding logic involves dividing the six-letter word into two equal halves of three letters each and reversing the sequence of letters within each half independently. In the case of MELODY, the first half MEL is reversed to LEM and the second half ODY is reversed to YDO, resulting in LEMYDO. Following the same pattern for PURPLE, the first half PUR becomes RUP and the second half PLE becomes ELP, forming RUPELP. Applying this rule to the word CLAUSE, the first half CLA is reversed to ALC and the second half USE is reversed to ESU. Concatenating these two parts results in the coded form ALCESU.

Explanation

Dictionary order is determined by comparing words letter by letter from left to right. All six words begin with the prefix Acc. Comparing the fourth letters of the words, we find e in Accepted and Accessary, i in Accident, l in Acclaimed, o in Accompany, and u in Accuracy. In the English alphabet, e comes before i, which comes before l, which comes before o, which comes before u. To differentiate between Accepted and Accessary, we look at the fifth letters, which are p and s respectively. Since p comes before s, Accepted (5) precedes Accessary (6). Placing the remaining words based on their fourth letters results in the sequence Accident (2), Acclaimed (4), Accompany (1), and Accuracy (3). The final chronological sequence is 5, 6, 2, 4, 1, 3.

Explanation

To arrange words in dictionary order, they are compared letter by letter from left to right. All the given words start with the prefix Ter-.

The fourth letter in Terminate (6) and Termite (4) is m. Comparing these two, the first five letters Termi- are identical. The sixth letter in Terminate is n, while in Termite it is t. Since n comes before t, the order is 6, 4.

The fourth letter in Terrace (2), Terrain (3), and Territory (5) is r. Comparing these three, Terrace and Terrain both have a as the fifth letter, while Territory has i. Between Terrace and Terrain, the sixth letter c in Terrace comes before the sixth letter i in Terrain, placing 2 before 3. Territory follows them because i comes after a, making the sequence 2, 3, 5.

The fourth letter in Tertiary (1) is t. Since t comes after m and r alphabetically, Tertiary is placed at the end. Combining these groups results in the final dictionary order: 6, 4, 2, 3, 5, 1.

Explanation

The letter-cluster BDFH follows a constant arithmetic progression where each letter is determined by adding 2 to the positional value of the preceding letter (A=1, B=2, …, Z=26). The positional values for B, D, F, and H are 2, 4, 6, and 8 respectively, creating a uniform +2, +2, +2 pattern. This specific sequence distinguishes BDFH from the other clusters in the set, which instead follow a pattern of adding +4, +1, and then +4 to the positional values of their letters.

Explanation

Substituting the signs from option d into the expression 45 86 23 36 18 * 2021 yields the equation 45 + 86 × 23 - 36 ÷ 18 = 2021. Following the BODMAS rule, we first perform the division operation 36 ÷ 18, which equals 2. Next, we solve the multiplication 86 × 23. Calculating 86 × 20 = 1720 and 86 × 3 = 258, the sum is 1720 + 258 = 1978. The equation then simplifies to 45 + 1978 - 2 = 2021. Adding 45 to 1978 results in 2023. Finally, subtracting 2 from 2023 gives 2021. Since the left-hand side equals the right-hand side, the equation is balanced.

Explanation

The given series follows a pattern of multiplication where each subsequent term is multiplied by a decreasing sequence of integers starting from 5.

2 × 5 = 10 10 × 4 = 40 40 × 3 = 120 120 × 2 = 240

Following this logic, the next multiplier in the sequence (5, 4, 3, 2) must be 1. Therefore, the next term is calculated as 240 × 1 = 240.

Explanation

Conclusion I follows from the intersection of the second and third statements. Since some moons are suns and all suns are satellites, the specific subset of moons that are suns must also be contained within the set of satellites. This ensures that some satellites are moons.

Conclusion III follows directly from the first statement through the logical rule of conversion. If all stars are moons, it means the entire set of stars is a subset of the set of moons. Consequently, there must be some moons that are stars, making the conclusion some moons are stars necessarily true.

Conclusion II does not logically follow because the statements do not establish a definite connection between stars and satellites. While all stars are moons and some moons are suns, there is no requirement for the star subset of moons to overlap with the sun subset of moons, and thus no guaranteed overlap with satellites.

