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

Explanation

Applying the mathematical signs from option b to the given sequence results in the equation 32 + 14 - 18 ÷ 9 × 12 = 22. To verify if this balances the equation, we apply the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction). First, we perform the division 18 ÷ 9 = 2. The equation then becomes 32 + 14 - 2 × 12 = 22. Next, we perform the multiplication 2 × 12 = 24, leading to 32 + 14 - 24 = 22. Proceeding with addition, 32 + 14 = 46, which simplifies the expression to 46 - 24 = 22. Finally, subtracting 24 from 46 gives 22. Since 22 = 22, the sequence of signs correctly balances the equation.

Explanation

The numbers in each triplet (n₁, n₂, n₃) follow a specific mathematical relationship where the product of the first number and 6 is equal to the product of the second and third numbers. This pattern is expressed by the formula n₁ × 6 = n₂ × n₃.

In the first triplet (3, 9, 2), the product of the first number and 6 is 3 × 6 = 18, which matches the product of the second and third numbers, 9 × 2 = 18.

In the second triplet (8, 6, 8), the product of the first number and 6 is 8 × 6 = 48, which matches the product of the second and third numbers, 6 × 8 = 48.

Following this pattern for the third triplet (5, 3, ?), the product of the first number and 6 is 5 × 6 = 30. To find the missing value, the product of the second and third numbers must also equal 30. Setting up the equation 3 × ? = 30 and solving for the unknown value results in 30 / 3 = 10.

Explanation

To determine the identity of the person in the picture, analyze the description provided by Azad step by step. Azad's mother's father is his maternal grandfather. The only granddaughter of Azad's maternal grandfather refers to Azad's sister. Since the person in the picture is the only brother of this granddaughter, and Azad is the only male sibling of his sister, the person in the picture is Azad himself.

Explanation

The series follows a specific pattern for the first and second letters of each term based on their positions in the English alphabet.

The first letters follow an arithmetic progression: C(3), E(5), G(7), I(9), K(11), M(13), and O(15). Each subsequent first letter is obtained by adding 2 to the previous one (+2 pattern). The next letter in this sequence is 15 + 2 = 17, which corresponds to the letter Q.

The second letters follow an alternating pattern of addition and subtraction with increasing values: M(13), P(16), O(15), S(19), Q(17), V(22), and S(19). The changes are +3, -1, +4, -2, +5, and -3. Following this logical progression, the next increment must be +6. Applying this to the last letter, 19 + 6 = 25, which corresponds to the letter Y. Combining the two results gives the term QY.

Explanation

The logic followed in the number pairs is (n - 2) × 2 = Result, where n is the first number in the pair. For the first pair 19:34, the calculation is (19 - 2) × 2 = 17 × 2 = 34. For the second pair 5:6, the calculation is (5 - 2) × 2 = 3 × 2 = 6. Applying the same mathematical pattern to the third pair 27:?, we get (27 - 2) × 2 = 25 × 2 = 50. Alternatively, the pattern can be expressed as 2n - 4, which yields 2(27) - 4 = 54 - 4 = 50.

Explanation

The relationship between the numbers in the given sets is based on the following pattern: (First number × Second number) + 4 = Third number.

Applying this logic to the provided sets: In (4, 3, 16): (4 × 3) + 4 = 12 + 4 = 16 In (6, 4, 28): (6 × 4) + 4 = 24 + 4 = 28

Following the same logic for the set in option b: In (8, 2, 20): (8 × 2) + 4 = 16 + 4 = 20

Explanation

In each of the given letter-clusters, the first and third letters are alphabetical opposites, meaning the sum of their numerical positions in the alphabet is 27: EBV: E(5) and V(22) ⟹ 5 + 22 = 27 GET: G(7) and T(20) ⟹ 7 + 20 = 27 BYY: B(2) and Y(25) ⟹ 2 + 25 = 27 JGQ: J(10) and Q(17) ⟹ 10 + 17 = 27

The odd cluster is identified by the parity of the sum of the place values of all three letters: EBV: 5 + 2 + 22 = 29 (an odd number) GET: 7 + 5 + 20 = 32 (an even number) BYY: 2 + 25 + 25 = 52 (an even number) JGQ: 10 + 7 + 17 = 34 (an even number)

Alternatively, the middle letter of EBV (B) is located at an even position (2), while the middle letters of the other three clusters (E=5, Y=25, G=7) are all located at odd positions in the alphabet.

