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

Explanation

The statements establish that all chargers are equipment and some chargers are phones. Because the group of chargers that are phones is entirely contained within the larger set of equipment, it follows that some equipment must be phones. This validates Conclusion I. Regarding Conclusion II, while all wires are chargers and some chargers are phones, there is no defined relationship or necessary overlap between the set of wires and the set of phones within the broader category of chargers. Since the connection between wires and phones is not guaranteed by the premises, Conclusion II does not logically follow.

Explanation

By substituting the sequence of signs ÷, ×, -, +, and = into the equation, we get the expression:

54 ÷ 36 × 12 - 18 + 24 = 24

Following the BODMAS rule, perform division first: ⁵⁴⁄₃₆ × 12 - 18 + 24 = 24 1.5 × 12 - 18 + 24 = 24

Next, perform the multiplication: 18 - 18 + 24 = 24

Finally, simplify the remaining addition and subtraction: 24 = 24

The calculation confirms that the left-hand side equals the right-hand side, which balances the equation.

Explanation

The coding logic follows the opposite letter pairing system, where each letter is replaced by the letter occupying the same position from the opposite end of the alphabet. In such a system, the sum of the numerical positions of the original letter and its coded version always equals 27 (calculated as Positionₒᵣᵢ_gᵢₙₐₗ + Positionₙₑ_w = 27).

In the word BACHELOR, the letters map as follows: B(2) to Y(25), A(1) to Z(26), C(3) to X(24), H(8) to S(19), E(5) to V(22), L(12) to O(15), O(15) to L(12), and R(18) to I(9).

Applying this logic to the word EDUCATION: E (5) maps to 27 - 5 = 22 (V) D (4) maps to 27 - 4 = 23 (W) U (21) maps to 27 - 21 = 6 (F) C (3) maps to 27 - 3 = 24 (X) A (1) maps to 27 - 1 = 26 (Z) T (20) maps to 27 - 20 = 7 (G) I (9) maps to 27 - 9 = 18 (R) O (15) maps to 27 - 15 = 12 (L) N (14) maps to 27 - 14 = 13 (M)

The resulting code sequence is VWFXZGRLM.

Explanation

In each of the letter-clusters, the positions of the letters in the English alphabet follow a specific numerical sequence. For the clusters MOS (13, 15, 19), LNR (12, 14, 18), and GIM (7, 9, 13), the difference between the first and second letter is +2, and the difference between the second and third letter is +4. Specifically:

M(13) + 2 = O(15) and O(15) + 4 = S(19) L(12) + 2 = N(14) and N(14) + 4 = R(18) G(7) + 2 = I(9) and I(9) + 4 = M(13)

In the cluster HJM, the positions are 8, 10, and 13. While the first difference is +2 because H(8) + 2 = J(10), the second difference is +3 because J(10) + 3 = M(13). This deviation from the +2, +4 pattern makes it the different letter-cluster.

Explanation

The series is completed by dividing it into five groups of four letters each. Each group contains four distinct letters from the set {P, Q, R, S, N}, with one letter being omitted in each group according to a specific cyclic order.

By sequentially placing the letters from option b) (S, R, Q, P, N, S, N, Q, P, R) into the blanks, the series is completed as follows: P (S) (R) N | (Q) (P) S R | (N) (S) Q P | (N) (Q) R (P) | (R) S N Q

Analyzing the groups formed: PSRN: The letter Q is omitted. QPSR: The letter N is omitted. NSQP: The letter R is omitted. NQRP: The letter S is omitted. RSNQ: The letter P is omitted.

The omitted letters (Q, N, R, S, P) follow a cyclic pattern, and each group of four letters systematically uses the remaining members of the set. This logical progression confirms that the combination of letters in option b correctly completes the series.

Explanation

The series follows a pattern where the difference between consecutive terms increases by a constant value of 2. Calculating the differences between the given numbers:

67 - 50 = 17 86 - 67 = 19 107 - 86 = 21

The differences are 17, 19, and 21, which form an arithmetic progression with a common difference of 2. Following this pattern, the next difference must be 21 + 2 = 23. To find the missing number, we add this difference to the last term: 107 + 23 = 130.

Explanation

When folding a two-dimensional net into a three-dimensional cube, faces that are positioned alternately in a straight line are always opposite to each other. In the provided layout, the vertical column consists of the sequence 5, 2, 3, and 6. Within this arrangement, the face numbered 5 and the face numbered 3 are separated by exactly one square, which is the face numbered 2. According to the geometric properties of cube nets, this alternate placement confirms that 3 and 5 will be on opposite faces of the resulting cube.

