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

Explanation

The relation follows the logic where the second number is obtained by squaring the first number and subtracting a constant value of 50. This can be expressed by the formula: y = x² - 50

Applying this logic to the given pairs: For 13: 13² - 50 = 169 - 50 = 119

For 9: 9² - 50 = 81 - 50 = 31

Applying the same logic to 8: 8² - 50 = 64 - 50 = 14

Explanation

The series follows a specific addition and subtraction pattern for each letter position in the clusters. For the first letter in each term, the pattern is +3 (A +3 D +3 G +3 J). For the second letter, the pattern is -1 (B -1 A -1 Z -1 Y). For the third letter, the pattern is +3 (N +3 Q +3 T +3 W). For the fourth letter, the pattern is -1 (I -1 H -1 G -1 F).

Applying these operations to the second term DAQH gives the next term in the sequence. The first letter D plus 3 positions results in G. The second letter A minus 1 position results in Z. The third letter Q plus 3 positions results in T. The fourth letter H minus 1 position results in G. Combining these results gives the term GZTG.

Explanation

Statement 2 establishes that all cartons are papers, while Statement 3 identifies that some cartons are utensils. Since the set of cartons is a subset of the set of papers, any item belonging to the intersection of cartons and utensils must also belong to the set of papers. This ensures that the intersection of papers and utensils is non-empty, making Conclusion (II) logically certain.

Conclusion (I) states that no box is a utensil. Statement 1 connects boxes to cartons, and Statement 3 connects cartons to utensils. However, the premises contain only affirmative statements and do not provide any negative constraints or exclusions between boxes and utensils. Without a premise stating that boxes or cartons are specifically excluded from being utensils, it is impossible to conclude that no box is a utensil. Since Conclusion (II) is the only one that can be definitively proven from the given statements, the logical result is that only conclusion (II) follows.

Explanation

The numbers in each set (A, B, C) follow a specific arithmetic relationship where the difference between the first and second number is 21, and the difference between the third and second number is 4. This can be expressed as: A - B = 21 C - B = 4

Evaluating the given sets: In (79, 58, 62): 79 - 58 = 21 and 62 - 58 = 4. In (54, 33, 37): 54 - 33 = 21 and 37 - 33 = 4.

Applying this pattern to the set in option c (66, 45, 49): 66 - 45 = 21 49 - 45 = 4

The relationship holds true, as the first number minus the second equals 21 and the third number minus the second equals 4.

Explanation

To find the code for the word chair, compare the two given statements to identify common elements. In the first statement, the phrase sit on chair is coded as sk mi cn. In the second statement, the phrase the chair broke is coded as gm fr mi. The only word that appears in both phrases is chair. Correspondingly, when comparing the two sets of codes, the only code that appears in both sets is mi. Therefore, by matching the common word with the common code, chair is represented by mi.

Explanation

The coding pattern requires reversing the original word and then modifying the alphabetical rank of each letter using an alternating sequence of +1 and -1.

For the word BELL, the letters are first reversed to L-L-E-B. Applying the logic: 12 + 1 = 13 (M), 12 - 1 = 11 (K), 5 + 1 = 6 (F), and 2 - 1 = 1 (A). This forms the code MKFA. Similarly, for the word BOND, the reversal is D-N-O-B. Applying the logic: 4 + 1 = 5 (E), 14 - 1 = 13 (M), 15 + 1 = 16 (P), and 2 - 1 = 1 (A), which results in the code EMPA.

To determine the code for the word BLEW, the letters are reversed to W-E-L-B. Following the same mathematical sequence: the first letter W (23) increases by 1 to become X (24); the second letter E (5) decreases by 1 to become D (4); the third letter L (12) increases by 1 to become M (13); and the fourth letter B (2) decreases by 1 to become A (1). Combining these transformations results in the code XDMA.

