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

Explanation

To determine if the equation in option b is correct after interchanging the × and - signs, we substitute - for × and × for - in the expression 8 × 6 - 9 ÷ 3 + 10 = 0. The new expression becomes 8 - 6 × 9 ÷ 3 + 10. Following the BODMAS rule, we first perform the division 9 ÷ 3 = 3. The expression then updates to 8 - 6 × 3 + 10. Next, we carry out the multiplication 6 × 3 = 18, which gives 8 - 18 + 10. Finally, performing the addition and subtraction, we have 8 + 10 - 18, which simplifies to 18 - 18 = 0. Since the calculated value matches the right-hand side of the equation, the interchange makes the equation correct.

Explanation

The relationship between the numbers in the given sets (a, b, c) is defined by fixed additions. The second number is 100 greater than the first, and the third number is 1000 greater than the second.

b = a + 100 c = b + 1000

For the set (99, 199, 1199): 99 + 100 = 199 199 + 1000 = 1199

For the set (15, 115, 1115): 15 + 100 = 115 115 + 1000 = 1115

Following this logic for the set (33, 133, 1133): 33 + 100 = 133 133 + 1000 = 1133

This pattern uses whole number operations as specified, adding 10² and 10³ sequentially.

Explanation

To determine the correct equation, the signs ÷ and + are interchanged. The original expression in option d is 7 + 21 × 42 ÷ 14 - 9 = 19. After interchanging the signs, the equation becomes 7 ÷ 21 × 42 + 14 - 9 = 19.

Following the BODMAS rule, operations are solved in the order of Division, Multiplication, Addition, and then Subtraction.

The division step yields 7 ÷ 21 = ⅓. The multiplication step follows as ⅓ × 42 = 14. The addition step yields 14 + 14 = 28. The final subtraction step is 28 - 9 = 19.

Since the calculated value matches the right-hand side of the equation, the mathematical statement is correct.

Explanation

The coding logic follows the number of letters in each word of the given phrase. In the first example, come (4), home (4), and soon (4) result in 444. In the second example, are (3), you (3), and coming (6) result in 336. Similarly, raining (7), badly (5), and outside (7) result in 757.

Applying this logic to the phrase kids are happy: kids contains 4 letters. are contains 3 letters. happy contains 5 letters.

By combining these counts in sequence, the code for kids are happy is 435.

Explanation

The relationship follows the hierarchical levels of biological organization in multicellular organisms. In this hierarchy, cells are the basic functional units that group together to form tissues. Following this logic, tissues group together to form organs, and multiple organs work together within organ systems to constitute the entire body. Therefore, just as tissues are composed of cells, the body is the higher-level structure composed of various organs.

Explanation

The relationship in the given pair is based on a professional and their primary place of work. A librarian is an individual whose job is to manage and work within a library. Similarly, a priest is a person whose professional or religious duties are performed within a temple. Both pairs follow the specific pattern of identifying a profession followed by its characteristic workplace.

Explanation

In each of the other three letter-clusters, the letters follow a consistent pattern where each letter is obtained by subtracting 3 from the positional value of the preceding letter in the English alphabet. For MJG, the positions are M (13), J (10), and G (7), with 13 - 3 = 10 and 10 - 3 = 7. For WTQ, the positions are W (23), T (20), and Q (17), where 23 - 3 = 20 and 20 - 3 = 17. For OLI, the positions are O (15), L (12), and I (9), following 15 - 3 = 12 and 12 - 3 = 9. In the cluster GEB, the positional values are G (7), E (5), and B (2). The difference between G and E is 7 - 5 = 2, which deviates from the constant -3 pattern observed in the other clusters.

Explanation

To arrange words in dictionary order, we compare them letter by letter from left to right. All five words begin with the prefix EMP. Comparing the fourth letter of each word, we find L in Employee (2) and Employer (5), O in Emporium (4), R in Empress (1), and T in Empty (3). According to the alphabet, L comes before O, R, and T. Between Employee and Employer, both share the first seven letters EMPLOYE. Comparing the eighth letter, E in Employee precedes R in Employer, so Employee (2) is first and Employer (5) is second. Among the remaining words, the fourth letter O in Emporium (4) comes next, followed by R in Empress (1). Finally, T in Empty (3) appears last. This results in the sequence 2, 5, 4, 1, 3.

