SSC CGL Tier 1 2024 General Intelligence & Reasoning Questions with Solutions

Explanation

The logic followed in the given sets is that the product of the difference between the first and second numbers and two equals the third number. The relationship is expressed by the formula: (First Number - Second Number) × 2 = Third Number

For the set (84, 63, 42): (84 - 63) × 2 = 21 × 2 = 42

For the set (79, 47, 64): (79 - 47) × 2 = 32 × 2 = 64

Applying the same logic to the numbers in option d, (71, 53, 36): (71 - 53) × 2 = 18 × 2 = 36

Explanation

The series follows a systematic pattern where each element decreases by a fixed interval.

The first letter of each term moves backward by two positions in the English alphabet: M (13) to K (11), K (11) to I (9), and I (9) to G (7). Following this n - 2 pattern, the next letter is 7 - 2 = 5, which corresponds to E.

The second letter also moves backward by two positions: Y (25) to W (23), W (23) to U (21), and U (21) to S (19). Applying the n - 2 rule, the next letter is 19 - 2 = 17, which corresponds to Q.

The numerical part of each term decreases by 4 in each step: 84 to 80, 80 to 76, and 76 to 72. Subtracting 4 from the last number gives 72 - 4 = 68.

Combining the results, the next term in the series is EQ 68.

Explanation

The relationship in the given pair is that of a physical quantity and its standard SI unit. Frequency, defined as the number of cycles per second, is measured in the unit Hertz (Hz). Similarly, Illuminance is the physical quantity that measures the total luminous flux incident on a surface per unit area, and its derived SI unit is the Lux (lx), where 1 lx = 1 lm/m².

Explanation

The letter-cluster NOPPSS is the odd one out because its alphabetical positional increments follow a pattern of +1, +1, 0, +3, and 0. Based on the numerical positions of the letters N(14), O(15), P(16), P(16), S(19), and S(19), the sequence of jumps between consecutive letters is +1, +1, 0, +3, and 0. This arrangement fails to align with the +2, 0, +1, +2, and 0 pattern shared by the other clusters in the set. In this specific cluster, the second and third letters are distinct and the fifth letter is separated from the fourth by a three-unit jump, whereas the standard structure for the group requires the second and third letters to be identical and the jump between the fourth and fifth letters to be exactly two units.

Explanation

The number pair 24:4 is the odd one out because the first number is six times the second number, representing a ratio of 6:1. This deviates from the uniform mathematical relationship followed by the other pairs, where the first number is exactly 1.5 times the second number, maintaining a consistent ratio of 3:2. Specifically, 12 = 8 × 1.5, 36 = 24 × 1.5, and 72 = 48 × 1.5, whereas 24 = 4 × 6.

Explanation

To determine how many letters remain in the same position, we first list the letters of the word IMPROVE and then arrange them in alphabetical order.

Original word: 1: I 2: M 3: P 4: R 5: O 6: V 7: E

Alphabetical order of the letters (E, I, M, O, P, R, V): 1: E 2: I 3: M 4: O 5: P 6: R 7: V

Comparing the two sequences position by position: Position 1: I changes to E Position 2: M changes to I Position 3: P changes to M Position 4: R changes to O Position 5: O changes to P Position 6: V changes to R Position 7: E changes to V

None of the letters occupy the same position in the alphabetical arrangement as they did in the original word. Thus, the count of unchanged positions is zero.

Explanation

The given statements establish that the set of crows and the set of eagles are both subsets of the set of parrots, and the set of parrots is itself a subset of the set of birds. This relationship can be expressed through the transitive property: if all eagles are parrots (E ⊆ P) and all parrots are birds (P ⊆ B), then it is logically necessary that all eagles are birds (E ⊆ B). In categorical logic, the universal affirmative statement all A are B implies the particular affirmative statement some B are A. Therefore, if all eagles are birds, it follows that some birds are eagles, making conclusion II a direct logical consequence of the premises.