Explanation

The cluster PTX follows an alphabetical progression of +4. By assigning numerical values to the letters based on their positions in the English alphabet (A = 1, B = 2, …, Z = 26), the positions are P = 16, T = 20, and X = 24. The difference between consecutive letters is 20 - 16 = 4 and 24 - 20 = 4. This constant increment of 4 identifies it as the odd one out because the general pattern of the group is defined by a constant increment of 5.

Explanation

The positional values of the letters in the English alphabet determine the pattern for each cluster. For the clusters NPR, HJL, and TVX, the difference between consecutive letters is consistently +2. Specifically, in NPR, the positions are 14, 16, and 18; in HJL, the positions are 8, 10, and 12; and in TVX, the positions are 20, 22, and 24. This follows the general formula n, n+2, n+4. In contrast, the cluster MOP uses the positional values 13, 15, and 16. While the first gap from M to O is +2, the second gap from O to P is only +1. This break in the established numerical progression makes MOP the odd one out.

Explanation

To solve the equation, we first interchange the operators as specified: + becomes -, - becomes +, × becomes ÷, and ÷ becomes ×. Applying these changes to the original expression 69 + 2485 × 5 - 912 ÷ 2, we get the new expression:

69 - 2485 ÷ 5 + 912 × 2

According to the BODMAS rule, we perform division and multiplication first:

2485 ÷ 5 = 497 912 × 2 = 1824

Substituting these results back into the expression, we have:

69 - 497 + 1824

Next, we perform the addition and subtraction:

1824 + 69 - 497 = 1893 - 497 = 1396

Explanation

The relationship shared by the given pairs is a constant addition of 51 to the first number to obtain the second number. In the first pair, 11 + 51 = 62. In the second pair, 13 + 51 = 64. Applying this same arithmetic logic to the pair in option c, the second number is derived as 16 + 51 = 67.

Explanation

The expression H × I - J ÷ K + L is decoded as follows based on the provided relations. H × I means H is the mother of I. I - J means I is the wife of J. J ÷ K means J is the father of K. K + L means K is the sister of L.

From these steps, we see that K and L are siblings sharing the same father J. Since I is the wife of J, I is the mother of L. Because H is the mother of I, H is the mother of L's mother. This relationship confirms that H is the mother's mother of L.

Explanation

The logical relationship between the categories can be established using set theory or Venn diagrams. Let S, P, J, and T represent the sets of shirts, pants, jackets, and trousers, respectively. The second and third statements establish a chain of inclusion where P ⊆ J and J ⊆ T, which implies that P ⊆ T. The first statement asserts that some shirts are pants, meaning S ∩ P ≠ ∅. Since P is a subset of T, any element that is in both S and P must also be in T. This necessitates an intersection between the sets of shirts and trousers (S ∩ T ≠ ∅), making conclusion I logically certain. Conclusion II does not follow because the premises only guarantee that some shirts are jackets (via their common intersection with pants), but they do not establish that the entire set of jackets is contained within the set of shirts.

Explanation

The series follows a specific arithmetic pattern for each letter position across the terms. Let the position of each letter in the alphabet be n (where A=1, B=2, …, Z=26).

For the first letter of each term, the pattern is +4: H(8) + 4 = L(12) L(12) + 4 = P(16) P(16) + 4 = T(20)

For the second letter of each term, the pattern is -2: D(4) - 2 = B(2) B(2) - 2 = Z(26) Z(26) - 2 = X(24)

For the third letter of each term, the pattern is +4: L(12) + 4 = P(16) P(16) + 4 = T(20) T(20) + 4 = X(24)

For the fourth letter of each term, the pattern is -2: B(2) - 2 = Z(26) Z(26) - 2 = X(24) X(24) - 2 = V(22)

Combining the resulting letters T, X, X, and V yields the term TXXV. This logic remains consistent for the final term in the series, XVBT, as T+4=X, X-2=V, X+4=B, and V-2=T.

