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

Explanation

To make the equation 95 × 5 + 19 ÷ 2 - 21 = 36 correct, we interchange the ÷ and × signs. The modified expression becomes 95 ÷ 5 + 19 × 2 - 21. Applying the BODMAS rule, we first perform the division: 95 ÷ 5 = 19. Next, we perform the multiplication: 19 × 2 = 38. The expression then simplifies to 19 + 38 - 21. Adding 19 and 38 results in 57, and subtracting 21 from 57 gives 36, which equals the value on the right-hand side of the equation.

Explanation

The coding logic follows a simple alphabetical shift where each letter in the word is replaced by the letter immediately preceding it in the English alphabet, which corresponds to a shift of -1 in positional value.

Applying this pattern to the word COLOR: C - 1 = B O - 1 = N L - 1 = K O - 1 = N R - 1 = Q

By subtracting one from the alphabetical position of each letter in COLOR, the resulting code is BNKNQ.

Explanation

The logical relationship between the terms is established through the transitive property of universal sets. Statement 2 (All cakes are ice creams) and Statement 3 (All ice creams are sweets) can be represented by the set notation Cakes ⊆ Ice creams ⊆ Sweets.

Conclusion III (All cakes are sweets) follows directly from this inclusion chain, as every element in the set of cakes is necessarily an element in the set of sweets.

Conclusion II (Some ice creams are cakes) follows from the rule of conversion. If the entire set of cakes is contained within the set of ice creams, it implies that at least a portion of the ice cream set is occupied by cakes.

Conclusion I (Some sweets are cakes) follows similarly from the derived relation that all cakes are sweets. If Cakes ⊆ Sweets, then the intersection of sweets and cakes is non-empty, meaning some sweets must be cakes. Since all three conclusions are logically valid based on the statements, they all follow.

Explanation

To arrange words in dictionary order, they must be compared letter by letter from left to right. All five words share the same initial prefix Una. The fourth letters of the words are f in Unaffected, r in Unarmed, s in Unasked, t in Unattached, and u in Unauthorized. Arranging these fourth letters in alphabetical order results in the sequence f, r, s, t, and u. This sequence places Unaffected in the first position, Unarmed in the second position, Unasked in the third position, Unattached in the fourth position, and Unauthorized in the fifth position.

Explanation

The relationship between the numbers in each set follows the formula n₁ = 2 × (n₂ + n₃), where the first number is twice the sum of the second and third numbers.

For the first given set (60, 17, 13), the calculation is 2 × (17 + 13) = 2 × 30 = 60. For the second given set (62, 14, 17), the calculation is 2 × (14 + 17) = 2 × 31 = 62.

Following this same logic for the set (56, 15, 13), the sum of the second and third numbers is 15 + 13 = 28. Multiplying this result by 2 yields 2 × 28 = 56, which matches the first number in the set.

Explanation

The series progresses by applying specific arithmetic increments to the alphabetical positions of each letter in the cluster. For the first letter, the pattern is +1, leading from E to F, then to G, H, and finally I. The second letter follows a +3 pattern, moving from D to G, then to J, M, and P. The third letter follows a +1 pattern, advancing from I to J, then to K, L, and M. The fourth letter follows a +3 pattern, shifting from C to F, then to I, L, and O. Combining the resulting letters G, J, K, and I for the third position in the series gives GJKI.

Explanation

To determine the values of the equations, we substitute the interchanged numbers 1 and 3 and the interchanged signs ÷ and ×.

For equation I: The expression 6 + 4 - 9 × 3 ÷ 1 transforms into 6 + 4 - 9 ÷ 1 × 3. Applying the BODMAS rule, we perform division first: 9 ÷ 1 = 9. Next, we perform multiplication: 9 × 3 = 27. Finally, we perform addition and subtraction: 6 + 4 - 27 = 10 - 27 = -17.

For equation II: The expression 4 × 3 - 1 + 8 ÷ 2 transforms into 4 ÷ 1 - 3 + 8 × 2. Applying the BODMAS rule, we perform division: 4 ÷ 1 = 4. Next, we perform multiplication: 8 × 2 = 16. Finally, we perform addition and subtraction: 4 - 3 + 16 = 1 + 16 = 17.

The resulting values for equation I and equation II are -17 and 17 respectively.

Explanation

The series is constructed by applying specific numerical patterns to each letter position in the triplets.