Explanation

The relationship between the terms is based on an increasing addition pattern applied to the positional values of the letters in the English alphabet. In the first pair CANOPY : DCQSUE, the letters are shifted forward by +1, +2, +3, +4, +5, and +6 respectively: C (3) +1 = 4 (D) A (1) +2 = 3 (C) N (14) +3 = 17 (Q) O (15) +4 = 19 (S) P (16) +5 = 21 (U) Y (25) +6 = 31 → 31 - 26 = 5 (E)

Applying this same logic to the third term TONSIL: T (20) +1 = 21 (U) O (15) +2 = 17 (Q) N (14) +3 = 17 (Q) S (19) +4 = 23 (W) I (9) +5 = 14 (N) L (12) +6 = 18 (R)

Combining these letters results in UQQWNR.

Explanation

The number of students who participated in at least one game is calculated by subtracting those who did not participate from the total number of students: 110 - 23 = 87. This total participating group, n(B ∪ C), consists of students playing only Badminton, only Chess, or both.

To find the number of students who participated in Badminton only, we subtract the total number of students who played Chess from the total number of participating students. Using the relation n(B only) = n(B ∪ C) - n(C), we substitute the values: 87 - 61 = 26.

This can also be verified by finding the intersection first. The number of students playing both games is n(B ∩ C) = n(B) + n(C) - n(B ∪ C), which is 45 + 61 - 87 = 19. Then, the number of students playing Badminton only is n(B) - n(B ∩ C), resulting in 45 - 19 = 26.

Explanation

The relationship can be decoded step-by-step from Varun's perspective. Varun's father-in-law's son is his brother-in-law. The only sister of this brother-in-law must be Varun's wife. The mother-in-law of Varun's wife is Varun's own mother. Since the lady in the photograph is Varun's mother, Varun is the son of that lady.

Explanation

The coding pattern is determined by the number of letters in each word of the sentence. In the first sequence, School contains 6 letters, education has 9, is has 2, free has 4, in has 2, and India has 5, which combines to form 692425. In the second sequence, College has 7 letters, education has 9, is has 2, and costly has 6, resulting in 7926.

Applying this logic to the phrase I want to become graduate, the number of letters in each word is as follows: I has 1 letter, want has 4 letters, to has 2 letters, become has 6 letters, and graduate has 8 letters. Putting these digits together in the order of the words results in the code 14268.

Explanation

The expression P + Q × R is decoded using the given definitions where + represents the brother relationship and × represents the sister relationship. The first part, P + Q, signifies that P is the brother of Q, which confirms that P is male and that P and Q are siblings. The second part, Q × R, signifies that Q is the sister of R, which confirms that Q and R are siblings. Since P is the sibling of Q and Q is the sibling of R, all three individuals belong to the same generation and share a sibling bond. Because P is a male sibling in this group, he is the brother of R.

Explanation

The logic followed in the given sets is that the square of the second number minus the first number results in the third number. The pattern can be expressed by the formula:

b² - a = c

Applying this to the first set (25, 9, 56): 9² - 25 = 81 - 25 = 56

Applying this to the second set (13, 14, 183): 14² - 13 = 196 - 13 = 183

Following the same logic for the set (27, 15, 198): 15² - 27 = 225 - 27 = 198

Explanation

The given sequence follows a geometric progression where each term is calculated by multiplying the preceding term by a constant factor of 2. The mathematical relationship for any term aₙ in the series is aₙ = aₙ₋₁ × 2.

Applying this common ratio to the numbers provided: The first term is 111. The second term is 111 × 2 = 222. The third term is 222 × 2 = 444. To find the missing fourth term, multiply the third term by 2, which gives 444 × 2 = 888.

The validity of this pattern is confirmed by the subsequent terms in the series: The fifth term is 888 × 2 = 1776. The sixth term is 1776 × 2 = 3552.

Explanation

By substituting the signs from the first option into the equation 17 ∗ 11 ∗ 42 ∗ 2 ∗ 7 = 18, we get the expression 17 - 11 + 42 × 2 ÷ 7. Following the BODMAS rule, we perform division first, then multiplication, followed by addition and subtraction.

First, solve the division and multiplication part: 42 × 2/7. Since 42 ÷ 7 = 6, the term becomes 6 × 2 = 12.

Now, substitute this back into the equation: 17 - 11 + 12.

Perform the addition and subtraction from left to right: 17 - 11 = 6, and then 6 + 12 = 18.

The left-hand side equals the right-hand side, so the equation is balanced.