Explanation

The series follows a pattern where the difference between consecutive terms increases by 1 at each step. Calculating the differences between the given numbers: 70 - 58 = 12 83 - 70 = 13 97 - 83 = 14 The differences are 12, 13, and 14. To find the next number in the series, the next difference must be 14 + 1 = 15. Adding this value to the last term of the series gives 97 + 15 = 112.

Explanation

The series progresses by applying a specific constant decrement to the alphabetical position of each letter in the clusters. For the first letter, the value decreases by 4 at each step: Z(26) → V(22) → R(18) → N(14) → J(10), which yields N. For the second letter, the value decreases by 3 at each step: V(22) → S(19) → P(16) → M(13) → J(10), yielding M. For the third letter, the value decreases by 2 at each step: R(18) → P(16) → N(14) → L(12) → J(10), yielding L. For the fourth letter, the value decreases by 1 at each step: N(14) → M(13) → L(12) → K(11) → J(10), yielding K. Combining these results in the cluster NMLK.

Explanation

The series is completed by dividing the letters into three groups of three characters each, where each group follows a cyclic shift pattern. The repeating unit consists of the letters I and J.

Pattern analysis: The sequence follows a right cyclic shift of the triplet IJI. Group 1: IJI Group 2: IIJ (The last letter I of the first group moves to the front) Group 3: JII (The last letter J of the second group moves to the front)

Applying this to the template I _ _ I _ _ J _ _: Group 1 (I _ _): To form IJI, the blanks are filled with J and I. Group 2 (I _ _): To form IIJ, the blanks are filled with I and J. Group 3 (J _ _): To form JII, the blanks are filled with I and I.

By sequentially placing the letters from option c (J, I, I, J, I, I) into the blanks, the full sequence becomes IJI IIJ JII. This perfectly matches the fixed positions of I at the start of the first and second groups and J at the start of the third group.

Explanation

The relationship between the numbers in the given triads follows the formula a² + b² = c, where a and b are the first and second numbers, and c is the result. In the first triad (4 - 5 - 41), calculating the sum of the squares gives 4² + 5² = 16 + 25 = 41. Similarly, in the second triad (2 - 3 - 13), the sum of the squares is 2² + 3² = 4 + 9 = 13. Applying the same logic to option c, the calculation 5² + 6² = 25 + 36 = 61 confirms that the numbers 5, 6, and 61 follow the same pattern.

Explanation

The mathematical relationship between the numbers in the group is defined by the formula 2 × Number₁ + 3 × Number₂ = Number₃. In the set 22 - 13 - 85, applying this operation to the whole numbers gives 2 × 22 + 3 × 13 = 44 + 39 = 83. Since the calculated result is 83 and the given third value is 85, this option does not conform to the common logic.

Explanation

The relationship between the numbers in the given triads follows the logic: (First number × Second number) - 1 = Third number.

Applying this logic to the provided triads: In (11, 1, 10): (11 × 1) - 1 = 11 - 1 = 10 In (13, 7, 90): (13 × 7) - 1 = 91 - 1 = 90

Applying the same logic to option d: In (4, 5, 19): (4 × 5) - 1 = 20 - 1 = 19

Explanation

The relationship in the given pair is Young : Adult. A larva is the juvenile or immature stage of an insect before it undergoes metamorphosis to become an adult. Similarly, a fawn is the young or juvenile form of a deer. Both pairs represent the developmental progression of a specific animal from its early life stage to its adult stage.

Explanation

To determine the code for the letter O, we compare the two given words and their corresponding codes using the method of elimination. The words PANTHER and ANOTHER share six common letters: A, N, T, H, E, and R. When comparing the digits in their codes, 0146283 and 2864109, we find six common digits: 0, 1, 2, 4, 6, and 8. The letter O is the only character present in the word ANOTHER that does not appear in the word PANTHER. Similarly, the digit 9 is the only value present in the code for ANOTHER that does not appear in the code for PANTHER. Through this direct comparison, it is established that the letter O corresponds to the digit 9.

Explanation

The series follows a pattern where the difference between consecutive terms is the square of consecutive even numbers.