Explanation

By interchanging + and -, the equation becomes 17 * 4 - 6 / 2 + 27. Following BODMAS, this simplifies to 68 - 3 + 27, which equals 65 + 27 = 92.

Explanation

The series follows a specific pattern for each position: the first letter increases by 4 (P to T to X to B to F), the second letter decreases by 2 (Q to O to M to K to I), the third letter increases by 3 (S to V to Y to B to E), and the fourth letter decreases by 1 (T to S to R to Q to P). Applying these patterns to TOVS results in XMYR.

Explanation

The expression N + D # Z B can be decoded based on the provided relationship definitions. N + D indicates that N is the husband of D, which establishes N as a male and D as his wife. D # Z signifies that D is the mother of Z. Since N is the husband of Z's mother, it follows that N is the father of Z. The final segment Z B states that Z is the father of B. Because N is the father of Z, and Z is the father of B, N is the father's father of B. This relationship identifies N as the paternal grandfather of B.

Explanation

To evaluate the conclusions, we analyze the logical relationships established by the statements. The first statement indicates an intersection between the set of rings and the set of fingers. The second statement indicates an intersection between the set of fingers and the set of toes. Since these are particular affirmative statements (Some), there is no mandatory overlap between the set of rings and the set of toes; they could be entirely separate. Thus, Conclusion II, which asserts that some toes are rings, is not a necessary consequence.

The third statement establishes that the set of toes and the set of earrings are disjoint (No toe is an earring). However, the premises provide no information regarding the relationship between earrings and rings or earrings and fingers. In the absence of a negative constraint linking earrings to rings, it is possible for an earring to be a ring. Therefore, the definite negative statement in Conclusion I, which claims no earring is a ring, cannot be logically deduced. Since neither conclusion is supported by the given premises, the logical result is that neither follows.

Explanation

The letter-series follows a pattern where the string is divided into four groups of five letters each: SRUCT, SRUDT, SRUET, and SRUFT. In this pattern, the first, second, third, and fifth letters of each group remain constant (S-R-U-T), while the fourth letter of each group progresses alphabetically (C-D-E-F). Inserting the letters from option C (R, U, D, S, T, U, F) into the blanks perfectly completes this logical sequence.

Explanation

The Royal Bengal Tiger is the national animal of India, and the Kangaroo is the national animal of Australia. Therefore, the relationship follows the pattern of country to its national animal.

Explanation

The series follows a pattern where the difference between consecutive terms is the sequence of squares of consecutive integers starting from 5. The differences are 5 squared (25), 6 squared (36), 7 squared (49), 8 squared (64), and 9 squared (81). Adding 36 to the second term (36 + 36) gives 72, and adding 49 to 72 confirms the next term as 121.

Explanation

The coding pattern follows an alternating shift of +2 and +3 for each letter: F+2=H, O+3=R, O+2=Q, and D+3=G. Applying this logic to FOOD results in HRQG.

Explanation

The logic applied in both provided sets (13, 17, 23) and (8, 12, 18) is that the difference between the first and second number is 4, and the difference between the second and third number is 6. Specifically: Set 1: 17 - 13 = 4; 23 - 17 = 6. Set 2: 12 - 8 = 4; 18 - 12 = 6. Checking the options: Option B follows this identical pattern: 22 - 18 = 4 and 28 - 22 = 6. No other option satisfies this consistent mathematical relationship.