Explanation

The relationship between the numbers in the similar pairs follows the rule y = x² - 2, where x is the number on the left and y is the number on the right. Applying this to the other options, we find 12² - 2 = 144 - 2 = 142, 8² - 2 = 64 - 2 = 62, and 4² - 2 = 16 - 2 = 14. For the pair in option d, the logic dictates 14² - 2 = 196 - 2 = 194. Since the provided value is 192, this pair does not follow the common pattern.

Explanation

The group (300- 30- 7) does not follow the consistent mathematical pattern where each subsequent number is one-tenth of the preceding number. In a sequence n₁, n₂, n₃ following this logic, the relationships are n₂ = n₁{10} and n₃ = n₂{10}. While the first operation 300 ÷ 10 = 30 is satisfied, the second operation 30 ÷ 10 results in 3, whereas the third number provided in this group is 7.

Explanation

Based on the statements, we can represent the relationship using set theory: N ⊆ K and K ⊆ P. This implies that all N are part of K, and all K are part of P, which further establishes that all N are part of P (N ⊆ P).

Conclusion I states that some P are not K. While this is possible if the set P is larger than K, the statements do not guarantee it; if P and K are identical sets, the conclusion is false. Since a conclusion must be true in all possible scenarios to follow logically, Conclusion I does not follow. Conclusion II states that no P is N. This contradicts the established relationship N ⊆ P, which confirms that at least all elements of N are also elements of P. Since both conclusions fail to logically follow from the premises, neither conclusion follows.

Explanation

The relationship chain H @ V @ U # W | bpm; E X # Z | bpm; R S is decoded as follows: H is the sister of V, and V is the sister of U, meaning H, V, and U are sisters. U is the wife of W, and W is the brother of E. This places H, V, U, W, and E in the same generation. E is the mother of X, and X is the wife of Z. Z is the brother of R, and R is the mother of S. This places X, Z, and R in the generation below E, while S is in the generation below R.

Z is the husband of X and the brother of R. In this structure, Z belongs to the second generation and is the son-in-law of E. He is not a grandfather to anyone in the sequence, and the character B does not appear in the given relationship string. Therefore, the statement that Z is the maternal grandfather of B is incorrect.

Explanation

In the expression P - Q ÷ R, the symbol ÷ indicates that the first person is the father of the second, so Q ÷ R means Q is the father of R. The symbol - indicates that the first person is the brother of the second, so P - Q means P is the brother of Q. By combining these relationships, P is the brother of R's father Q. Therefore, P is the paternal uncle of R.

Explanation

The given equation is 189 ÷ 2 × 30 + 18 - 5 = 159. To make this equation correct by interchanging the numbers 18 and 30 and the signs ÷ and -, we rewrite the expression as follows:

189 - 2 × 18 + 30 ÷ 5 = 159

According to the BODMAS rule, we perform division and multiplication before addition and subtraction.

First, solve the division part: 30 ÷ 5 = 6

The equation becomes: 189 - 2 × 18 + 6 = 159

Next, solve the multiplication part: 2 × 18 = 36

The equation becomes: 189 - 36 + 6 = 159

Now, solve the addition and subtraction from left to right: 153 + 6 = 159 159 = 159

The calculation confirms that the left-hand side matches the right-hand side.

Explanation

The series follows a specific addition pattern for each corresponding letter in the clusters.

For the first letter, the pattern is +1: L +1 M +1 N +1 O +1 P. For the second letter, the pattern is +2: A +2 C +2 E +2 G +2 I. For the third letter, the pattern is +1: F +1 G +1 H +1 I +1 J. For the fourth letter, the pattern is +3: I +3 L +3 O +3 R +3 U.

By applying these increments to the second cluster MCGL, we get M+1=N, C+2=E, G+1=H, and L+3=O. The resulting cluster is NEHO.