For the first letter, the pattern involves subtracting 6 from the alphabetical position of the previous term. Starting with G (7), 7 - 6 = 1 (A), 1 - 6 ≡ 21 (U), and 21 - 6 = 15 (O). Subtracting 6 from 15 gives 9, which corresponds to the letter I.

For the second letter, the pattern involves subtracting 3 from the alphabetical position. Starting with A (27), 27 - 3 = 24 (X), 24 - 3 = 21 (U), and 21 - 3 = 18 (R). Subtracting 3 from 18 gives 15, which corresponds to the letter O.

For the third letter, the pattern involves adding 1 to the alphabetical position. Starting with R (18), 18 + 1 = 19 (S), 19 + 1 = 20 (T), and 20 + 1 = 21 (U). Adding 1 to 21 gives 22, which corresponds to the letter V.

Assembling these letters yields IOV.

Explanation

The letter-cluster BXCY follows a pattern where the third letter is one position ahead of the first (B + 1 = C) and the fourth letter is one position ahead of the second (X + 1 = Y). This deviates from the consistent logic observed in the group, where the third letter is two positions behind the first (L₃ = L₁ - 2) and the fourth letter is one position ahead of the second (L₄ = L₂ + 1). As a result, BXCY is the only cluster that does not adhere to the L₁ - 2 = L₃ relationship.

Explanation

The group (47- 43- 37) is the odd group because it fails to maintain a constant difference of 4 between its consecutive terms. Specifically, the difference between the first and second terms is 47 - 43 = 4, but the difference between the second and third terms is 43 - 37 = 6. This deviation from the uniform subtraction of 4 distinguishes this group from the consistent arithmetic pattern observed in the other sets.

Explanation

To make the equation correct, we interchange the numbers 78 and 456 and swap the operators ÷ and ×. The modified equation becomes:

456 + 78 - 45 ÷ 12 × 4 = 519

Applying the BODMAS rule, we first perform the division and multiplication:

456 + 78 - (45 / 12) × 4 = 519

456 + 78 - 3.75 × 4 = 519

456 + 78 - 15 = 519

Next, we perform the addition:

534 - 15 = 519

Finally, performing the subtraction yields:

519 = 519

Explanation

The given sequence follows a simple arithmetic progression where each successive term is obtained by adding a constant difference of 2 to the preceding term. Starting from the first term, we have 123 + 2 = 125 and 125 + 2 = 127. Applying the same logic to the third term, the missing number is 127 + 2 = 129. This pattern remains consistent throughout the rest of the series, as 129 + 2 = 131 and 131 + 2 = 133.

Explanation

In the expression P× Q + R, the relation P× Q indicates that P is the father of Q. The relation Q + R indicates that Q is the brother of R. Since Q is the brother of R, Q is necessarily male. Because P is the father of Q and Q is male, it follows that Q is the son of P.

Explanation

The expression O PB@F defines the relationships between the individuals step by step. Starting from the right, B@F indicates that B is the husband of F, which identifies F as the wife and mother in this relationship. Moving left, PB denotes that P is the son of B, and since B and F are married, P is also the son of F. Finally, O P signifies that O is the sister of P. Given that O is the sister of F's son, it concludes that O is the daughter of F.

Explanation

The given statements follow the A + A → A syllogistic pattern. Combining Statement I (All O are C) and Statement II (All C are D) results in the conclusion All O are D.

Conclusion I follows directly from Statement I through conversion. In formal logic, if a universal affirmative statement All A are B is true, its converse Some B are A must also be true. Therefore, All O are C guarantees that Some C are O.

Conclusion II follows from Statement II through the same principle of conversion. Since All C are D is true, the particular affirmative statement Some D are C is logically valid.

Conclusion III (No O is D) is a logical contradiction of the derived fact All O are D. Since both premises are universal affirmative statements, they cannot yield a negative conclusion. Consequently, only conclusions I and II are logically sound.

Explanation

The pattern follows a split-and-reverse logic applied to the letter clusters. Each word consists of seven letters, which are divided into the first four letters and the last three letters. Both segments are then reversed independently to form the new cluster.

For ABILITY, the first four letters ABIL are reversed to LIBA, and the last three letters ITY are reversed to YTI, resulting in LIBAYTI.

For CHRONIC, the first four letters CHRO are reversed to ORHC, and the last three letters NIC are reversed to CIN, resulting in ORHCICIN.