Explanation

The expression E ÷ F × J + L = M can be decoded step-by-step based on the given relations. The segment E ÷ F indicates that E is the wife of F. The next part, F × J, signifies that F is the brother of J. The relation J + L establishes that J is the daughter of L. Since F is the brother of J and J is the daughter of L, it follows that F is the son of L. The final part, L = M, confirms that L is the father of M, which establishes L as a male and the father of the siblings F, J, and M. Because L is the father of F, and E is the wife of F, L is the father-in-law of E.

Explanation

The logic followed in the given pairs is that the second number is the cube of the first number, defined by the relation n : n³. Applying this rule to the alternatives, we see that 4³ = 64, 5³ = 125, and 6³ = 216. In the case of the pair 3 - 44, the cube of 3 is 3 × 3 × 3 = 27. Because 44 does not equal 27, this pair does not satisfy the mathematical relationship shared by the other three options.

Explanation

The pattern followed in the given sets is that the second number is obtained by multiplying the sum of the first and third numbers by 3.

Mathematical relation: Second Number = 3 × (First Number + Third Number)

Applying this to the given sets: For (30, 93, 1): 3 × (30 + 1) = 3 × 31 = 93 For (42, 132, 2): 3 × (42 + 2) = 3 × 44 = 132

Following the same logic for the set in option d: For (3, 30, 7): 3 × (3 + 7) = 3 × 10 = 30

Explanation

The relationship expressed is between an organism and its natural habitat. Sparrows are birds that utilize trees for nesting, shelter, and habitation. Similarly, fish are aquatic animals that live and survive in water, which serves as their primary dwelling environment. Both pairs demonstrate a consistent pattern where the first word identifies a living creature and the second word identifies the specific medium or location where it resides.

Explanation

The coding pattern involves taking the opposite letter of each character in the alphabet and then subtracting 5 from its numerical position. The position of an opposite letter is calculated as P_opp = 27 - P_orig, where P_orig is the standard alphabetical position of the letter. The final coded position is derived using the formula C = (27 - P_orig) - 5.

For the word GHOST: G (7) yields (27 - 7) - 5 = 15 (O) H (8) yields (27 - 8) - 5 = 14 (N) O (15) yields (27 - 15) - 5 = 7 (G) S (19) yields (27 - 19) - 5 = 3 (C) T (20) yields (27 - 20) - 5 = 2 (B)

Applying this logic to the word RULES: R (18) yields (27 - 18) - 5 = 4 (D) U (21) yields (27 - 21) - 5 = 1 (A) L (12) yields (27 - 12) - 5 = 10 (J) E (5) yields (27 - 5) - 5 = 17 (Q) S (19) yields (27 - 19) - 5 = 3 (C)

The resulting code for RULES is DAJQC.

Explanation

The instruction is to interchange the plus and minus signs. In equation (c), the original expression is 18 ÷ 3 + 8 × 5 - 4 = 30. Replacing the + with - and the - with +, the expression becomes 18 ÷ 3 - 8 × 5 + 4. Following the BODMAS rule, we first perform the division: 18 ÷ 3 = 6. The expression now stands as 6 - 8 × 5 + 4. Next, we perform the multiplication: 8 × 5 = 40, which gives 6 - 40 + 4. Finally, performing the addition and subtraction yields 6 + 4 - 40 = 10 - 40 = -30. Because the result -30 does not match the right-hand side value of 30, the equation is not correct.

Explanation

The series is constructed by applying a specific mathematical pattern to the alphabetical position of each letter in the triplets. By converting the letters to their numerical positions (A=1, B=2, ..., Z=26), the logic for each position is as follows:

For the first letter of each triplet, there is a constant decrease of 6 places. The sequence starts with A (1), and subtracting 6 gives 1 - 6 = -5. In a 26-letter alphabet, -5 corresponds to position 21 (U). Continuing this pattern, 21 - 6 = 15 (O), 15 - 6 = 9 (I), and 9 - 6 = 3, which corresponds to the letter C.

For the second letter of each triplet, there is a constant decrease of 3 places. Starting with C (3), subtracting 3 results in 0, which corresponds to position 26 (Z). Following this, 26 - 3 = 23 (W), 23 - 3 = 20 (T), and 20 - 3 = 17, which corresponds to the letter Q.

For the third letter of each triplet, there is a constant increase of 1 place. The sequence starts with C (3), followed by D (4), E (5), and F (6). Adding 1 to the last position gives 6 + 1 = 7, which corresponds to the letter G.