Explanation

Option B provides the correct sequence of signs to balance the equation: 7 + 5 - 4 / 2 - 3 = 7. Following the BODMAS rule, 4 / 2 is 2, and then 7 + 5 - 2 - 3 equals 7, which matches the right side of the equation.

Explanation

The logic used in the analogies is to split the seven-letter word into two groups: the first four letters and the last three letters, and then reverse the sequence of each group independently. For FOREIGN, reversing the first four letters (FORE) gives EROF, and reversing the last three letters (IGN) gives NGI, resulting in the combination EROFNGI.

Explanation

The series is completed by dividing the sequence into five groups of four letters each. By sequentially placing the letters from the correct option into the eight available blanks, the sequence becomes LTRM RALM TALM TRAL MTRA. This arrangement follows a rigorous logical structure based on the set of five letters {A, L, M, T, R}. Each four-letter block contains a unique combination of letters where exactly one letter from the set is omitted in each group. The omitted letters follow the sequence A, T, R, M, and L, ensuring that every letter in the set is excluded once across the five blocks. Additionally, the internal distribution of letters remains consistent; for instance, the second and third positions in each block follow a symmetric pattern (T-A-A-R-T and R-L-L-A-R respectively), which establishes a clear periodicity and confirms the sequence.

Explanation

Conclusion I does not follow because there is no statement linking streaks and flashes that necessitates an overlap. Conclusion II is false because since all bands are flashes and some lines are bands, there must be an intersection between flashes and lines. Therefore, neither conclusion logically follows from the given statements.

Explanation

The relationship follows the logic: (First number - Second number) + 100 = Third number. Applying this to the given sets: (239 - 127) + 100 = 212 and (96 - 64) + 100 = 132. For option C, (167 - 89) + 100 = 78 + 100 = 178, which satisfies the pattern.

Explanation

The logic followed is: Consonants are increased by 4 (Consonant + 4) and Vowels are decreased by 3 (Vowel - 3). Applying this to KIDNAP: K(+4)=O, I(-3)=F, D(+4)=H, N(+4)=R, A(-3)=X, P(+4)=T, resulting in OFHRXT.

Explanation

The pattern follows a logic where the letters of the word are divided into pairs, and each pair is shifted backward by a specific even number. The first pair is shifted by -2, the second pair by -4, the third pair by -6, and the fourth pair by -8.

Applying this to EQUATION: The first pair (E, Q) undergoes a -2 shift: E (5) - 2 = 3 (C) and Q (17) - 2 = 15 (O). The second pair (U, A) undergoes a -4 shift: U (21) - 4 = 17 (Q) and A (1 or 27) - 4 = 23 (W). The third pair (T, I) undergoes a -6 shift: T (20) - 6 = 14 (N) and I (9) - 6 = 3 (C). The fourth pair (O, N) undergoes an -8 shift: O (15) - 8 = 7 (G) and N (14) - 8 = 6 (F).

Concatenating these results gives the letter-cluster COQWNCGF.

Explanation

To balance the equation 76 34 23 12 6 * 21, the mathematical signs from option d are substituted sequentially to form the expression 76 - 34 - 23 + 12 ÷ 6 = 21. Following the BODMAS rule, the division operation is performed first, where 12 ÷ 6 = 2. This simplifies the equation to 76 - 34 - 23 + 2 = 21.

Next, performing the subtraction and addition from left to right, we calculate 76 - 34 = 42. Then, 42 - 23 = 19. Finally, adding the result of the division, we have 19 + 2 = 21. Since the result on the left-hand side matches the right-hand side (21 = 21), the combination of signs -, -, +, ÷, = correctly balances the given equation.

Explanation

The logic followed in these pairs is that the first term is the product of two consecutive integers, where the smaller integer is one greater than the second term. This can be expressed by the formula Term 1 = (Term 2 + 1) × (Term 2 + 2).

In the first pair 132 : 10, the calculation is (10 + 1) × (10 + 2) = 11 × 12 = 132. In the second pair 42 : 5, the calculation is (5 + 1) × (5 + 2) = 6 × 7 = 42.