27 - 23 = 4 = 2² 43 - 27 = 16 = 4² 79 - 43 = 36 = 6² 143 - 79 = 64 = 8²

Following this logic, the difference between the next term and 143 should be the square of the next even number, which is 10.

Next Difference = 10² = 100 Missing Number = 143 + 100 = 243

Explanation

The code for each word is generated by replacing every letter with its reverse positional value in the English alphabet. The reverse position R of a letter is calculated using its standard forward position P with the formula R = 27 - P.

For the word MUSIC, the calculation is as follows: The letter M is the 13th letter, so its reverse value is 27 - 13 = 14. The letter U is the 21st letter, so its reverse value is 27 - 21 = 6. The letter S is the 19th letter, so its reverse value is 27 - 19 = 8. The letter I is the 9th letter, so its reverse value is 27 - 9 = 18. The letter C is the 3rd letter, so its reverse value is 27 - 3 = 24.

Concatenating these values in sequence results in the code 14681824. This logic is consistent with the provided examples: CYCLE is coded by the reverse values of C(24), Y(2), C(24), L(15), and E(22), while FINAL is coded by F(21), I(18), N(13), A(26), and L(15).

Explanation

The pattern followed in the given pairs involves a specific shift in the alphabetical positions of each letter. For the first two letters of the string, the position is shifted backward by 2 units, and for the last two letters, the position is shifted forward by 2 units.

In the first example, M (13) moves to K (11), P (16) moves to N (14), Q (17) moves to S (19), and O (15) moves to Q (17). In the second example, D (4) moves to B (2), G (7) moves to E (5), H (8) moves to J (10), and F (6) moves to H (8).

Applying this logic to EINW: The first letter E (5) is shifted as 5 - 2 = 3, which is C. The second letter I (9) is shifted as 9 - 2 = 7, which is G. The third letter N (14) is shifted as 14 + 2 = 16, which is P. The fourth letter W (23) is shifted as 23 + 2 = 25, which is Y.

Combining these results gives the string CGPY.

Explanation

The equation is solved by interchanging the operators as per the standard mathematical logic for such problems: × is interchanged with ÷, and + is interchanged with -.

Given original equation: 49 × 7 - 6 ÷ 8 + 13 = ?

After interchanging the signs (× to ÷, ÷ to ×, + to -, and - to +), the equation becomes: 49 ÷ 7 + 6 × 8 - 13

To solve this, apply the BODMAS rule (Division, Multiplication, Addition, Subtraction):

Step 1: Perform Division 49 ÷ 7 = 7 The expression becomes: 7 + 6 × 8 - 13

Step 2: Perform Multiplication 6 × 8 = 48 The expression becomes: 7 + 48 - 13

Step 3: Perform Addition 7 + 48 = 55 The expression becomes: 55 - 13

Step 4: Perform Subtraction 55 - 13 = 42

Explanation

To find the number of letters whose positions remain unchanged, we compare the original sequence of the word DRAFTING with its letters rearranged in alphabetical order.

Original Word: D, R, A, F, T, I, N, G Alphabetical Order: A, D, F, G, I, N, R, T

We can map the letters to their positions to check for matches: First position: D changes to A Second position: R changes to D Third position: A changes to F Fourth position: F changes to G Fifth position: T changes to I Sixth position: I changes to N Seventh position: N changes to R Eighth position: G changes to T

Comparing the two sequences shows that every letter in the word DRAFTING moves to a different position when sorted alphabetically. Since no letter occupies the same index in both the original and the rearranged strings, the total count of unchanged positions is zero.

Explanation

The expression P | Q % L # R | K establishes the family relationships through the given symbols. P | Q means P is the wife of Q, which identifies Q as a male. Q % L states that Q is the father of L. L # R means L is the sister of R, which makes L and R siblings from the same generation sharing the same parents. Since Q is the father of L, and R is the sibling of L, Q is the father of R. The final segment R | K identifies R as the wife of K, confirming R is the daughter of Q and Q is the father of R.