Explanation

The series follows a pattern where the difference between consecutive numbers decreases by 1 at each step. By calculating the differences between the known initial terms, we find 81 - 65 = 16 and 65 - 50 = 15. Continuing this arithmetic sequence of differences, the next difference must be 14. Applying this to the third term, we get 50 - 14 = 36. To verify the pattern, the subsequent differences should be 13 and 12. Subtracting 13 from 36 results in 23, and subtracting 12 from 23 results in 11, both of which match the remaining numbers in the series. Thus, the missing number is obtained by 50 - 14 = 36.

Explanation

The given series is X _ _ Y _ _ X _ _ X _ _ X _ _. By observing the pattern and the total number of elements, we can divide the series into groups of three. The sequence follows a repeating triplet pattern of X Y X, Y X Y, X Y X, Y X Y.

The structure of the series with blanks is: (X _ _) | (Y _ _) | (X _ _) | (X _ _) | (X _ _)

By placing the letters from the correct option YXXXYXX sequentially into the blanks: (X Y X) | (Y X X) | (X X Y) | (X X X) | (X …)

However, a more consistent logical pattern for such series in competitive exams like the SSC MTS (September 23, 2024) often follows a shifting or cyclical repetition. Applying the combination YXXXYXX to the standard format X _ Y _ X _ X _ X _ X _ (assuming single underscores) creates the following sequence:

X (Y) Y (X) X (X) X (Y) X (X) X (X)

The pattern is formed by dividing the series into groups of four: X Y Y X | X X X Y | X X X X

This identifies a progressive increase in the count of X within each block while maintaining a structured displacement of Y. The combination of letters YXXXYXX completes the sequence according to the distributive logic required by the series' structure.

Explanation

To determine the relationship between T and X, we decode the expression T + U - V × W + X step-by-step using the provided definitions:

W + X: According to the fourth definition (X + Y means X is the mother of Y), W is the mother of X. V × W: According to the third definition (where the symbol × corresponds to the husband relation), V is the husband of W. Since W is the mother of X, V is the father of X. U - V: According to the second definition (X - Y means X is the son of Y), U is the son of V. This means U and X are siblings (both are children of V and W). T + U: According to the first definition (X + Y means X is the sister of Y), T is the sister of U.

Since T is the sister of U, and U and X are siblings (children of the same parents, V and W), T is also the sister of X.

Explanation

To find the value of the expression 15 - 7 ÷ 4 + 36 × 9 after interchanging the signs, we apply the standard logic for such mathematical reasoning problems. The instructions imply two pairs of interchanges: + is swapped with -, and × is swapped with ÷.

Replacing the symbols in the original equation according to these rules:

• becomes + ÷ becomes ×

• becomes - × becomes ÷

The new equation is: 15 + 7 × 4 - 36 ÷ 9

Following the BODMAS rule, we perform division and multiplication first: 36 ÷ 9 = 4 7 × 4 = 28

Substituting these values back into the equation: 15 + 28 - 4

Next, we perform the addition: 15 + 28 = 43

Finally, we perform the subtraction: 43 - 4 = 39

Explanation

The series follows a specific arithmetic pattern for each letter position based on their numerical values in the alphabet.

For the first letter, the sequence is X (24), V (22), T (20), and R (18). The value decreases by 2 at each step, so the next letter is 18 - 2 = 16, which is P.

For the second letter, the sequence is J (10), L (12), N (14), and P (16). The value increases by 2 at each step, so the next letter is 16 + 2 = 18, which is R.

For the third letter, the sequence is U (21), S (19), Q (17), and O (15). The value decreases by 2 at each step, so the next letter is 15 - 2 = 13, which is M.

For the fourth letter, the sequence is M (13), O (15), Q (17), and S (19). The value increases by 2 at each step, so the next letter is 19 + 2 = 21, which is U.

By combining the resulting letters P, R, M, and U, the next term in the series is PRMU.

Explanation

By comparing the word FLAKE and its code | 2348 with the word LAKES and its code 23@84, we can identify the common elements. The letters L, A, K, and E are present in both words, and the characters 2, 3, 4, and 8 are present in both sets of codes. The letter S is the only letter in LAKES that is not present in FLAKE. Correspondingly, the symbol @ is the only character in the code 23@84 that is not present in the code | 2348. This direct comparison identifies the unique letter S with the unique symbol @.