Explanation

The relationship established in the first pair is based on the natural dwelling or habitat of the animal. Birds typically build or inhabit nests as their primary place of shelter and for rearing their young. In the same manner, rabbits are known to live in burrows, which are holes or tunnel systems they excavate in the ground to provide protection and a safe environment for their offspring.

Explanation

The numbers in the given sets follow the pattern of squares of three consecutive integers, represented by n², (n+1)², (n+2)². In the first set (4, 9, 16), the numbers are 2², 3², and 4². In the second set (25, 36, 49), the numbers are 5², 6², and 7². Following this logic, the set (49, 64, 81) consists of 7², 8², and 9², which are the squares of the consecutive integers 7, 8, and 9.

Explanation

Conclusion I is logically valid due to the transitive property of set inclusion. The premises state that All pigs are bears (P ⊆ B) and All bears are tigers (B ⊆ T). By combining these categorical syllogisms, it follows that All pigs are tigers (P ⊆ T).

Conclusion III is a direct logical consequence of Conclusion I. In standard categorical logic, the universal affirmative statement All pigs are tigers (P ⊆ T) implies the particular affirmative statement Some tigers are pigs (T ∩ P ≠ ∅), assuming the existence of the subjects. Since every pig is a tiger, any tiger that is a pig satisfies the condition for Some tigers are pigs.

Conclusion II cannot be definitively concluded. While the statements show that All gorillas are tigers (G ⊆ B ⊆ T), this establishes that gorillas are a subset of tigers, not that all tigers are gorillas. The set of tigers may contain elements outside the set of gorillas. Thus, only conclusions I and III follow.

Explanation

The numerical positions of the letters in the English alphabet for the cluster OIGE are O = 15, I = 9, G = 7, and E = 5. The differences between the positions of consecutive letters are calculated using the relation Diff = Pₙ - Pₙ₊₁. For this cluster, the specific differences are 15 - 9 = 6, 9 - 7 = 2, and 7 - 5 = 2. While the standard pattern followed by the other clusters in the set is to subtract 6, then 1, and then 2, OIGE deviates in the second step by subtracting 2. This inconsistency in the middle difference identifies OIGE as the odd letter-cluster.

Explanation

The pattern followed in the given sets relates the numbers A, B, and C as follows: (A + C) × 3 = B

In the first set (12, 51, 5), the sum of the first and third numbers is multiplied by 3 to obtain the second number: (12 + 5) × 3 = 17 × 3 = 51

In the second set (8, 30, 2), the same logic is applied: (8 + 2) × 3 = 10 × 3 = 30

For the set in option d (11, 51, 6), the sum of the first number 11 and the third number 6 is 17. Multiplying this sum by 3 yields the second number 51: (11 + 6) × 3 = 17 × 3 = 51

Explanation

The coding logic follows a constant addition of 3 to the numerical position of each letter in the English alphabet. For the word LUNGS, the transformation is L(12)+3=O(15), U(21)+3=X(24), N(14)+3=Q(17), G(7)+3=J(10), and S(19)+3=V(22). In the word POWER, the same logic applies as P(16)+3=S(19), O(15)+3=R(18), W(23)+3=Z(26), E(5)+3=H(8), and R(18)+3=U(21).

Applying this +3 shift to ELOQUENT, we get E(5)+3=H(8), L(12)+3=O(15), O(15)+3=R(18), Q(17)+3=T(20), U(21)+3=X(24), E(5)+3=H(8), N(14)+3=Q(17), and T(20)+3=W(23). This results in the code HORTXHQW.

Explanation

After interchanging the numbers 7 and 3 in the equation 7 + 3× 2 - 4÷ 1 = 13, the expression becomes 3 + 7× 2 - 4÷ 1. Using the BODMAS rule, the division operation is performed first, giving 4÷ 1 = 4. Next, the multiplication is performed, resulting in 7× 2 = 14. The expression then simplifies to 3 + 14 - 4. Adding 3 and 14 gives 17, and subtracting 4 from 17 results in 13. This matches the value on the right-hand side of the equation.