Explanation

The logic follows the sum of the reverse alphabetical positions of the letters in each word plus a constant value of 6. The reverse position of a letter is calculated by subtracting its standard rank from 27. For EACH, the reverse positions are E = 22, A = 26, C = 24, and H = 19. The sum is 22 + 26 + 24 + 19 = 91. Adding the constant 6 gives 91 + 6 = 97. Similarly, for EASY, the reverse positions are E = 22, A = 26, S = 8, and Y = 2. The sum is 22 + 26 + 8 + 2 = 58. Adding 6 gives 58 + 6 = 64. Following this same pattern for ECHO, the reverse positions are E = 22, C = 24, H = 19, and O = 12. The sum of these positions is 22 + 24 + 19 + 12 = 77. Adding the constant 6 results in 77 + 6 = 83.

Explanation

The numbers in the given sets follow the mathematical relationship where the third number is obtained by adding 3 to the sum of the first two numbers. The formula is: First Number + Second Number + 3 = Third Number.

In the first set (47, 11, 61), the sum of the first two numbers is 47 + 11 = 58. Adding the constant 3 gives 58 + 3 = 61.

In the second set (13, 68, 84), the sum of the first two numbers is 13 + 68 = 81. Adding the constant 3 gives 81 + 3 = 84.

Following the same logic for the set (52, 88, 143), the sum of the first two numbers is 52 + 88 = 140. Adding the constant 3 gives the third number: 140 + 3 = 143.

Explanation

The numbers in the given sets follow the logic a² + b² = c, where the sum of the squares of the first two numbers equals the third number. For the set (2, 9, 85), the relation is 2² + 9² = 4 + 81 = 85. For the set (3, 9, 90), the relation is 3² + 9² = 9 + 81 = 90. Applying the same pattern to the option (7, 9, 130), we calculate 7² + 9² = 49 + 81 = 130.

Explanation

The relationship is based on reversing the given letter-cluster and then adding consecutive integers starting from 1 to the alphabetical position of each letter in the reversed sequence.

For SCOOTER: The reverse of SCOOTER is RETOOCS. Adding consecutive integers to the positional values (A=1, B=2, …, Z=26): R(18) + 1 = 19 (S) E(5) + 2 = 7 (G) T(20) + 3 = 23 (W) O(15) + 4 = 19 (S) O(15) + 5 = 20 (T) C(3) + 6 = 9 (I) S(19) + 7 = 26 (Z) The resulting cluster is SGWSTIZ.

For AEROPLANE: The reverse is ENALPOR E A. Adding consecutive integers: E(5) + 1 = 6 (F) N(14) + 2 = 16 (P) A(1) + 3 = 4 (D) L(12) + 4 = 16 (P) P(16) + 5 = 21 (U) O(15) + 6 = 21 (U) R(18) + 7 = 25 (Y) E(5) + 8 = 13 (M) A(1) + 9 = 10 (J) The resulting cluster is FPDPUUYMJ.

For HELICOPTER: The reverse is RETPOCILEH. Adding consecutive integers: R(18) + 1 = 19 (S) E(5) + 2 = 7 (G) T(20) + 3 = 23 (W) P(16) + 4 = 20 (T) O(15) + 5 = 20 (T) C(3) + 6 = 9 (I) I(9) + 7 = 16 (P) L(12) + 8 = 20 (T) E(5) + 9 = 14 (N) H(8) + 10 = 18 (R) The resulting letter-cluster is SGWTTIPNTR.

Explanation

Substituting the sequence of signs into the given expression 12 70 5 5 5 11 2 results in the following equation:

12 + 70 - 5 × 5 = 5 × 11 + 2

To solve this, we apply the BODMAS rule, which dictates that multiplication must be performed before addition and subtraction.

Calculating the Left Hand Side (LHS): LHS = 12 + 70 - (5 × 5) LHS = 12 + 70 - 25 LHS = 82 - 25 = 57

Calculating the Right Hand Side (RHS): RHS = (5 × 11) + 2 RHS = 55 + 2 = 57

Since the value of the LHS (57) is equal to the value of the RHS (57), the equation is balanced.