Explanation

The series consists of three patterns involving the first letter, the second letter, and the numerical value of each term.

For the first letter, the sequence is F, E, D, C. Converting these to their positions in the alphabet gives 6, 5, 4, 3. This is a decreasing sequence with a common difference of -1. The next letter in the sequence corresponds to position 2, which is B.

For the second letter, the sequence is M, K, I, G. Converting these to their positions in the alphabet gives 13, 11, 9, 7. This is a decreasing sequence with a common difference of -2. The next letter in the sequence corresponds to position 5, which is E.

For the numerical part, the sequence is 61, 58, 55, 52. This is an arithmetic progression where the common difference is -3. The next number is obtained by subtracting 3 from 52, resulting in 49.

By combining the predicted components, the next term in the series is BE49.

Explanation

The logic followed by the numbers in the sets is (n₁ - n₂) × 9 = n₃. For the set 21- 14- 72, the difference between the first and second numbers is 21 - 14 = 7. Multiplying this difference by 9 results in 7 × 9 = 63. Since the third number in this set is 72 instead of 63, it does not follow the mathematical pattern established in the other groups.

Explanation

The series follows a specific pattern of alphabetical shifts for each position in the four-letter clusters. For the first letter, there is a constant increment of +4: J (10) to N (14) to R (18) to V (22) to Z (26). For the second letter, there is a constant decrement of -2: H (8) to F (6) to D (4) to B (2) to Z (26/0). For the third letter, there is a constant increment of +4: O (15) to S (19) to W (23) to A (1/27) to E (5/31). For the fourth letter, there is a constant decrement of -2: Q (17) to O (15) to M (13) to K (11) to I (9). Combining these shifts for the third term, we calculate the letters from the second term NFSO as N+4=R, F-2=D, S+4=W, and O-2=M, resulting in the term RDMW.

Explanation

The coding logic follows an alternating pattern of +1 and -1 applied to each letter of the word. For 'RADIO': R+1=S, A-1=Z, D+1=E, I-1=H, O+1=P. Applying this pattern to 'TELEVISION' (T+1, E-1, L+1, E-1, V+1, I-1, S+1, I-1, O+1, N-1) results in U, D, M, D, W, H, T, H, P, M. Therefore, 'TELEVISION' is written as UDMDWHTHPM, which corresponds to option B.

Explanation

When the letters of the word MOBILE are arranged in English alphabetical order, the sequence changes from M-O-B-I-L-E to B-E-I-L-M-O. Comparing the positions of the letters in both sequences: M becomes B, O becomes E, B becomes I, I becomes L, L becomes M, and E becomes O. Since every letter changes its position, the number of letters that remain unchanged is zero (None).

Explanation

The logic follows a pattern where each number x is multiplied by a varying multiplier M and then a varying subtrahend S is subtracted: x × M - S.

For the first pair, 12 → 235: 12 × 20 - 5 = 240 - 5 = 235

For the second pair, 14 → 287: The increase in x is Δ x = 14 - 12 = 2. The multiplier M increases by (Δ x / 2)² = (2 / 2)² = 1. So, the new multiplier is 20 + 1 = 21. The subtrahend S increases by (increase in M) + 1 = 1 + 1 = 2. So, the new subtrahend is 5 + 2 = 7. Calculation: 14 × 21 - 7 = 294 - 7 = 287

For the third pair, 18 → ?: The increase in x from the previous number is Δ x = 18 - 14 = 4. The multiplier M increases by (Δ x / 2)² = (4 / 2)² = 4. So, the new multiplier is 21 + 4 = 25. The subtrahend S increases by (increase in M) + 1 = 4 + 1 = 5. So, the new subtrahend is 7 + 5 = 12. Calculation: 18 × 25 - 12 = 450 - 12 = 438

Explanation

The series follows a specific pattern for each component of the terms:

First Letter: The first letters B, C, D, and E follow a consecutive alphabetical sequence (+1 increment). The next letter in this sequence is F. Second Letter: The second letters H, J, L, and N increase by two positions in the alphabet (+2 increment). The next letter in this sequence is P (since N is 14 and 14 + 2 = 16, which is P). Number: The numbers 14, 17, 20, and 23 follow a simple arithmetic progression with a common difference of +3. The next number is 23 + 3 = 26.