Explanation

The transformation follows a pattern where the first and fourth letters of the cluster are swapped, while the second and third letters remain stationary. For the cluster BASE, the first letter B moves to the fourth position and the fourth letter E moves to the first position, resulting in EASB. In MINE, the letters M and E are swapped to form EINM. Applying the same logic to the cluster CALM, the first letter C is swapped with the fourth letter M, while the middle letters A and L stay in place, yielding the cluster MALC.

Explanation

The series follows a specific addition pattern for each position of the letters in the terms. By converting the letters to their numerical positions (A=1, B=2, …, Z=26), the patterns are as follows:

For the first letter: A(1) +7 H(8) +7 O(15) +7 V(22) +7 29 ≡ 3 (C)

For the second letter: B(2) +5 G(7) +5 L(12) +5 Q(17) +5 22 (V)

For the third letter, the differences follow a repeating cycle of +9, +2, +16: N(14) +9 W(23) +2 Y(25) +16 41 ≡ 15 (O) +9 24 (X)

For the fourth letter, the differences follow a repeating cycle of +11, +18, +4: C(3) +11 N(14) +18 32 ≡ 6 (F) +4 10 (J) +11 21 (U)

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

Explanation

To determine the dictionary order of the given words, we compare them character by character from left to right. All the words share the common prefix Tele. Examining the fifth letter of each word provides the following sequence: Telecast has c, Telegram has g, both Telephone and Telepath have p, and Telescope has s. In alphabetical order, c appears first, g appears second, p appears third and fourth, and s appears fifth. To distinguish between the two words starting with Telep, we move to the sixth letter. Telepath features the letter a, while Telephone features the letter h. Since a alphabetically precedes h, Telepath is positioned before Telephone. Consequently, the ordered list is Telecast, Telegram, Telepath, Telephone, and Telescope, placing Telepath in the third position.

Explanation

The numbers in each set follow the logic n₁ + 3 × n₂ = 2 × n₃, where n₁, n₂, and n₃ represent the first, second, and third numbers of the set respectively.

In the first set (52, 10, 41): 52 + 3 × 10 = 52 + 30 = 82 2 × 41 = 82 The relation holds as 82 = 82.

In the second set (46, 18, 50): 46 + 3 × 18 = 46 + 54 = 100 2 × 50 = 100 The relation holds as 100 = 100.

Following the same logic for the set in option a) (68, 26, 73): 68 + 3 × 26 = 68 + 78 = 146 2 × 73 = 146 The relation holds as 146 = 146.

Explanation

The given series follows a pattern of constant subtraction, where each subsequent term is obtained by subtracting 28 from the preceding term.

98 - 28 = 70 70 - 28 = 42 42 - 28 = 14

Following this logic, the missing number is calculated by subtracting 28 from the fourth term:

14 - 28 = -14

We can verify this by checking the final term in the series:

-14 - 28 = -42

This confirms that the missing value in the arithmetic progression is -14.

Explanation

The coding logic involves splitting the word into two equal halves of six letters each. The second half of the word is reversed and placed at the beginning, followed by the first half in its original order. For the word APPRECIATION, the first six letters are APPREC and the last six letters are IATION. Reversing the sequence of the second half, IATION, results in NOITAI. Combining this reversed second half with the original first half, APPREC, produces the code NOITAIAPPREC.

Explanation

This series follows an arithmetic progression pattern where each subsequent term is determined by subtracting a constant value of 35 from the preceding term. The common difference is verified as follows: 600 - 565 = 35, 565 - 530 = 35, 530 - 495 = 35, and 495 - 460 = 35. Applying this same logic to find the missing term, subtract 35 from the last given number: 460 - 35 = 425.

Explanation

The relationship between the terms in each pair follows the mathematical pattern n : 7n².

For the first pair, given n = 8, the second term is calculated as 7 × 8² = 7 × 64 = 448.

For the third pair, given n = 11, the sixth term is calculated as 7 × 11² = 7 × 121 = 847.