Explanation

To arrange the words in alphabetical order, compare them letter by letter from left to right. All words share the first four letters P-a-n-d. Words 4 (Pandanus) and 5 (Pandarus) have a as their fifth letter, while words 1, 2, and 3 have e. Since a comes before e, 4 and 5 are placed first. Comparing 4 and 5 at the sixth letter, n in Pandanus precedes r in Pandarus, establishing the sequence 4, 5.

For the remaining words 1 (Pandemonium), 2 (Pandemic), and 3 (Pandering), we compare the sixth letter. Words 1 and 2 have m, while word 3 has r. Because m comes before r, word 3 is placed after 1 and 2. Finally, comparing 1 and 2 at the seventh letter, i in Pandemic precedes o in Pandemonium. Therefore, word 2 comes before word 1, leading to the final dictionary order of 4, 5, 2, 1, 3.

Explanation

The given series consists of 20 characters which can be divided into four groups of five letters each. By placing the letters C, N, P, and S from the selected option into the blanks, the series is organized as follows: (ACMPS), (ACNPS), (ACOPS), and (ACPPS).

The pattern reveals that each five-letter block begins with the prefix AC and ends with the suffix PS. The third letter in each block follows a sequential alphabetical progression. In the first group, the middle letter is M. In the second group, it advances to N. In the third group, it becomes O, and in the final group, it reaches P. This consistent structure of fixed outer letters combined with an incrementing central letter completes the logical sequence.

Explanation

The series follows a systematic decrement pattern for each corresponding letter position across the terms OTLN, MSJM, KRHL, and IQFK.

For the first letter of each term, the positions in the English alphabet decrease by 2: O (15) to M (13), M (13) to K (11), and K (11) to I (9). Following this, I (9) - 2 results in 7, which corresponds to the letter G.

For the second letter, the positions decrease by 1: T (20) to S (19), S (19) to R (18), and R (18) to Q (17). Following this, Q (17) - 1 results in 16, which corresponds to the letter P.

For the third letter, the positions decrease by 2: L (12) to J (10), J (10) to H (8), and H (8) to F (6). Following this, F (6) - 2 results in 4, which corresponds to the letter D.

For the fourth letter, the positions decrease by 1: N (14) to M (13), M (13) to L (12), and L (12) to K (11). Following this, K (11) - 1 results in 10, which corresponds to the letter J.

The combination of these resulting letters identifies GPDJ as the next term in the sequence.

Explanation

The original equation 117 ÷ 13 + 16 × 540 - 40 = 644 results in a very large value because of the term 16 × 540. To reduce the result to 644, we interchange the + and × signs. Substituting these signs, the equation becomes:

117 ÷ 13 × 16 + 540 - 40 = 644

Applying the BODMAS rule, we first perform the division: 9 × 16 + 540 - 40 = 644

Next, we perform the multiplication: 144 + 540 - 40 = 644

Then, performing the addition and subtraction: 684 - 40 = 644 644 = 644

The left hand side equals the right hand side after the interchange.

Explanation

The relationship in the given pair is between a physical quantity and its SI unit of measurement. Energy is measured in Joules. Similarly, Current is a physical quantity whose standard SI unit of measurement is the Ampere.

Explanation

The pattern followed in the given sets is based on two mathematical relationships between the three numbers (n₁, n₂, n₃). First, the second number is obtained by doubling the first number and adding one: n₂ = 2 × n₁ + 1. Second, the third number is the arithmetic mean of the first and second numbers: n₃ = (n₁ + n₂) / 2.

In the first set (7, 15, 11): 7 × 2 + 1 = 15 (7 + 15) / 2 = 22 / 2 = 11

In the second set (9, 19, 14): 9 × 2 + 1 = 19 (9 + 19) / 2 = 28 / 2 = 14

In the third set (11, 23, 17): 11 × 2 + 1 = 23 (11 + 23) / 2 = 34 / 2 = 17

The set (11, 23, 17) perfectly satisfies both conditions established by the logic of the initial sets.