To find the missing number related to the fifth term 272, we solve for x in the equation (x + 1) × (x + 2) = 272. Expanding the equation gives x² + 3x + 2 = 272, which simplifies to the quadratic equation x² + 3x - 270 = 0. We can factor this equation as (x + 18)(x - 15) = 0. Taking the positive root suitable for the given options, we find x = 15. This is verified by the fact that 16 × 17 = 272.

Explanation

The series follows an addition pattern where the difference between consecutive terms increases by 2. By examining the gaps between the given numbers, we find that the difference between the first and second terms is 26 - 19 = 7, while the differences between the last three terms are 59 - 46 = 13 and 74 - 59 = 15. This reveals a pattern of differences consisting of consecutive odd numbers: 7, 9, 11, 13, and 15. To find the missing value, we apply the next difference in the sequence to the second term: 26 + 9 = 35. This result is consistent with the rest of the series, as adding the subsequent difference of 11 to 35 yields the next given term, 35 + 11 = 46.

Explanation

The series follows a repeating pattern of the 4-letter block ABCC. By counting the total number of characters in the sequence, including the blanks, we find 16 positions. Dividing these into groups of four reveals the repetition:

(A B C ) | (A _ C C) | (A B _ C) | ( B _ C)

To maintain the uniform block ABCC across all four groups, the blanks must be filled as follows: First blank: C (completing ABCC) Second blank: B (completing ABCC) Third blank: C (completing ABCC) Fourth blank: A (completing ABCC) Fifth blank: C (completing ABCC)

Placing these letters from left to right gives the sequence CBCAC.

Explanation

The coding logic follows a specific pattern based on the alphabetical positional values of letters. For consonants, the code uses their direct positional value in the English alphabet (A=1, B=2, ..., Z=26). For vowels (A, E, I, O, U), the positional value is multiplied by 2.

In CURD: C is 3 (consonant), U is 21 × 2 = 42 (vowel), R is 18 (consonant), and D is 4 (consonant), resulting in 342184.

In BREAD: B is 2 (consonant), R is 18 (consonant), E is 5 × 2 = 10 (vowel), A is 1 × 2 = 2 (vowel), and D is 4 (consonant), resulting in 2181024.

Applying this logic to BUTTER: B (consonant) = 2 U (vowel) = 21 × 2 = 42 T (consonant) = 20 T (consonant) = 20 E (vowel) = 5 × 2 = 10 R (consonant) = 18

Combining these values gives the code 24220201018.

Explanation

The logic followed in the given sets is B² - A = C, where A, B, and C represent the first, second, and third numbers of the set respectively.

In the first set (26, 14, 170): 14² - 26 = 196 - 26 = 170

In the second set (31, 7, 18): 7² - 31 = 49 - 31 = 18

Similarly, in the set (21, 9, 60): 9² - 21 = 81 - 21 = 60

Explanation

The triad 4:16:20 is the odd one out because it fails to follow the mathematical pattern (x : 4x - 1 : 5x) that defines the group. Taking the first number x = 4, the second number according to the rule should be 4 × 4 - 1 = 15 and the third number should be 4 × 5 = 20. While the third number matches, the second number in this triad is 16, which is a direct multiple (4 × 4) rather than following the subtraction operation. This deviation from the shared logic of the set makes it the triad that does not belong.

Explanation

To make the equation 912 - 456 × 28 + 390 ÷ 2 = 444 correct, the signs ÷ and - are interchanged. The modified expression becomes 912 ÷ 456 × 28 + 390 - 2. Following the BODMAS rule, the calculation is performed as follows:

First, solve the division: 912 ÷ 456 = 2

Second, solve the multiplication: 2 × 28 = 56

Third, perform the addition: 56 + 390 = 446

Fourth, perform the subtraction: 446 - 2 = 444

Since the calculated value is 444, the equation is balanced.