Applying this logic to HEAVILY, the first four letters HEAV are reversed to VAEH, and the last three letters ILY are reversed to YLI. Combining these two reversed segments gives VAEHYLI.

Explanation

To check the validity of the equation, we interchange the numbers 4 and 8. The original equation is: [(√(256))÷ 4]³ + (6)² - (12× 8) + 66 + (36÷ 12) = 65

By swapping 4 and 8, the Left Hand Side (LHS) becomes: [(√(256))÷ 8]³ + (6)² - (12× 4) + 66 + (36÷ 12)

Now, we evaluate the expression using the BODMAS rule: First, solve the square root and the innermost brackets: √(256) = 16. [16 ÷ 8]³ + 36 - 48 + 66 + 3 (2)³ + 36 - 48 + 66 + 3

Next, calculate the cube and combine the terms: 8 + 36 - 48 + 66 + 3 44 - 48 + 69 -4 + 69 = 65

The calculated value is 65, which matches the Right Hand Side (RHS) of the equation.

Explanation

The logic followed in the given sets is based on the geometric progression of numbers, where the square of the middle term is equal to the product of the first and third terms. This can be expressed by the formula b² = a × c.

In the set (4, 6, 9): a = 4, b = 6, c = 9 a × c = 4 × 9 = 36 b² = 6² = 36

In the set (25, 10, 4): a = 25, b = 10, c = 4 a × c = 25 × 4 = 100 b² = 10² = 100

Applying the same logic to the set (6, 36, 216): a = 6, b = 36, c = 216 a × c = 6 × 216 = 1296 b² = 36² = 1296

Since a × c = b², the numbers in this set are related in the same way as the numbers in the given sets.

Explanation

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

For TOP: T = 20, O = 15, P = 16 Sum = 20 + 15 + 16 = 51 Code = 51 × 2 = 102

For BAD: B = 2, A = 1, D = 4 Sum = 2 + 1 + 4 = 7 Code = 7 × 2 = 14

Applying the same logic to DOG: D = 4, O = 15, G = 7 Sum = 4 + 15 + 7 = 26 Code = 26 × 2 = 52

Explanation

The logic follows a pattern where the letters of the cluster are taken in reverse order and incremented by consecutive even numbers +2, +4, +6, and +8 respectively. In LAMP : RQGT, the last letter P (16) + 2 = R (18), the third letter M (13) + 4 = Q (17), the second letter A (1) + 6 = G (7), and the first letter L (12) + 8 = T (20).

Similarly, in GAME : GQGO, the fourth letter E (5) + 2 = G (7), the third letter M (13) + 4 = Q (17), the second letter A (1) + 6 = G (7), and the first letter G (7) + 8 = O (15).

Applying this logic to GOAT: T (20) + 2 = V (22) A (1) + 4 = E (5) O (15) + 6 = U (21) G (7) + 8 = O (15)

The resulting letter-cluster is VEUO.

Explanation

The relationship between the numbers in each pair follows the mathematical rule y = 3x - 6, where x is the first number and y is the second number.

For the first pair 6:12, the first number 6 is multiplied by 3 and then 6 is subtracted from the result to obtain the second number: 6 × 3 - 6 = 18 - 6 = 12

For the second pair 9:21, the same logic is applied to the first number 9: 9 × 3 - 6 = 27 - 6 = 21

To find the missing number related to the fifth number 3, we apply the established pattern: 3 × 3 - 6 = 9 - 6 = 3

Explanation

The coding logic is determined by the number of letters in each word of the phrase. In the first example, Laptop has 6 letters, is has 2, a has 1, and computer has 8, resulting in the code 6218. In the second example, Computer has 8 letters, is has 2, a has 1, and machine has 7, forming the code 8217. Applying this same rule to the phrase Machine makes our life easy, we count the letters in each word: Machine (7), makes (5), our (3), life (4), and easy (4). Combining these counts in sequence gives the code 75344.

Explanation

By placing the employees according to the given conditions, the sequence from left to right is R, M, L, K, O, N, P, Q, and S. In this order, O is at the fifth position and L is at the third position. Since there is only one person, K, between L and O, L is positioned second to the left of O. The statement claiming L is third to the left of O is inaccurate because the person sitting three places to the left of O is actually M.