Applying the same logic to the second pair where n = 9, the missing term is determined by the calculation 7 × 9² = 7 × 81 = 567.

Explanation

The relationship in the first pair follows a male-to-female gender pattern, as a Bull is a male bovine and a Cow is a female bovine. Applying the same logic to the second pair, a Gander is the term used for a male goose, while the female is referred to as a Goose.

Explanation

The letter-clusters follow a numerical pattern based on their positions in the alphabet where A=1, B=2, …, Z=26. The standard rule for the group is an increment of +1 from the first letter to the second, followed by an increment of +2 from the second letter to the third. For the cluster UVZ, the positions are U=21, V=22, and Z=26. Although the first jump follows the rule (21 + 1 = 22), the second jump is an increment of +4 (22 + 4 = 26) instead of the expected +2. This deviation from the consistent +1 and +2 sequence identifies it as the odd one out.

Explanation

In the expression A - C + B, A - C indicates that A is the brother of C, and C + B indicates that C is the father of B. Therefore, A is the brother of B's father, which defines A as the paternal uncle of B.

Explanation

The series progresses by applying consecutive prime number increments to the first letter and equivalent decrements to the second letter of each cluster.

For the first letter of each cluster: D (4) + 2 = F (6) F (6) + 3 = I (9) I (9) + 5 = N (14) N (14) + 7 = U (21) The values being added are the sequence of prime numbers: 2, 3, 5, and 7. Following this pattern, the next prime number to be added is 11. Adding 11 to U (21) results in 32. In the English alphabet, 32 corresponds to 32 - 26 = 6, which is the letter F.

For the second letter of each cluster: W (23) - 2 = U (21) U (21) - 3 = R (18) R (18) - 5 = M (13) M (13) - 7 = F (6) The values being subtracted are also the sequence of prime numbers: 2, 3, 5, and 7. The next prime number to be subtracted is 11. Subtracting 11 from F (6) results in -5. In the cyclic alphabet, -5 corresponds to 26 - 5 = 21, which is the letter U.

Additionally, each cluster consists of a pair of letters that are opposites in the alphabet, meaning the sum of their numerical positions is 27. Since the first letter of the missing cluster is determined to be F (6), its opposite letter must be 27 - 6 = 21, which is U. Combining these results in the cluster FU.

Explanation

The given statements follow the transitive property of categorical syllogisms. Statement I asserts that all T are G (T ⊆ G), and Statement II asserts that all G are H (G ⊆ H). By combining these two universal affirmative premises, we establish a nested relationship: T ⊆ G ⊆ H. This chain logically necessitates that every member of category T is also a member of category H (T ⊆ H). Conclusion I accurately represents this derived relationship, as it is a direct logical consequence of the containment of T within G and G within H.

Explanation

By swapping the numbers 20 and 40 and the mathematical signs + and -, the equation is rewritten as: 20 + 220 ÷ 2 × 2 - 40 = 200

Following the BODMAS rule, the division operation is performed first: 220 ÷ 2 = 110 The expression becomes: 20 + 110 × 2 - 40

Next, the multiplication operation is executed: 110 × 2 = 220 The expression becomes: 20 + 220 - 40

Performing the addition step: 20 + 220 = 240

Finally, the subtraction is performed: 240 - 40 = 200

The calculated value matches the right-hand side of the equation, making it correct.

Explanation

To make the equation correct, the signs ÷ and + are interchanged. Replacing these signs in the given equation 7 ÷ 9 + 3 × 7 - 3 = 25 results in the following expression:

7 + 9 ÷ 3 × 7 - 3 = 25

Following the BODMAS rule, the operations are performed in order. First, the division operation is executed: 9 ÷ 3 = 3 The equation becomes 7 + 3 × 7 - 3 = 25.

Second, the multiplication operation is executed: 3 × 7 = 21 The equation becomes 7 + 21 - 3 = 25.

Third, the addition operation is performed: 7 + 21 = 28 The equation becomes 28 - 3 = 25.

Finally, the subtraction operation is performed: 28 - 3 = 25 The resulting value is 25, which matches the right-hand side of the equation.