Alternatively, a consistent mathematical rule links the letters and the number in each term: (Position of Letter 1 + Position of Letter 2) + 4 = Number. Term 1 (BH14): (2 + 8) + 4 = 14 Term 2 (CJ17): (3 + 10) + 4 = 17 Term 3 (DL20): (4 + 12) + 4 = 20 Term 4 (EN23): (5 + 14) + 4 = 23

For the fifth term, using the expected letters F (6) and P (16): (6 + 16) + 4 = 26. Option b) PF26 is the only choice that utilizes the correct letters (F and P) and satisfies the numerical increment and the sum-based rule.

Explanation

The relationship between the numbers in the given triads follows the pattern where the third number is the sum of the first and second numbers. In the first triad (25, 22, 47), the sum is 25 + 22 = 47. In the second triad (31, 24, 55), the sum is 31 + 24 = 55.

Applying this logic to the options, the triad (18, 21, 39) follows the same rule because 18 + 21 = 39.

Explanation

The series follows a pattern where the difference between consecutive terms is a sequence of consecutive prime numbers.

420 - 389 = 31 457 - 420 = 37 498 - 457 = 41 541 - 498 = 43

The differences are 31, 37, 41, and 43. These are consecutive prime numbers. The next prime number in the sequence after 43 is 47. Adding this prime number to the last term of the series gives the next number:

541 + 47 = 588

Explanation

The letter clusters are formed using the concept of opposite letters in the English alphabet, where the sum of the numerical positions of two letters is exactly 27. In the consistent clusters, the first and third letters are opposites, and the second and fourth letters are also opposites. Specifically, in TWGD, T (20) and G (7) sum to 27, while W (23) and D (4) also sum to 27. In MPNK, M (13) and N (14) sum to 27, and P (16) and K (11) sum to 27. In JMQN, J (10) and Q (17) sum to 27, and M (13) and N (14) sum to 27. In the cluster PSKI, although the first and third letters P (16) and K (11) are opposites (16 + 11 = 27), the second and fourth letters S (19) and I (9) sum to 28, making it the odd one out.

Explanation

Based on the standard logic for operator interchange problems, the signs in the equation are replaced according to the given rules. In such competitive exam questions, the instruction usually implies a complete swap of the operational pairs.

Interchange rules:

• and - are interchanged ⟹ + becomes - and - becomes + × and ÷ are interchanged ⟹ × becomes ÷ and ÷ becomes ×

Applying these changes to the original equation: Original: 25 + 3 ÷ 9 - 14 × 2 Transformed: 25 - 3 × 9 + 14 ÷ 2

Now, solve the transformed equation using the BODMAS rule:

Division: 14 ÷ 2 = 7 The equation becomes: 25 - 3 × 9 + 7

Multiplication: 3 × 9 = 27 The equation becomes: 25 - 27 + 7

Addition and Subtraction: 25 + 7 - 27 = 32 - 27 = 5

Explanation

The relationship between the numbers in the given pairs follows the mathematical logic y = (x × 3) + 3, where x represents the first number and y represents the second number. In the first pair 40:123, multiplying the first number 40 by 3 gives 120, and adding 3 to this product results in 123. In the second pair 63:192, multiplying 63 by 3 gives 189, and adding 3 results in 192. Applying this same rule to the numbers in option b, multiplying 39 by 3 yields 117, and adding 3 gives the second number 120.

Explanation

The relationship established in the given pair is between a country and its recognized national bird symbol. The Gallic Rooster is a historical and national symbol of France. Similarly, the Emu is the national bird of Australia. It is a large, flightless bird endemic to the Australian continent and holds significant cultural importance, appearing on the Australian coat of arms alongside the kangaroo to represent the nation.