Explanation

The numerical positions of the letters in the English alphabet reveal a specific pattern of addition between consecutive letters. In the clusters TWY (T=20, W=23, Y=25), LOQ (L=12, O=15, Q=17), and BEG (B=2, E=5, G=7), the difference between the first and second letter is +3, while the difference between the second and third letter is +2. However, in GJM (G=7, J=10, M=13), the pattern is a constant addition of +3 for both steps since 7+3=10 and 10+3=13. This deviation from the +3, +2 logic identifies GJM as the different cluster.

Explanation

The logic follows a 3-1-3 split of the letters in the word. Each part undergoes a specific transformation:

Last three letters (LVE): Replace each letter with its opposite letter in the alphabet (where the sum of positional values is 27) and reverse the order. L (12) → O (15) V (22) → E (5) E (5) → V (22) Reversing the opposites (O, E, V) gives VEO.

Middle letter (O): Subtract 6 from its positional value. O (15) - 6 = 9 (I)

First three letters (RES): Add 3 to the positional value of each letter and reverse the order. R (18) + 3 = 21 (U) E (5) + 3 = 8 (H) S (19) + 3 = 22 (V) Reversing the results (U, H, V) gives VHU.

Combining these segments in order results in VEOIVHU.

To verify with HARMONY: ONY: Opposites are L, M, B. Reversed → BML. M: 13 - 6 = 7 (G). HAR: H+3=11 (K), A+3=4 (D), R+3=21 (U). Reversed → UDK. Result: BMLGUDK.

Explanation

The coding pattern follows a simple addition of 3 to the numerical position of each letter in the English alphabet. In the word ESTEEM, the transformations are E (5) + 3 = H (8), S (19) + 3 = V (22), T (20) + 3 = W (23), E (5) + 3 = H (8), E (5) + 3 = H (8), and M (13) + 3 = P (16).

Applying this logic to the word DOCTOR, the transformations are: D (4) + 3 = G (7) O (15) + 3 = R (18) C (3) + 3 = F (6) T (20) + 3 = W (23) O (15) + 3 = R (18) R (18) + 3 = U (21)

Following this sequence, the coded word for DOCTOR is GRFWRU.

Explanation

By replacing the letters with their respective mathematical operators, where A denotes addition (+), B denotes multiplication (×), C denotes subtraction (-), and D denotes division (÷), the given expression is converted as follows: 66 + (132 ÷ 12) - (4 + 3) × (15 ÷ 5) + 16 × (-3)

Following the BODMAS rule, the operations within the parentheses are solved first: 132 ÷ 12 = 11 4 + 3 = 7 15 ÷ 5 = 3

Substituting these values back into the expression, we get: 66 + 11 - 7 × 3 + 16 × (-3)

Next, perform the multiplication operations: 7 × 3 = 21 16 × (-3) = -48

The expression now simplifies to: 66 + 11 - 21 - 48

Finally, perform the addition and subtraction from left to right: 77 - 21 - 48 56 - 48 = 8

Explanation

Substitute the given symbols with their respective mathematical operators to rewrite the expression: 23 + 105 ÷ 15 × 6 - 29. Following the BODMAS rule, perform the operations in the order of Division, Multiplication, Addition, and then Subtraction.

First, perform the division: 105 ÷ 15 = 7. The expression simplifies to 23 + 7 × 6 - 29.

Next, perform the multiplication: 7 × 6 = 42. The expression simplifies to 23 + 42 - 29.

Now, perform the addition: 23 + 42 = 65. The expression becomes 65 - 29.

Finally, perform the subtraction: 65 - 29 = 36.

Explanation

The series is completed by dividing the sequence into four groups of six letters each. The pattern involves a cyclical shift or a structured permutation of the letters g, f, o, d, k, and m. By sequentially placing the letters from option b) into the blanks, the series follows a logical progression:

Group 1: g f o d k m Group 2: f o k g o d Group 3: m o k g f o Group 4: d k m o k g

When the letters from fokgodmok are inserted into the blanks of the provided string g_o_d_k_m_f_o_k_k_g_f_o_d_k_m, it creates a repeating and shifting structure of these six distinct letters. The complete sequence formed is:

g (f) o (o) d (k) m (g) f (o) k (d) k (m) g (o) f (o) d (k) m (k) ...

This arrangement ensures that each segment contains the core letters of the set, maintaining the internal logic of the letter-series completion.