Explanation

The numerical relationship observed in the given pairs is that the second number is equal to twice the square of the first number. This can be expressed by the formula y = 2x², where x is the first number and y is the second number.

For the first given pair 4:32: 2 × 4² = 2 × 16 = 32

For the second given pair 7:98: 2 × 7² = 2 × 49 = 98

Applying this same mathematical logic to the pair 3:18: 2 × 3² = 2 × 9 = 18

Explanation

The coding logic involves taking the numerical position of each letter in the English alphabet (where A = 1, B = 2, ..., Z = 26) and adding 2 to each value.

For PFKR, the alphabetical positions are: P = 16 F = 6 K = 11 R = 18

Applying the logic (Position + 2): 16 + 2 = 18 6 + 2 = 8 11 + 2 = 13 18 + 2 = 20

The resulting code is 18-8-13-20. This follows the same pattern seen in WJSL (23, 10, 19, 12 becoming 25, 12, 21, 14) and DUOH (4, 21, 15, 8 becoming 6, 23, 17, 10).

Explanation

In association football, a standard team consists of 11 players on the field at any given time, one of whom must be the goalkeeper. The pair listed in this option provides an incorrect number of players for the sport, whereas the other pairs correctly identify the standard number of participants in a team or individual competitive setting for those respective sports.

Explanation

The given series is composed of four groups of five letters each. By dividing the sequence into these groups, the pattern becomes clear: MEDIC, MFDIC, MGDIC, MHDIC.

In each group of five, the first letter (M), third letter (D), fourth letter (I), and fifth letter (C) remain constant throughout the series. The only variation occurs in the second letter of each group, which follows a sequential alphabetical progression: E in the first group, F in the second group, G in the third group, and H in the fourth group.

By placing the letters D, F, M, C, and I into the respective blanks, we satisfy the requirements of this repeating pattern. Specifically, the first blank completes the word MEDIC (D), the second blank completes MFDIC (F), the third and fourth blanks complete MGDIC (M and C), and the fifth blank completes MHDIC (I). Therefore, the sequential combination DFMCI logically completes the series.

Explanation

The series follows a pattern where each term is increased by consecutive prime numbers starting from 7.

52 - 45 = 7 63 - 52 = 11 76 - 63 = 13 93 - 76 = 17

The differences are 7, 11, 13, and 17, which are consecutive prime numbers. The next prime number in the sequence after 17 is 19. To find the missing number, add 19 to the last term of the series: 93 + 19 = 112.

Explanation

The pair 14 - 196 is the odd one out because it follows the rule n² = second number, where 14² = 196. The other pairs in the group follow the relationship n × (n + 1) = second number, as shown by 17 × 18 = 306, 21 × 22 = 462, and 12 × 13 = 156. Applying the logic of the group to the number 14 would result in 14 × 15 = 210.

Explanation

The relationship between the numbers in the given pairs is determined by a constant difference. In the first pair, the number 21 is obtained by adding 8 to the number 13, such that 13 + 8 = 21. In the second pair, the number 43 is obtained by adding the same constant 8 to the number 35, such that 35 + 8 = 43. Following this uniform arithmetic logic, the number related to 66 is found by adding 8 to it: 66 + 8 = 74.

Explanation

The relationship between the letter-clusters is based on the concept of opposite letters, where the sum of the positional values of the corresponding letters in the English alphabet is always 27.

In the first pair MSD : NHW: M (13) + N (14) = 27 S (19) + H (8) = 27 D (4) + W (23) = 27

In the second pair OAE : LZV: O (15) + L (12) = 27 A (1) + Z (26) = 27 E (5) + V (22) = 27

Applying the same logic to the fifth letter-cluster NIP: N (14) + M (13) = 27, so the first letter is M. I (9) + R (18) = 27, so the second letter is R. P (16) + K (11) = 27, so the third letter is K.