Explanation

PROPOSED: [c]

To find the value of the expression 63 × 7 ÷ 13 - 64 + 42, we apply the interchanged operations as defined in the question. In such mathematical reasoning problems, the instruction "'+' and '-' are interchanged and 'x' and '+' are interchanged" is typically a typographical error for "× and ÷ are interchanged and + and - are interchanged," as this allows for a consistent mapping of all four arithmetic operators.

Following the standard interpretation where × ↔ ÷ and + ↔ -:

Replace × with ÷: 63 ÷ 7 Replace ÷ with ×: 63 ÷ 7 × 13 Replace - with +: 63 ÷ 7 × 13 + 64 Replace + with -: 63 ÷ 7 × 13 + 64 - 42

Now, solve the expression using the BODMAS rule (Brackets, Orders, Division/Multiplication, Addition/Subtraction):

Step 1: Perform the Division 63 ÷ 7 = 9

Step 2: Perform the Multiplication 9 × 13 = 117

Step 3: Perform the Addition 117 + 64 = 181

Step 4: Perform the Subtraction 181 - 42 = 139

Alternatively, calculating the tail end first: 117 + (64 - 42) = 117 + 22 = 139

Explanation

The series follows a pattern where groups of letters are written in alphabetical order, with exactly three letters of the alphabet skipped between each group. The length of the letter groups alternates or follows a specific count to fit the given string.

The sequence progresses as follows: Write 2 letters: A, B Skip 3 letters: C, D, E Write 4 letters: F, G, H, I Skip 3 letters: J, K, L Write 4 letters: M, N, O, P Skip 3 letters: Q, R, S Write 4 letters: T, U, V, W Skip 3 letters: X, Y, Z Write 4 letters: A, B, C, D Skip 3 letters: E, F, G Write 2 letters: H, I

By placing the letters from the sequence into the blanks of the given string ABF_HI_NOP_U_WABCDH_, we get: ABF (G) HI (M) NOP (T) U (V) WABCDH (I)

The letters filled in the blanks are G, M, T, V, and I in sequential order.

Explanation

The given expression J % K # L @ M α N | Z can be broken down step by step to determine the relationship between J and Z. J % K means J is the mother of K. K # L signifies K is the sister of L, which implies that J is the mother of both K and L. L @ M indicates L is the wife of M. M α N means M is the father of N, and since L is the wife of M, L must be the mother of N. Finally, N | Z means N is the brother of Z, which shows that N and Z are siblings sharing the same parents, L and M. Consequently, L is the mother of Z. Since J is the mother of L, it follows that J is the mother of Z's mother.

Explanation

The letters of the word DICTIONARY are D, I, C, T, I, O, N, A, R, and Y. Arranging these letters in alphabetical order results in the letter-cluster: A, C, D, I, I, N, O, R, T, Y.

In this newly formed cluster, the fourth alphabet from the left end is I. The second alphabet from the right end is T. To find the number of alphabets between I and T in the standard English alphabetical series, we use their respective numerical positions. The position of I is 9 and the position of T is 20.

The number of alphabets between two letters with positions n₁ and n₂ is given by the formula (n₂ - n₁) - 1. Substituting the values for T and I, we get (20 - 9) - 1, which simplifies to 11 - 1 = 10. The ten alphabets located between I and T are J, K, L, M, N, O, P, Q, R, and S.

Explanation

The coding pattern follows a simple addition logic where each letter in the word is shifted forward by two positions in the English alphabetical sequence. This can be expressed as the transformation n → n + 2. In the word BOTH, the letters B, O, T, and H are shifted by two places to become D, Q, V, and J respectively. Similarly, in the word DARE, D shifts to F, A shifts to C, R shifts to T, and E shifts to G. Applying this same +2 increment to the word WILL, W moves to Y, I moves to K, and both instances of L move to N. This results in the coded form YKNN.