Explanation

The series follows a consistent decrement pattern for each position within the letter-clusters. For the first letter of each cluster, the position in the English alphabet decreases by 4: R(18) - 4 = N(14), N(14) - 4 = J(10), J(10) - 4 = F(6), and F(6) - 4 = B(2).

For the second letter, the position decreases by 2: S(19) - 2 = Q(17), Q(17) - 2 = O(15), O(15) - 2 = M(13), and M(13) - 2 = K(11).

For the third letter, the position decreases by 1: X(24) - 1 = W(23), W(23) - 1 = V(22), V(22) - 1 = U(21), and U(21) - 1 = T(20).

Applying these operations to the last known cluster FMU results in the letter-cluster BKT.

Explanation

The words are arranged in a logical sequence based on an increasing order of spatial scale and layers, moving from the internal structure of a planet to the vastness of space. The Core (1) represents the innermost part of a planetary body. Moving outward, the next layer is the Surface (4). Above the surface lies the Atmosphere (2), which is the gaseous envelope surrounding the planet. Expanding to a cosmic scale, a planet exists within a Galaxy (5), which is a massive system of stars and solar systems. Finally, the Universe (3) is the most inclusive category, encompassing all galaxies, matter, and energy in existence.

Explanation

The relationship between the numbers in each pair follows the pattern n : n × ¹⁶⁄₃.

In the first pair, the first number is 21. Applying the pattern, 21 × ¹⁶⁄₃ = 7 × 16 = 112.

In the third pair, the first number is 51. Applying the pattern, 51 × ¹⁶⁄₃ = 17 × 16 = 272.

To find the missing number related to 36, we apply the same calculation: 36 × ¹⁶⁄₃ = 12 × 16 = 192.

Explanation

Using the method of alligation, the ratio of the number of male teachers to female teachers is found by comparing the differences between the individual averages and the overall average.

Ratio of Males to Females = (Overall Average - Female Average) : (Male Average - Overall Average) Ratio = (2000 - 1200) : (2500 - 2000) Ratio = 800 : 500 = 8 : 5

The number of male teachers is given as 16, which corresponds to 8 parts in the calculated ratio. Therefore, 1 part represents 2 teachers (16 / 8 = 2). Since the number of female teachers is represented by 5 parts, the total count is: 5 × 2 = 10

Explanation

The matrix follows a specific logic where the third column is derived from the first two columns using a combination of a decreasing multiplier and an adjustment based on an arithmetic progression. The formula is: (Column 1 + Column 2) × Multiplier - Adjustment = Column 3

For the first row: (12 + 8) × 6 - 20 = 20 × 6 - 20 = 120 - 20 = 100

For the second row: (18 + 6) × 5 - 9 = 24 × 5 - 9 = 120 - 9 = 111

For the third row: (15 + 4) × 4 - (-2) = 19 × 4 + 2 = 76 + 2 = 78

In this pattern, the multipliers are in a decreasing sequence (6, 5, 4), and the adjustments (20, 9, -2) follow an arithmetic progression with a common difference of -11 (9 - 20 = -11 and -2 - 9 = -11). Applying this logic, the missing number is 78.

Explanation

The statement All bats are birds implies that the set of bats is a subset of the set of birds (B ⊆ Br). The statement Some rats are bats indicates that there is a non-empty intersection between the set of rats and the set of bats (R ∩ B ≠ ∅). Since every bat is a bird, any rat that belongs to the bat category must necessarily belong to the bird category, which confirms that some rats are birds. Furthermore, the universal statement All bats are birds can be logically converted into the particular statement Some birds are bats. Because the statements establish the existence of bats, it follows that there are members of the bird category that are also bats. Therefore, both conclusions I and II are logically sound.

Explanation

The coding logic follows the pattern where the code is equal to the sum of the reverse positional values of the letters minus the total number of letters in the word. The reverse positional value is calculated as 27 minus the forward alphabetical position of the letter.