Explanation

To arrange the words in dictionary order, we compare them letter by letter from left to right. All six words begin with the same three letters Ref. Comparing the fourth letters, Reference (3) has e, Refinery (1) and Refillable (5) have i, Reflect (2) has l, Reformist (6) has o, and Refugee (4) has u. Since e comes first alphabetically, Reference (3) is the first word. Between Refinery (1) and Refillable (5), we compare the fifth letters n and l respectively; since l precedes n, Refillable (5) comes second and Refinery (1) comes third. Continuing with the remaining fourth letters, l comes before o and u, so Reflect (2) is fourth. Then o comes before u, making Reformist (6) fifth and Refugee (4) sixth. The resulting sequence of indices is 3, 5, 1, 2, 6, 4.

Explanation

The pattern followed in the given sets of numbers is: (First number - Second number) + 4 = Third number

Applying this rule to the provided triplets: First triplet: (6, 4, 6) ⟹ (6 - 4) + 4 = 2 + 4 = 6 Second triplet: (18, 9, 13) ⟹ (18 - 9) + 4 = 9 + 4 = 13 Third triplet: (8, 6, ?) ⟹ (8 - 6) + 4 = 2 + 4 = 6

By applying the same mathematical operation to the third set, the missing value that completes the pattern is 6.

Explanation

The pattern followed in the given analogy is based on the formula (n × 2)³ - 1, where n represents the first number in each pair.

In the first pair 1 : 7, the calculation is (1 × 2)³ - 1 = 2³ - 1 = 8 - 1 = 7.

In the second pair 3 : 215, the calculation is (3 × 2)³ - 1 = 6³ - 1 = 216 - 1 = 215.

Applying the same pattern to the fifth number 4, the missing number is calculated as (4 × 2)³ - 1 = 8³ - 1 = 512 - 1 = 511.

Explanation

In the expression C + B - E + A × F - D, the relationships are determined as follows:

The segment B - E indicates that B is the mother of E. Since E + A defines E and A as siblings, B is also the mother of A.

Moving to the next segment, A × F establishes that A is the husband of F. Consequently, F is the wife of A. The final part, F - D, states that F is the mother of D.

Since A is the husband of F and F is the mother of D, A is the father of D. Given that B is the mother of A, B is the paternal grandmother of D. This makes D the grandchild of B, rather than the daughter. Therefore, the statement claiming D is the daughter of B is incorrect.

Explanation

The coding logic follows a specific pattern: the first letter of the word remains in its original position, while all the remaining letters are written in reverse order.

For the word DICTATOR: The first letter is D. The remaining letters are I-C-T-A-T-O-R. Reversing these letters gives R-O-T-A-T-C-I. Combining them results in DROTATCI.

For the word GLIMPSE: The first letter is G. The remaining letters are L-I-M-P-S-E. Reversing these letters gives E-S-P-M-I-L. Combining them results in GESPMLI (the provided prompt GESPML follows this logic but omits the final letter).

Applying this logic to the word CONDEMN: The first letter is C. The remaining letters are O-N-D-E-M-N. Reversing these letters gives N-M-E-D-N-O. Combining the first letter with the reversed sequence results in CNMEDNO.

Explanation

The relationship in the first pair is based on a professional and their area of specialization; a Dietician is an expert who manages and advises on matters related to diet and nutrition. Following the same logic, high blood sugar is a clinical condition typically associated with diabetes, and a Diabetologist is the medical specialist dedicated to the diagnosis, treatment, and clinical management of patients with diabetes and blood glucose imbalances.

Explanation

The logic of the series involves a constant addition of +5 to the positional value of each letter in the cluster. By representing the letters as numerical positions in the English alphabet (A=1, B=2, ..., Z=26), we can determine the missing cluster.

For the first letter of each cluster: D(4) + 5 = I(9). Moving forward, I(9) + 5 = N(14), N(14) + 5 = S(19), and S(19) + 5 = X(24). This identifies the first letter as I.