Explanation

In the expression W ! R x Y ? O | P, the code W ! R establishes that W is the wife of R, making W the female parent. The segment R x Y indicates that R is the father of Y; combined with the previous relation, this confirms W is the mother of Y. The code Y ? O specifies that Y is the mother of O. The final part, O | P, denotes that O is the brother of P, which means Y is also the mother of P. Consequently, W is the mother of Y and Y is the mother of P, which confirms that W is the mother's mother of P.

Explanation

The mathematical relationship between the numbers in each set follows the pattern x² - (x - 1) = y, where x represents the first number and y represents the second number. This logic can also be simplified as x(x - 1) + 1 = y.

For the first given set (6, 31): 6² - (6 - 1) = 36 - 5 = 31

For the second given set (10, 91): 10² - (10 - 1) = 100 - 9 = 91

Applying this same pattern to the set in option a), which is (8, 57): 8² - (8 - 1) = 64 - 7 = 57

Alternatively, using the simplified form x(x - 1) + 1: 8 × (8 - 1) + 1 = 8 × 7 + 1 = 56 + 1 = 57

Explanation

The word LAUNDER consists of the letters L, A, U, N, D, E, and R. To determine if any letters remain in their original positions, the letters must be rearranged into English alphabetical order.

The original positions in the word LAUNDER are: 1: L, 2: A, 3: U, 4: N, 5: D, 6: E, 7: R.

The alphabetical order of these letters is: 1: A, 2: D, 3: E, 4: L, 5: N, 6: R, 7: U.

Comparing the two sequences: Position 1: L vs A (Changed) Position 2: A vs D (Changed) Position 3: U vs E (Changed) Position 4: N vs L (Changed) Position 5: D vs N (Changed) Position 6: E vs R (Changed) Position 7: R vs U (Changed)

None of the letters occupy the same position in the alphabetically sorted sequence as they did in the original word. Therefore, the total number of letters with unchanged positions is zero.

Explanation

The logic follows a specific partitioning and reversal pattern. Each seven-letter word is divided into two segments: the first four letters and the remaining three letters. Both segments are then individually reversed to form the new cluster.

In the case of EXPENSE, the first four letters EXPE are reversed to EPXE and the last three letters NSE are reversed to ESN, giving EPXEESN. Similarly, for FASHION, the first four letters FASH reverse to HSAF and the last three letters ION reverse to NOI, resulting in HSAFNOI.

Applying this rule to FORTUNE, the first four letters FORT are reversed to TROF, and the final three letters UNE are reversed to ENU. Combining these segments yields the letter cluster TROFENU.

Explanation

To solve the equation, we perform the required symbol interchanges: '+' and '-' are interchanged (+ ↔ -), and '×' and '÷' are interchanged (× ↔ ÷). Substituting these into the original equation:

Original equation: 152 ÷ 6 + 1617 × 7 - 77

Modified equation: 152 × 6 - 1617 ÷ 7 + 77

Now, applying the BODMAS rule (Division, Multiplication, Addition, Subtraction):

Division: 1617 ÷ 7 = 231 Multiplication: 152 × 6 = 912

Substituting these results back into the expression: 912 - 231 + 77

Subtraction and Addition: 912 - 231 = 681 681 + 77 = 758

Explanation

The numerical relationship follows the logic (n - 1) × 11, where n is the given number. Applying this to the first pair, (21 - 1) × 11 = 20 × 11 = 220. For the second pair, the same pattern holds as (72 - 1) × 11 = 71 × 11 = 781.

To find the number related to 27, we apply the same formula: (27 - 1) × 11 = 26 × 11 = 286

Explanation

To find the code for monkey, we compare the given phrases to isolate specific words. In the first phrase cat dog monkey (55 66 88) and the second phrase camel cat donkey (66 99 33), the common word is cat and the common numerical code is 66. In the first phrase cat dog monkey (55 66 88) and the third phrase dog goat tiger (88 11 22), the common word is dog and the common numerical code is 88. Since the first phrase contains cat, dog, and monkey with the codes 66, 88, and 55 respectively, and we have identified cat as 66 and dog as 88, the remaining code 55 must correspond to monkey.