For ROUBST (6 letters): R = 27 - 18 = 9 O = 27 - 15 = 12 U = 27 - 21 = 6 B = 27 - 2 = 25 S = 27 - 19 = 8 T = 27 - 20 = 7 Sum of reverse values = 9 + 12 + 6 + 25 + 8 + 7 = 67 Code = 67 - 6 = 61

For FORTUNATE (9 letters): F = 27 - 6 = 21 O = 27 - 15 = 12 R = 27 - 18 = 9 T = 27 - 20 = 7 U = 27 - 21 = 6 N = 27 - 14 = 13 A = 27 - 1 = 26 T = 27 - 20 = 7 E = 27 - 5 = 22 Sum of reverse values = 21 + 12 + 9 + 7 + 6 + 13 + 26 + 7 + 22 = 123 Code = 123 - 9 = 114

Explanation

The series follows a pattern where each subsequent number is obtained by adding the square of consecutive natural numbers starting from 3. The differences between consecutive terms are calculated as follows:

67 - 58 = 9 = 3² 83 - 67 = 16 = 4² 108 - 83 = 25 = 5²

Following this logic, the next difference in the sequence must be 6² = 36. Adding this value to the last term gives the missing number: 108 + 36 = 144.

Explanation

Decoding the expression W @ S % K G | U | T @ R + C involves tracing the family tree through the defined symbols. W @ S indicates W is the brother of S, and S % K means S is the son of K, implying K is the father of W and S. The sequence K G | U establishes that K is the husband of G and G is the mother of U, which makes G the mother of W, S, and U. Further, U | T shows U is the mother of T, and T @ R confirms T and R are siblings. Since U is the mother of T and R, and G is the mother of U, G is the mother of R's mother. This relationship defines G as the maternal grandmother of R.

Explanation

The code language used here is based on the number of letters in each word of the sentence. In the phrase Taj is in Agra, the word Taj consists of 3 letters, is consists of 2, in consists of 2, and Agra consists of 4, forming the code 3224. Similarly, in the phrase Agra is near Delhi, Agra has 4 letters, is has 2, near has 4, and Delhi has 5, resulting in the code 4245. Applying this logic to the phrase I like all fruits, the word I contains 1 letter, like contains 4 letters, all contains 3 letters, and fruits contains 6 letters. Combining these counts in the order they appear gives the code 1436.

Explanation

By substituting the signs ×, ÷, =, +, - into the given expression, we get:

15 × 1411 ÷ 83 = 137 + 218 - 100

To solve the Left-Hand Side (LHS), first perform the division according to the BODMAS rule: 1411 ÷ 83 = 17 Now multiply the result by 15: 15 × 17 = 255

Next, solve the Right-Hand Side (RHS): 137 + 218 - 100 355 - 100 = 255

Since the LHS evaluates to 255 and the RHS evaluates to 255, the equation is balanced.

Explanation

Let the present ages of Charvi and Vaishnavi be 4x and 5x respectively. According to the given conditions, Yuvika's age can be represented in two different ways. Since Yuvika is 2 years older than Charvi, her age is 4x + 2. Since she is also 5 years younger than Vaishnavi, her age is 5x - 5.

By equating these two expressions for Yuvika's age: 4x + 2 = 5x - 5 5x - 4x = 2 + 5 x = 7

The present age of Vaishnavi is 5x, which is 5 × 7 = 35 years.

Explanation

The series follows a logic of increasing differences between consecutive terms. By subtracting each term from the one following it, the differences are 53 - 39 = 14, 69 - 53 = 16, and 87 - 69 = 18. These differences are in an arithmetic progression where each subsequent difference increases by 2. Therefore, the next difference after 18 is 18 + 2 = 20. The missing number is obtained by adding this difference to the previous term: 87 + 20 = 107.

Explanation

The cluster UT is unique because it contains a vowel, U, whereas the other clusters consist entirely of consonants. In terms of alphabetical positions, U = 21 and T = 20, resulting in a difference of 21 - 20 = 1. This contrasts with the other clusters where the difference between the letters (or the final two letters) is consistently 2, as seen in J(10) - H(8) = 2, P(16) - N(14) = 2, and T(20) - R(18) = 2.

Explanation

The pattern followed in the given analogy is (n - 1)², where n is the first number in each pair. In the first pair, 28 : 729, the calculation is (28 - 1)² = 27² = 729. Applying the same logic to the second pair, 32 : ?, we subtract one from the third number and square the result: (32 - 1)² = 31². Since 31 × 31 = 961, the missing number is 961.

Explanation

The given series is completed by dividing it into four groups of five letters each. By placing the letters from option a) sequentially into the blanks, the series follows a pattern where each group contains the letters K, L, M, and N, with certain letters repeated:

First Group (1-5): K L M M N The letters used are K, L, M, and N, with the letter M appearing twice.