For the second letter of each cluster: N(14) + 5 = S(19). Moving forward, S(19) + 5 = X(24), X(24) + 5 = 29, which corresponds to C(3) in the alphabetical cycle, and C(3) + 5 = H(8). This identifies the second letter as S.

For the third letter of each cluster: U(21) + 5 = Z(26). Moving forward, Z(26) + 5 = 31, which corresponds to E(5) in the alphabetical cycle, E(5) + 5 = J(10), and J(10) + 5 = O(15). This identifies the third letter as Z.

Combining these results, the missing letter-cluster is ISZ.

Explanation

In the letter-clusters AFKP, SXCH, and JOTY, the positional values of the letters in the English alphabet follow a consistent pattern of adding 5 to the preceding letter. For AFKP, the positions are 1, 6, 11, 16 with differences of +5, +5, +5. For JOTY, the positions are 10, 15, 20, 25 with differences of +5, +5, +5. For SXCH, the positions are 19, 24, 3, 8 where 24+5 = 29, and 29 26 = 3 (C), and 3+5=8 (H), maintaining the +5 constant. In contrast, GKPS follows the sequence G(7), K(11), P(16), S(19). The increments between these letters are +4 (11-7), +5 (16-11), and +3 (19-16). This lack of a uniform +5 increment distinguishes it from the rest.

Explanation

The expression A + B - C ÷ D × E - F establishes the following relationships: A + B implies A is the sister of B; B - C implies B is the brother of C; thus A, B, and C are siblings. C ÷ D indicates C is the wife of D, making D the brother-in-law of A and B. D × E means D is the father of E, and E - F means E is the brother of F. Consequently, E and F are the children of C and D. Since B is the brother of C, and E is the son of C, E is the nephew of B. The statement that E is the brother of B is false because they belong to different generations.

Explanation

The numbers in each set follow a consistent arithmetic pattern based on the first number. The second number is obtained by subtracting 61 from the first number, and the third number is obtained by adding 48 to the first number.

For the set (85, 24, 133): 85 - 61 = 24 85 + 48 = 133

For the set (97, 36, 145): 97 - 61 = 36 97 + 48 = 145

Applying the same logic to the set (79, 18, 127): 79 - 61 = 18 79 + 48 = 127

Explanation

The logic follows the sum of the reverse alphabetical positions of the letters, where each letter value is calculated using the formula R = 27 - P, with P being the standard forward position (A=1, B=2, ..., Z=26).

For PDU: P is the 16th letter, so R = 27 - 16 = 11. D is the 4th letter, so R = 27 - 4 = 23. U is the 21st letter, so R = 27 - 21 = 6. Sum = 11 + 23 + 6 = 40.

For HXO: H is the 8th letter, so R = 27 - 8 = 19. X is the 24th letter, so R = 27 - 24 = 3. O is the 15th letter, so R = 27 - 15 = 12. Sum = 19 + 3 + 12 = 34.

Applying the same logic to BMW: B is the 2nd letter, so R = 27 - 2 = 25. M is the 13th letter, so R = 27 - 13 = 14. W is the 23rd letter, so R = 27 - 23 = 4. Sum = 25 + 14 + 4 = 43.

Explanation

To make the equation 625÷ 25 + 7× 318 - 112 = 381 correct, we interchange the signs + and ×. The modified equation becomes:

625÷ 25 × 7 + 318 - 112 = 381

Applying the BODMAS rule (Division, Multiplication, Addition, Subtraction):

First, perform the division: 25 × 7 + 318 - 112 = 381

Next, perform the multiplication: 175 + 318 - 112 = 381

Then, perform the addition: 493 - 112 = 381

Finally, perform the subtraction: 381 = 381

Since the Left Hand Side (LHS) equals the Right Hand Side (RHS), the interchange of + and × makes the equation correct.

Explanation

The series follows an alternating subtraction pattern where 4 and 8 are subtracted from the preceding terms. Calculating the differences between consecutive terms reveals the logic: 512 - 508 = 4, 508 - 500 = 8, and 500 - 496 = 4. Since the pattern of differences is -4, -8, -4, the next difference in the sequence must be -8. Subtracting 8 from the last term gives 496 - 8 = 488.