Explanation

The letter series follows a recurring mathematical pattern based on the alphabetical positions of the letters. The numerical positions of the given letters are S(19), Y(25), A(1 or 27), F(6), I(9), K(11), M(13), S(19), U(21), and W(23).

By analyzing the gaps between the known letters, we observe a cyclic pattern of differences: +3, +3, +2, +2. Applying this pattern to the series:

19 (S) + 3 = 22 (V) 22 (V) + 3 = 25 (Y) 25 (Y) + 2 = 27, which corresponds to 1 (A) 1 (A) + 2 = 3 (C) 3 (C) + 3 = 6 (F) 6 (F) + 3 = 9 (I) 9 (I) + 2 = 11 (K) 11 (K) + 2 = 13 (M) 13 (M) + 3 = 16 (P) 16 (P) + 3 = 19 (S) 19 (S) + 2 = 21 (U) 21 (U) + 2 = 23 (W)

The sequence of differences +3, +3, +2, +2 repeats three times. The letters required to fill the blanks from left to right are V, C, and P.

Explanation

The logic followed in the given sets (3, 9, 27) and (4, 16, 64) is based on the powers of the first number. In each set, the numbers follow the pattern (n, n², n³), where n is the first number.

For the first set (3, 9, 27): 3¹ = 3 3² = 9 3³ = 27

For the second set (4, 16, 64): 4¹ = 4 4² = 16 4³ = 64

Applying this same logic to the set (7, 49, 343): 7¹ = 7 7² = 49 7³ = 343

Each number in the set is a successive power of the base number 7, maintaining the consistency of the mathematical operation performed in the original examples.

Explanation

To solve the equation 6408 × 8 + 27 - 15 ÷ 10 = ?, we apply the rules for interchanging the mathematical operators. Based on the standard logic for such problems, the rules + ↔ - and × ↔ ÷ (noting a likely typographical substitution of + for ÷ in the second rule of the prompt) are applied to the given expression.

The original operators in the equation are: × (multiplication)

• (addition)

• (subtraction) ÷ (division)

Applying the interchanges (+ ↔ - and × ↔ ÷): The × becomes ÷. The + becomes -. The - becomes +. The ÷ becomes ×.

Substituting these into the equation: 6408 ÷ 8 - 27 + 15 × 10 = ?

Now, solve using the BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction) rule:

Perform the division: 6408 ÷ 8 = 801

Perform the multiplication: 15 × 10 = 150

The equation now stands as: 801 - 27 + 150 = ?

Perform the addition and subtraction: 801 - 27 = 774 774 + 150 = 924

Explanation

The statements establish a nested logical hierarchy using the transitive property of set inclusion. Given that all peas are vegetables (P ⊆ V) and all vegetables are greens (V ⊆ G), it follows that all peas are greens (P ⊆ G). This confirms that conclusion I is logically valid.

In categorical logic, the universal affirmative statement All A are B implies the particular converse Some B are A. Since the deduction All peas are greens is established, the statement some greens are peas must also be true. This validates conclusion III. Therefore, both conclusions I and III are derived directly from the given premises.

Explanation

The coding logic follows an incremental addition pattern where the numerical position of each letter in the alphabet is increased by a decreasing sequence starting from +4. For the word BAKE, B (2) + 4 = 6 (F), A (1) + 3 = 4 (D), K (11) + 2 = 13 (M), and E (5) + 1 = 6 (F), resulting in FDMF. Similarly, for TURN, T (20) + 4 = 24 (X), U (21) + 3 = 24 (X), R (18) + 2 = 20 (T), and N (14) + 1 = 15 (O), resulting in XXTO.

Applying this +4, +3, +2, +1 pattern to MOCK: M (13) + 4 = 17 (Q) O (15) + 3 = 18 (R) C (3) + 2 = 5 (E) K (11) + 1 = 12 (L)

The resulting code for MOCK is QREL.