Second Group (6-10): L M N K K The letters used are L, M, N, and K, with the letter K appearing twice.

Third Group (11-15): N L L N K The letters used are N, L, and K. Here, the letters L and N are repeated.

Fourth Group (16-20): K M N L M The letters used are K, M, N, and L, with the letter M appearing twice.

By filling the blanks with the letters L, M, M, M, K, L, K, N, we get: K L M M N | L M N K K | N L L N K | K M N L M

This arrangement perfectly matches the fixed letters provided in the original string: K (1), N (5), L (6), N (8), K (9), N (11), L (13), N (14), K (15), M (17), L (19), and M (20).

Explanation

The numbers in the matrix follow a column-wise pattern where the third row element is the product of the first row element and the successor of the second row element. This relationship is defined by the formula Row₁ × (Row₂ + 1) = Row₃.

In the first column, the calculation is 7 × (3 + 1) = 7 × 4 = 28.

In the second column, the calculation is 9 × (8 + 1) = 9 × 9 = 81.

In the third column, let the unknown number be x. Using the established formula, we set up the equation 5 × (x + 1) = 50. Solving for x: x + 1 = ⁵⁰⁄₅ x + 1 = 10 x = 9

Explanation

The logic followed in the given sets is that the third number is the product of the first and second numbers. In the first set (11, 13, 143), the operation is 11 × 13 = 143. In the second set (17, 11, 187), the operation is 17 × 11 = 187. Applying the same logic to the numbers in option c, we get 3 × 4 = 12.

Explanation

The coding logic involves shifting each letter of the word forward by 10 positions in the alphabet. For the word GATE, the alphabetical positions are G=7, A=1, T=20, and E=5. Adding 10 to each gives 17(Q), 11(K), 30 (which is 30-26=4, or D), and 15(O), resulting in the code QKDO. Applying this same +10 shift to the word PLAN, where the positions are P=16, L=12, A=1, and N=14, we get 16+10=26(Z), 12+10=22(V), 1+10=11(K), and 14+10=24(X). The letter sequence is ZVKX. The prefix 4 in the code represents the total number of letters in the word PLAN, which consists of four letters, resulting in the code 4ZVKX.

Explanation

The series follows a pattern where the positional value of each letter in the cluster increases according to a sequence of decreasing increments: +5, +4, and +3.

For the first letter of each cluster, the progression is G(7) + 5 = L(12), L(12) + 4 = P(16), and P(16) + 3 = S(19).

For the second letter of each cluster, the progression is H(8) + 5 = M(13), M(13) + 4 = Q(17), and Q(17) + 3 = T(20).

For the third letter of each cluster, the progression is B(2) + 5 = G(7), G(7) + 4 = K(11), and K(11) + 3 = N(14).

Following this logic, the cluster that replaces the question mark is composed of the letters S, T, and N.

Explanation

The relationship between the terms is based on the numerical position (rank) of each letter in the English alphabet. The transformation follows a specific rule depending on whether the rank is a single digit or a double digit:

Letters with an alphabet rank from 1 to 9 (A to I) are incremented by 1. Letters with an alphabet rank from 10 to 26 (J to Z) are incremented by 2.

Applying this rule to DOGMATIC: D (4) is ≤ 9, so 4 + 1 = 5 (E) O (15) is > 9, so 15 + 2 = 17 (Q) G (7) is ≤ 9, so 7 + 1 = 8 (H) M (13) is > 9, so 13 + 2 = 15 (O) A (1) is ≤ 9, so 1 + 1 = 2 (B) T (20) is > 9, so 20 + 2 = 22 (V) I (9) is ≤ 9, so 9 + 1 = 10 (J) C (3) is ≤ 9, so 3 + 1 = 4 (D) The resulting code is EQHOBVJD.

Applying the same rule to PRODUCTS: P (16) is > 9, so 16 + 2 = 18 (R) R (18) is > 9, so 18 + 2 = 20 (T) O (15) is > 9, so 15 + 2 = 17 (Q) D (4) is ≤ 9, so 4 + 1 = 5 (E) U (21) is > 9, so 21 + 2 = 23 (W) C (3) is ≤ 9, so 3 + 1 = 4 (D) T (20) is > 9, so 20 + 2 = 22 (V) S (19) is > 9, so 19 + 2 = 21 (U)

The resulting code is RTQEWDVU.