Explanation

Dictionary order is determined by comparing letters from left to right. All words share the common prefix Str. Comparing the fourth letters, Strange (a), Stranger (a), and Strategy (a) precede the others. Among these, the fifth letter n in Strange and Stranger comes before t in Strategy. Between Strange and Stranger, the shorter word Strange appears first, followed by Stranger. This establishes the initial sequence as 6, 3, 1. Next, the words Strength and Stretch are compared based on their fourth letter e. Comparing their fifth letters, n in Strength precedes t in Stretch, placing Strength before Stretch. Finally, Struggle is placed last because its fourth letter u comes after a and e. The final dictionary order is 6, 3, 1, 2, 4, 5.

Explanation

The relationship between the letter-clusters is based on a constant backward shift of 7 positions in the English alphabetical order for every letter in the cluster.

In the pair BET : UXM, the numerical positions of the letters are B(2), E(5), and T(20). Subtracting 7 from each gives: 2 - 7 = -5, which corresponds to U (21) in a circular alphabetical system. 5 - 7 = -2, which corresponds to X (24). 20 - 7 = 13, which corresponds to M (13).

In the pair SYP : LRI, the numerical positions are S(19), Y(25), and P(16). Subtracting 7 from each gives: 19 - 7 = 12, which is L. 25 - 7 = 18, which is R. 16 - 7 = 9, which is I.

Applying this -7 shift to HOX, where the positions are H(8), O(15), and X(24): 8 - 7 = 1, which is A. 15 - 7 = 8, which is H. 24 - 7 = 17, which is Q.

The resulting cluster is AHQ.

Explanation

The pattern follows a simple adjacent letter swapping logic within each letter-cluster. In each word, the letters are divided into consecutive pairs, and the positions within each pair are interchanged.

For MAGNET, the pairs are (M, A), (G, N), and (E, T). Swapping the positions within these pairs results in (A, M), (N, G), and (T, E), which forms AMNGTE.

For FAMILY, the pairs are (F, A), (M, I), and (L, Y). Swapping the positions within these pairs results in (A, F), (I, M), and (Y, L), which forms AFIMYL.

Applying the same logic to BLOCKS, the letters are paired as (B, L), (O, C), and (K, S). Swapping the positions within these pairs results in (L, B), (C, O), and (S, K). Concatenating these swapped pairs gives the letter-cluster LBCOSK.

Explanation

The series follows a specific addition pattern for each corresponding position across the letter-clusters. The first letter of each cluster increases by 4, moving from G to K to O to S, which means the next letter is S (19) + 4 = W (23). The second letter increases by 3, moving from T to W to Z to C, which means the next letter is C (3) + 3 = F (6). The third letter increases by 2, moving from C to E to G to I, which means the next letter is I (9) + 2 = K (11). The fourth letter increases by 1, moving from L to M to N to O, which means the next letter is O (15) + 1 = P (16). Applying these systematic increments to the last cluster SCIO results in WFKP.

Explanation

Reema's daughter's father is Reema's husband. The statement says that the boy's father is the father of Reema's daughter, which means the boy's father is Reema's husband. Since the boy and Reema's daughter share the same father, the boy is the brother of Reema's daughter.

Explanation

The alphabetical positions of the letters in MOQX are M (13), O (15), Q (17), and X (24). The differences between consecutive letters are 15 - 13 = 2, 17 - 15 = 2, and 24 - 17 = 7. This sequence of intervals (+2, +2, +7) differs from the common pattern of +4, +3, and +2 shared by the other clusters in the set. In those clusters, the position increases by 4 from the first to the second letter, by 3 from the second to the third, and by 2 from the third to the fourth.

Explanation

By interchanging the signs + and ÷ in the given equation 1000 - 448 + 14÷ 15× 2 = 998, the new expression becomes 1000 - 448 ÷ 14 + 15 × 2.

Applying the BODMAS rule:

First, perform the division: 448 ÷ 14 = 32

Next, perform the multiplication: 15 × 2 = 30

The equation now reads: 1000 - 32 + 30

Finally, perform addition and subtraction from left to right: 1000 - 32 = 968 968 + 30 = 998

The resulting value matches the right-hand side of the equation.