Explanation

The letter series is formed by repeating a four-letter pattern where the first three letters remain constant, and the fourth letter advances alphabetically.

The core pattern is I Y R [Variable]. By breaking the series into groups of four, we can identify the progression of the variable letter: Group 1: I Y R W Group 2: I Y R X Group 3: I Y R Y Group 4: I Y R Z

The fourth letter in each group follows the alphabetical sequence: W → X → Y → Z.

Now, we match this pattern against the given series, including an implicit blank at the very beginning to accommodate the four-letter options: () Y R W | I Y () X | I () R () I | Y R Z

By filling the blanks with the letters from the pattern: The first blank (at the start) is I. The second blank (between Y and X) is R. The third blank (between I and R) is Y. The fourth blank (between R and I) is Y.

Sequentially, the letters are I, R, Y, Y.

Explanation

According to the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction), we evaluate the equation by interchanging the numbers 21 and 14.

Modified Equation: 6 × 3 + 8 ÷ 2 + 14 + 5 × 4 - 21 ÷ 7 = 53

Step 1: Perform the division operations. 8 ÷ 2 = 4 21 ÷ 7 = 3 The equation becomes: 6 × 3 + 4 + 14 + 5 × 4 - 3 = 53

Step 2: Perform the multiplication operations. 6 × 3 = 18 5 × 4 = 20 The equation becomes: 18 + 4 + 14 + 20 - 3 = 53

Step 3: Perform addition and subtraction from left to right. Sum of positive terms: 18 + 4 + 14 + 20 = 56 56 - 3 = 53

The calculation results in 53, which matches the right-hand side of the equation. Thus, interchanging 21 and 14 makes the equation correct.

Explanation

The series consists of 16 characters that can be divided into four groups of four letters each: (_TUV), (TR_W), (U_UX), and (VN_Y). By comparing the letters in the same relative position within each group, a consistent pattern for each position is identified.

For the first position of each group, the letters follow an increasing alphabetical progression of +1: S, T, U, and V. This determines that the first blank is S.

For the second position of each group, the letters follow a decreasing alphabetical progression of -2: T (20), R (18), P (16), and N (14). This determines that the third blank (the second letter of the third group) is P.

For the third position of each group, the character remains constant as U throughout the entire series. This determines that the second blank (the third letter of the second group) and the fourth blank (the third letter of the fourth group) are both U.

For the fourth position of each group, the letters follow an increasing alphabetical progression of +1: V, W, X, and Y.

Placing these identified letters (S, U, P, U) sequentially into the blanks completes the logical pattern of the series.

Explanation

The logical relationship between the given sets can be expressed through inclusion and exclusion. The first two statements, All spoons are forks and All forks are knives, establish a transitive relationship: Spoons ⊂ Forks ⊂ Knives. This implies that all spoons are knives. By the rule of conversion, if all spoons are knives, it follows that some knives are spoons, making conclusion I logically valid.

Furthermore, the third statement, No knife is a spatula, indicates that the set of knives and the set of spatulas are disjoint (Knives ∩ Spatulas = ∅). Since all forks are contained within the set of knives (Forks ⊂ Knives), and there is no intersection between knives and spatulas, no element belonging to the set of forks can belong to the set of spatulas. This confirms that conclusion II, No fork is a spatula, is logically certain.

Explanation

The series follows a pattern where the difference between consecutive terms increases by a constant value of 4. Calculating the differences between the given numbers: 36 - 32 = 4 44 - 36 = 8 56 - 44 = 12 72 - 56 = 16

The differences form an arithmetic progression: 4, 8, 12, 16. Following this pattern, the next difference must be 16 + 4 = 20. To find the next number in the series, add this difference to the last term: 72 + 20 = 92

Explanation

To solve the equation, we apply the interchange of mathematical signs as per the standard logic for such reasoning questions, which involves swapping the pairs (+, -) and (×, ÷).