Explanation

The pattern follows a logic where each letter of the word is replaced by the two letters that immediately follow it in the alphabetical sequence. Each single letter in the input corresponds to a pair of letters in the output.

In the first pair BULL, the letter B is followed by C and D, U is followed by V and W, L is followed by M and N, and the second L is also followed by M and N. Concatenating these pairs gives the cluster CDVWMNMN.

Applying the same logic to TENS: The letter T is followed by U and V. The letter E is followed by F and G. The letter N is followed by O and P. The letter S is followed by T and U.

Combining these resulting pairs in order yields the letter-cluster UVFGOPTU.

Explanation

The letter series follows a repetitive pattern where a specific group of five letters, CNPSR, is repeated multiple times. To solve such series, we first determine the total length of the sequence, including the blanks. By observing the options, which consist of 8 letters, and the provided string, we can determine that the complete sequence contains 20 letters, divided into four identical groups of five.

The repeating unit is identified as CNPSR. Breaking the sequence into these groups of five, we get:

Group 1: C _ _ S R Group 2: C N P _ _ Group 3: _ N _ S R Group 4: C _ P S _

By filling the blanks in each group to match the pattern CNPSR, we identify the missing letters:

Group 1: C (N) (P) S R Group 2: C N P (S) (R) Group 3: (C) N (P) S R Group 4: C (N) P S (R)

Sequentially, the letters filled in the blanks are N, P, S, R, C, P, N, and R. Comparing this result with the given options, we find that it matches option d exactly.

Explanation

The cluster KQP is identified as the odd one out by analyzing the positional values of the letters in the English alphabet. The general pattern followed by the clusters in this set is that the first and third letters are alphabetical opposites, meaning the sum of their positional values is 27, and the second letter is derived by adding 5 to the positional value of the first letter.

In the case of KQP, the first letter K has a value of 11 and the third letter P has a value of 16. These satisfy the first condition because 11 + 16 = 27. However, the second letter Q has a positional value of 17. The relationship between the first and second letter is 11 + 6 = 17. This increment of 6 deviates from the consistent increment of 5 required by the rule, thereby making KQP the different cluster.

Explanation

The relationship followed by the numbers in the given sets is that the middle number is three times the product of the first and the third numbers. The formula is:

Middle Number = (First Number × Third Number) × 3

In the first set (2, 114, 19): (2 × 19) × 3 = 38 × 3 = 114

In the second set (12, 216, 6): (12 × 6) × 3 = 72 × 3 = 216

Following this logic in option b) (6, 144, 8): (6 × 8) × 3 = 48 × 3 = 144

Explanation

The given mathematical operators are redefined according to the instructions. By mapping the symbols in the expression to their new functions, we establish the following replacements: minus becomes multiplication, division becomes addition, plus becomes division, and multiplication becomes subtraction.

Substituting these into the original expression: 14 - 4 ÷ 133 + 7 × 17 becomes: 14 × 4 + 133 ÷ 7 - 17

Following the BODMAS rule (Division, Multiplication, Addition, and Subtraction), we calculate the value step-by-step:

First, perform the division: 133 ÷ 7 = 19

Next, perform the multiplication: 14 × 4 = 56

Finally, solve the addition and subtraction: 56 + 19 - 17 75 - 17 = 58

Explanation

The numbers in each set follow the logic that the third number is equal to three times the product of the first and second numbers, minus two. The relationship is defined by the formula c = (a × b) × 3 - 2.

In the first set (6, 2, 34): (6 × 2) × 3 - 2 = 12 × 3 - 2 = 36 - 2 = 34

In the second set (1, 5, 13): (1 × 5) × 3 - 2 = 5 × 3 - 2 = 15 - 2 = 13

Applying the same logic to the third set (9, 1, ?): (9 × 1) × 3 - 2 = 9 × 3 - 2 = 27 - 2 = 25