Explanation

By interchanging the numbers 34 and 15 and the signs + and ÷, the given equation 15 ÷ 80 - 34 + 10 × 8 = 102 is transformed into:

34 + 80 - 15 ÷ 10 × 8 = 102

Applying the BODMAS rule, we first perform the division: 15 ÷ 10 = 1.5

Next, we perform the multiplication: 1.5 × 8 = 12

Substitute the product back into the expression: 34 + 80 - 12

Finally, we perform the addition and subtraction: 114 - 12 = 102

Since the left-hand side equals the right-hand side, the interchange of numbers and signs satisfies the equation.

Explanation

The pattern followed in the given sets is that the middle number is the square of the sum of the first and third numbers. This can be expressed by the formula (First Number + Third Number)² = Middle Number.

In the first set (4, 81, 5), adding the first and third numbers gives 4 + 5 = 9. Squaring this sum results in 9² = 81, which is the middle number.

In the second set (3, 144, 9), adding the first and third numbers gives 3 + 9 = 12. Squaring this sum results in 12² = 144, which is the middle number.

Applying this logic to the set (2, 100, 8), the sum of the first and third numbers is 2 + 8 = 10. Squaring this sum results in 10² = 100, which is the middle number.

Explanation

The pattern followed in the pairs is y = (ˣ⁄₂ + 1)². For the pair 36:365, applying this operation to the first number x = 36 gives (³⁶⁄₂ + 1)² = (18 + 1)² = 19² = 361. Since the second number provided in the pair is 365 rather than 361, it fails to follow the consistent mathematical rule.

Explanation

According to the statements, all tools are a subset of spanners, and the set of spanners has no intersection with the set of irons. This implies that no tool can be an iron, rendering conclusion I incorrect. Furthermore, since some spanners are utensils and no spanner is an iron, the specific utensils that are also spanners cannot be irons. This logically validates conclusion III, which states that some utensils are not iron. There is no definitive information provided to establish a necessary connection between utensils and tools, so conclusion II does not logically follow.

Explanation

The logic of these statements can be understood through the transitive property of categorical syllogisms. The statement All tuberculosis are diseases combined with All diseases are curable establishes a logical chain where tuberculosis is a subset of diseases, and diseases is a subset of curable entities. If T ⊆ D and D ⊆ Cu, then T ⊆ Cu must be true, which validates Conclusion I.

Similarly, combining the statement All cancers are diseases with All diseases are curable creates a chain where cancers is a subset of diseases, and diseases is a subset of curable entities. If C ⊆ D and D ⊆ Cu, then C ⊆ Cu must be true, which validates Conclusion III. However, although both cancers and tuberculosis are subsets of diseases, there is no statement defining the relationship between cancers and tuberculosis directly. Consequently, Conclusion II does not logically follow from the given premises. Thus, only conclusions I and III are valid.

Explanation

The coding logic follows a pattern where the word is divided into two equal halves of three letters each, and each half is reversed independently. For the word XPDJOA, the first half XPD is reversed to DPX and the second half JOA is reversed to AOJ, forming DPXAOJ. In the case of THBRUC, the first half THB becomes BHT and the second half RUC becomes CUR, forming BHTCUR. Applying this same logic to GILDZM, the first three letters GIL are reversed to LIG, and the last three letters DZM are reversed to MZD. Joining these two reversed segments results in LIGMZD.

Explanation

The numerical series 214, 207, 193, ?, 144, 109 follows a pattern of decreasing values where the difference between consecutive terms increases by a constant factor of 7. Specifically, each term is calculated by subtracting the next multiple of 7 from the previous term. The difference between the first two terms is 214 - 207 = 7, which is 7 × 1. The difference between the second and third terms is 207 - 193 = 14, which is 7 × 2. To find the missing number, we continue this pattern by subtracting the third multiple of 7, which is 7 × 3 = 21, from the third term: 193 - 21 = 172. This pattern is validated by the subsequent terms in the sequence. Subtracting the fourth multiple of 7, 7 × 4 = 28, from 172 gives 172 - 28 = 144. Subtracting the fifth multiple of 7, 7 × 5 = 35, from 144 gives 144 - 35 = 109, confirming the consistency of the rule throughout the entire series.