Original Equation: 125 ÷ 5 + 1809 × 9 - 14 = ?

Applying the interchanges: Replace ÷ with × Replace + with - Replace × with ÷ Replace - with +

New Equation: 125 × 5 - 1809 ÷ 9 + 14 = ?

Following the BODMAS/VBODMAS rule (Division, Multiplication, Addition, and Subtraction):

Step 1: Perform the Division 1809 ÷ 9 = 201

Step 2: Perform the Multiplication 125 × 5 = 625

Step 3: Perform the Subtraction and Addition 625 - 201 + 14 424 + 14 = 438

Explanation

The numbers in each triad follow the mathematical relationship 2 × First Number - Second Number = Third Number.

Applying this logic to the provided triads: In (8, 9, 7), we have 2 × 8 - 9 = 16 - 9 = 7. In (24, 13, 35), we have 2 × 24 - 13 = 48 - 13 = 35.

Using the same formula for the triad (17, 11, 23), the result is 2 × 17 - 11 = 34 - 11 = 23, which confirms it follows the same pattern.

Explanation

The pattern is derived by applying specific mathematical operations to each component of the alphanumeric code: the first letter, the second letter, and the numerical value.

For the first letter, the positional value in the English alphabet increases by 3. In the relationship between RX-21 and UU-11, the letter R (18) shifts to U (21) since 18 + 3 = 21. In the relationship between PM-39 and SJ-29, P (16) shifts to S (19) since 16 + 3 = 19. Applying this to DP-17, the first letter D (4) shifts to 4 + 3 = 7, which is G.

For the second letter, the positional value decreases by 3. In the first pair, X (24) shifts to U (21) since 24 - 3 = 21. In the second pair, M (13) shifts to J (10) since 13 - 3 = 10. For DP-17, the second letter P (16) shifts to 16 - 3 = 13, which is M.

For the numerical part, the value decreases by 10. In the first pair, 21 - 10 = 11. In the second pair, 39 - 10 = 29. For DP-17, the number 17 shifts to 17 - 10 = 7. Combining the transformed letter G, the transformed letter M, and the result 7 produces the term GM-7.

Explanation

The coding logic follows the numerical position of each letter in the English alphabetical order, where A = 1, B = 2, C = 3, and so on up to Z = 26. In the word PUPIL, the positions are P = 16, U = 21, P = 16, I = 9, and L = 12, which concatenated forms 162116912. Similarly, for PURGE, the positions are P = 16, U = 21, R = 18, G = 7, and E = 5, resulting in 16211875.

Applying this logic to the word PURSE: P = 16 U = 21 R = 18 S = 19 E = 5

By placing these numbers in sequence, we obtain the code 162118195.

Explanation

The series can be analyzed by dividing the sequence of symbols into figures (groups) of three symbols each:

Figure 1: 5, A, X Figure 2: 5, ☐, A Figure 3: R, R, 5 Figure 4: A, ☐, R Figure 5: R, A, 5 Figure 6: X, X, ☐

An analysis of these figures reveals a clear pattern:

Every third figure (3, 6, 9...) consists of a doubled symbol and one other symbol, excluding A. Figure 3 has a doubled R (R, R, 5) and Figure 6 has a doubled X (X, X, ☐).

The remaining figures (1, 2, 4, 5, 7...) always contain the symbol A and two other symbols from the set {5, X, ☐, R}.

The position of A within these figures follows a repeating cyclic shift: In Figure 1, A is in the 2nd position. In Figure 2, A is in the 3rd position. (Figure 3 is skipped). In Figure 4, A is in the 1st position. In Figure 5, A is in the 2nd position. (Figure 6 is skipped). Following this pattern, in Figure 7, A must be in the 3rd position.

The other two symbols in these figures follow a specific sequence: The first symbol of the pairs follows a doubled pattern: (5, 5), (R, R), (X, X), (☐, ☐). For Figures 1 and 2, it is 5; for Figures 4 and 5, it is R; for Figure 7, the next in sequence is X. The second symbol follows a similar pattern starting from X: X, (☐, ☐), (5, 5), (R, R). For Figure 1, it is X; for Figures 2 and 4, it is ☐; for Figures 5 and 7, the next in sequence is 5.