Explanation

The problem requires interchanging the signs × and - and the numbers 4 and 2 in the given equations. Following the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction), the calculations are as follows:

For Equation I: 7 - 5 × 4 + 8 ÷ 2 Applying the interchange of signs (× ↔ -) and numbers (4 ↔ 2), the expression becomes: 7 × 5 - 2 + 8 ÷ 4 Division: 8 ÷ 4 = 2 Multiplication: 7 × 5 = 35 Result: 35 - 2 + 2 = 35

For Equation II: 7 × 3 - 8 ÷ 2 + 4 Applying the interchange of signs (× ↔ -) and numbers (4 ↔ 2), the expression becomes: 7 - 3 × 8 ÷ 4 + 2 Division: 8 ÷ 4 = 2 Multiplication: 3 × 2 = 6 Result: 7 - 6 + 2 = 1 + 2 = 3

The resulting values for equations I and II are 35 and 3.

Explanation

The day of the week repeats every 7 days. To determine the day after a specific number of days, we calculate the remainder when that number is divided by 7 to find the number of odd days.

55 ÷ 7 = 7 weeks and 6 odd days.

Since the remainder is 6, the day after 55 days will be 6 days after Friday. Counting 6 days forward from Friday results in Saturday, Sunday, Monday, Tuesday, Wednesday, and finally Thursday. Alternatively, adding 6 days to a specific day is mathematically equivalent to subtracting 1 day (6 - 7 = -1), and one day before Friday is Thursday.

Explanation

The relationship between the numbers in the given sets follows the logic that the second number is the sum of the first and third numbers, expressed by the formula n₁ + n₃ = n₂.

In the first set (19, 23, 4), the calculation is 19 + 4 = 23. In the second set (13, 27, 14), the calculation is 13 + 14 = 27.

Applying this logic to the set (25, 27, 2), the sum of the first and third numbers results in the second number: 25 + 2 = 27.

Explanation

The expression Z A B - C D % E can be decoded step-by-step to establish the family relationships. Z A indicates that Z is the sister of A. A B indicates that A is the son of B. B - C indicates that B is the mother of C. C D indicates that C is the sister of D. Combining these relations, we find that Z, A, C, and D are all siblings, specifically children of B. Finally, D % E indicates that D is the husband of E. Since Z is the sister of D, and D is the husband of E, it follows that Z is the husband's sister of E.

Explanation

The relationship between the numbers in the provided sets is defined by the following mathematical formula: First - (Second)/(2) = Third

To verify this pattern, consider the first set (182, 170, 97). When half of the second number is subtracted from the first number, the result is the third number: 182 - ¹⁷⁰⁄₂ = 182 - 85 = 97

Applying the same rule to the second set (156, 128, 92): 156 - ¹²⁸⁄₂ = 156 - 64 = 92

In option d, the set (138, 130, 73) follows this logic. Using the whole numbers as required: 138 - ¹³⁰⁄₂ = 138 - 65 = 73

Explanation

The series follows a specific numerical pattern for each letter position across the terms. For the first letter, the sequence progresses by adding 3: N (14) + 3 = Q (17), Q + 3 = T (20), T + 3 = W (23), and W + 3 = Z (26). The second letter follows a pattern of subtracting 6: T (20) - 6 = N (14), N - 6 = H (8), H - 6 = B (2), and B (2) - 6 = V (22). The third letter advances by adding 9: S (19) + 9 = B (28 mod 26), B (2) + 9 = K (11), K + 9 = T (20), and T (20) + 9 = C (29 mod 26). The fourth letter advances by adding 14: M (13) + 14 = A (27 mod 26), A (1) + 14 = O (15), O (15) + 14 = C (29 mod 26), and C (3) + 14 = Q (17). Applying these shifts to the last term WBTC results in the next term ZVCQ.

Explanation

The coding pattern follows a specific structural rearrangement where a seven-letter word is divided into three parts: the first three letters, the middle letter, and the last three letters. The first three letters are reversed, the fourth letter remains fixed in its original position, and the last three letters are reversed.