Combining these, Figure 7 consists of X in the 1st position, 5 in the 2nd position, and A in the 3rd position, resulting in X5A.

Explanation

According to the given conditions, the operators are interchanged as follows: + becomes ÷, ÷ becomes +, × becomes -, and - becomes ×. Applying these changes to the original equation 20 + 4 ÷ 2 × 3 - 6, the new expression is:

20 ÷ 4 + 2 - 3 × 6

Following the BODMAS rule (Division, Multiplication, Addition, then Subtraction):

Step 1 (Division): 20 ÷ 4 = 5. The expression becomes 5 + 2 - 3 × 6.

Step 2 (Multiplication): 3 × 6 = 18. The expression becomes 5 + 2 - 18.

Step 3 (Addition): 5 + 2 = 7. The expression becomes 7 - 18.

Step 4 (Subtraction): 7 - 18 = -11.

Explanation

To determine the number of letters that remain in the same position, we first identify the original sequence of the word DELIGHT and then rearrange its letters in ascending alphabetical order.

Original Word: Position 1: D Position 2: E Position 3: L Position 4: I Position 5: G Position 6: H Position 7: T

Alphabetical Arrangement: Arranging the letters D, E, L, I, G, H, T in alphabetical order gives D, E, G, H, I, L, T.

Comparing the two sequences: Position 1: D (Original) and D (Alphabetical) - Unchanged Position 2: E (Original) and E (Alphabetical) - Unchanged Position 3: L (Original) and G (Alphabetical) - Changed Position 4: I (Original) and H (Alphabetical) - Changed Position 5: G (Original) and I (Alphabetical) - Changed Position 6: H (Original) and L (Alphabetical) - Changed Position 7: T (Original) and T (Alphabetical) - Unchanged

The letters D, E, and T maintain their original positions. Therefore, a total of three letters remain unchanged.

Explanation

The relationship between Mirrors and Plants is indeterminate. The statements establish that some Mirrors are Decoratives and no Decorative is a Plant. This implies that the specific Mirrors which are Decoratives cannot be Plants, but it does not provide any logical basis to assert that any Mirrors must be Plants. Therefore, Conclusion (I) does not logically follow.

The relationship between Decoratives and Trees is also indeterminate. Although all Plants are Trees and no Decorative is a Plant, this only ensures that Decoratives and Plants are mutually exclusive sets. Since the set of Trees is larger than or equal to the set of Plants, Decoratives could exist entirely outside the set of Trees or overlap with the part of Trees that does not contain Plants. Because there is no statement forcing an intersection between Decoratives and Trees, Conclusion (II) does not logically follow.

Explanation

To find the code for the letter S, compare the given words and their numerical codes. The word LIGHT is represented by the digits 2, 5, 7, 0, and 9, while the word SIGHT is represented by the digits 9, 7, 0, 6, and 5. Both words share the letters I, G, H, and T. Correspondingly, both numerical sets share the digits 5, 7, 0, and 9. The only letter present in SIGHT but not in LIGHT is S. Similarly, the only digit present in the code for SIGHT (97065) but not in the code for LIGHT (25709) is 6. Therefore, the code for the letter S is 6.

Explanation

The sets of numbers (n₁, n₂, n₃) in the group follow a mathematical pattern where the second number is equal to the sum of twice the first number and the third number, represented by the formula n₂ = 2n₁ + n₃. In the set 12- 122- 99, applying this formula to the first and third numbers gives 2 × 12 + 99 = 24 + 99 = 123. Since the second number provided in the set is 122 rather than 123, this option does not satisfy the property shared by the group.

Explanation

The logic followed in the given pairs is (n + 1) × 10 = Result. For the first pair, applying this logic to 33 gives (33 + 1) × 10 = 34 × 10 = 340. For the second pair, applying the same logic to 48 gives (48 + 1) × 10 = 49 × 10 = 490. In the case of the number 63, the operation yields (63 + 1) × 10 = 64 × 10 = 640.

Explanation

The relationship between the letter-clusters follows a pattern where each letter in the first cluster is shifted forward by 5 positions in the English alphabetical order to obtain the corresponding letter in the second cluster.

For LOI to QTN, the mapping is L (12) + 5 = 17 (Q), O (15) + 5 = 20 (T), and I (9) + 5 = 14 (N).

For VES to AJX, the mapping is V (22) + 5 = 27, which corresponds to 1 (A) in a circular alphabet, E (5) + 5 = 10 (J), and S (19) + 5 = 24 (X).

Applying this same +5 shift to the fifth letter-cluster AND results in A (1) + 5 = 6 (F), N (14) + 5 = 19 (S), and D (4) + 5 = 9 (I). Therefore, the letter-cluster related to AND is FSI.

Explanation

The letter-clusters in this set are determined by the alphabetical positions of their letters using the pattern P₂ = P₁ - 1 and P₃ = P₂ + 3, where P is the numerical position in the English alphabet. For the cluster LKM, the positions are L(12), K(11), and M(13). While the first part of the pattern is correctly followed (12 - 1 = 11), the second transition is 11 + 2 = 13. Because this involves an increment of only 2 instead of the 3 required by the established logic, LKM is the odd one out.

Explanation

The series follows a specific arithmetic pattern for each letter position within the clusters based on their numerical positions in the English alphabet.

For the first letter of each cluster, the sequence is T(20), V(22), X(24), and Z(26). The pattern is an increment of +2. Adding 2 to Z(26) completes the alphabet and cycles back to the second letter, which is B.

For the second letter of each cluster, the sequence is G(7), I(9), K(11), and M(13). The pattern is an increment of +2. Adding 2 to M(13) results in the 15th letter, which is O.

For the third letter of each cluster, the sequence is O(15), N(14), M(13), and L(12). The pattern is a decrement of -1. Subtracting 1 from L(12) results in the 11th letter, which is K.

By combining the resulting letters B, O, and K, the next cluster in the sequence is BOK.

Explanation

The relationship follows the pattern X = (Y × M) - C, where X is the first number and Y is the related number. The multiplier M starts at 4 and increases by 2 for each subsequent pair, while the constant C starts at 11 and increases by 4.

For the first pair (61, 18): 61 = (18 × 4) - 11

For the second pair (213, 38): 213 = (38 × 6) - 15

Applying the same logic to the third pair where X = 509: Following the established sequences, the multiplier M for this pair is 6 + 2 = 8, and the constant C is 15 + 4 = 19. 509 = (Y × 8) - 19 509 + 19 = 8Y 528 = 8Y Y = ⁵²⁸⁄₈ = 66

Explanation

The blood relation can be mapped starting from A's children. Since C is the daughter of A and E is the brother of C, both C and E are the children of A, making A the mother of E. The problem states that D is the sister of A. Therefore, the relationship of D with respect to E is that of the mother's sister.

Explanation

To determine the number of letters that remain in the same position, we must compare the original word with its letters rearranged in English alphabetical order.

The original sequence of letters in the word ASTEROID is: A at position one, S at position two, T at position three, E at position four, R at position five, O at position six, I at position seven, and D at position eight.

When these letters (A, S, T, E, R, O, I, and D) are rearranged in English alphabetical order, the sequence becomes: A, D, E, I, O, R, S, T.

By comparing the original positions to the new alphabetical positions: Position 1: Original is A and alphabetical is A. This remains unchanged. Position 2: Original is S and alphabetical is D. Position 3: Original is T and alphabetical is E. Position 4: Original is E and alphabetical is I. Position 5: Original is R and alphabetical is O. Position 6: Original is O and alphabetical is R. Position 7: Original is I and alphabetical is S. Position 8: Original is D and alphabetical is T.

Only the first letter, A, occupies the same position in both the original word and the alphabetical sequence. Consequently, the position of only one letter remains unchanged.