In the word ANIMISM, the first three letters ANI become INA, the fourth letter M remains M, and the last three letters ISM become MSI, resulting in INAMMSI. Similarly, in EAGERLY, the first three letters EAG become GAE, the fourth letter E remains E, and the last three letters RLY become YLR, resulting in GAEEYLR.

Applying this logic to FULFILL, the first three letters FUL are reversed to LUF. The middle letter F remains at the fourth position. The last three letters ILL are reversed to LLI. Combining these segments yields the code LUFFLLI.

Explanation

The relationship in the given pair is based on a professional and the primary tool they use to perform their work. A carpenter is a skilled worker who uses a hammer as one of their most essential instruments for construction and repair. Following this same logic, a fisherman uses a net as a fundamental tool to catch fish and carry out their profession. This worker-to-tool relationship is consistently maintained in the pair Fisherman : Net.

Explanation

The coding logic involves splitting the given word into two equal halves and reversing the order of letters within each half. Each letter is then shifted forward by two positions in the alphabetical sequence, which corresponds to adding 2 to its positional value (A=1, B=2, ..., Z=26).

For the word SUPRISED, it is divided into two halves: SUPR and ISED.

In the first half, SUPR, the letters are reversed to become RPUS. Applying the +2 shift to each: R (18) + 2 = T (20) P (16) + 2 = R (18) U (21) + 2 = W (23) S (19) + 2 = U (21) The first part of the code is TRWU.

In the second half, ISED, the letters are reversed to become DESI. Applying the +2 shift to each: D (4) + 2 = F (6) E (5) + 2 = G (7) S (19) + 2 = U (21) I (9) + 2 = K (11) The second part of the code is FGUK.

Combining both parts results in the coded word TRWUFGUK.

Explanation

The logic followed in the given sets is that the sum of the first and second numbers is equal to three times the third number. This relationship can be expressed by the formula First + Second = 3 × Third.

In the first set (56, 22, 26): 56 + 22 = 78 3 × 26 = 78

In the second set (34, 20, 18): 34 + 20 = 54 3 × 18 = 54

In the set (78, 54, 44): 78 + 54 = 132 3 × 44 = 132

Explanation

The series follows a specific addition pattern for each corresponding letter position within the clusters. The first letter of each cluster increases by 3 in alphabetical order: C (3) to F (6), F (6) to I (9), I (9) to L (12), and L (12) to O (15). The second letter increases by an increment of 1: B (2) to C (3), C (3) to D (4), D (4) to E (5), and E (5) to F (6). The third letter increases by 2: O (15) to Q (17), Q (17) to S (19), S (19) to U (21), and U (21) to W (23). The fourth letter increases by 1: M (13) to N (14), N (14) to O (15), O (15) to P (16), and P (16) to Q (17). Applying these consistent increments to the cluster FCQN results in the first letter being I (6 + 3), the second letter being D (3 + 1), the third letter being S (17 + 2), and the fourth letter being O (14 + 1), which forms the cluster IDSO.

Explanation

A dentist is a medical professional who specializes in the study, diagnosis, prevention, and treatment of diseases and conditions of the oral cavity, specifically the teeth and gums. Following the same logic of medical specialization, a dermatologist is a physician who specializes in dermatology, which is the branch of medicine dealing with the skin. Dermatologists are trained to diagnose and treat disorders related to the skin, as well as its appendages such as hair and nails.

Explanation

The logic followed in the given sets is that the middle number is the square of the average of the first and third numbers. The relationship is defined by the formula:

Middle Number = ((First Number + Third Number)/(2))²

Applying this to the first given set (21, 225, 9): ((21 + 9)/(2))² = (³⁰⁄₂)² = 15² = 225

Applying this to the second given set (12, 49, 2): ((12 + 2)/(2))² = (¹⁴⁄₂)² = 7² = 49

Following the same pattern for the numbers in option a) (14, 64, 2): ((14 + 2)/(2))² = (¹⁶⁄₂)² = 8² = 64