Combining the letters derived from these patterns—C for the first position, Q for the second, and G for the third—the next term in the series is CQG.

Explanation

Dictionary order is established by comparing words letter by letter. All five words begin with the prefix S-I-C-K. The word Sick, having no additional letters, comes 1st. Among the remaining words, the 5th letter e in Sicken alphabetically precedes l and n, making Sicken the 2nd word. Comparing the words starting with S-I-C-K-L, the 6th letter e in Sickle precedes the 6th letter y in Sickly, placing Sickle in the 3rd position.

Explanation

In syllogism, a statement of the form Some L are R establishes only a partial intersection between the two sets, which does not support the universal conclusion that All R are L. Similarly, the statement Some A are R indicates an overlap between A and R but provides no logical connection or information regarding the relationship between set A and set L. Because there is no mediated or direct link confirming that every element of A is in L, or that every element of R is in L, neither conclusion follows from the given premises.

Explanation

The relationship between the words is based on an object and its designated storage place. A closet is a furniture item or a small room specifically designed for the organized storage of clothes. Similarly, an armoury is a specialized place or building where guns, ammunition, and other military equipment are kept and maintained. Therefore, just as clothes are kept in a closet, guns are kept in an armoury.

Explanation

To determine the correct equation, the signs + and - must be swapped, and the numbers 2 and 4 must be interchanged within the given expression. In option c, the original equation is 7 × 4 - 2 ÷ 1 + 5 = 13. Applying the required changes, the number 4 becomes 2, the minus sign - becomes plus +, the number 2 becomes 4, and the plus sign + becomes minus -.

The modified left-hand side of the equation is 7 × 2 + 4 ÷ 1 - 5. Following the BODMAS rule, the operations are performed in the order of division, multiplication, addition, and finally subtraction:

7 × 2 + 4 - 5 14 + 4 - 5 18 - 5 13

The calculated value matches the right-hand side of the equation exactly.

Explanation

The series follows a consistent pattern for each position within the letter-clusters. For the first letter, there is an increment of 3: C (3) +3 F (6) +3 I (9) +3 L (12) +3 O (15). The second letter decreases by 2: Z (26) -2 X (24) -2 V (22) -2 T (20) -2 R (18). The third letter increases by 1: N (14) +1 O (15) +1 P (16) +1 Q (17) +1 R (18). The fourth letter decreases by 1: M (13) -1 L (12) -1 K (11) -1 J (10) -1 I (9). Applying these transformations to the third cluster IVPK results in the missing cluster LTQJ.

Explanation

The letter-clusters follow a specific pattern based on the numerical positions of letters in the English alphabet where A=1, B=2, …, Z=26. In three of the clusters, the letters are determined by subtracting 5, 4, and 2 sequentially from the preceding letter's position. For example, in QLHF, the sequence is 17 (Q) - 5 = 12 (L), 12 - 4 = 8 (H), and 8 - 2 = 6 (F). Similarly, VQMK follows 22 (V) - 5 = 17 (Q), 17 - 4 = 13 (M), and 13 - 2 = 11 (K), while SNJH follows 19 (S) - 5 = 14 (N), 14 - 4 = 10 (J), and 10 - 2 = 8 (H).

In the cluster IDAY, the numerical positions are I=9, D=4, A=1, and Y=25. While the first transition follows the pattern 9 - 5 = 4 (D), the subsequent transition is 4 - 3 = 1 (A), and the final transition is 27 (A) - 2 = 25 (Y). The deviation occurs at the second step, where the subtraction is 3 instead of the 4 observed in all other clusters, making IDAY the odd cluster.

Explanation

The coding logic follows a two-step process: reversing the word and then applying an alternating increment of +1 and +2 to each letter.

For the word EARLY: Reverse: Y L R A E Apply increments: Y + 1 = Z L + 2 = N R + 1 = S A + 2 = C E + 1 = F Result: ZNSCF

For the word GAUGE: Reverse: E G U A G Apply increments: E + 1 = F G + 2 = I U + 1 = V A + 2 = C G + 1 = H Result: FIVCH

Following the same logic for INBOX: Reverse: X O B N I Apply increments: X + 1 = Y O + 2 = Q B + 1 = C N + 2 = P I + 1 = J Result: YQCPJ

Explanation

The statements establish a hierarchical subset relationship between the categories. Given that all bears are rabbits and all rabbits are dogs, the transitive property of inclusion ensures that the entire set of bears is contained within the set of dogs. This makes the statement all bears are dogs logically certain, validating Conclusion III. Since all bears are dogs, it follows by definition that there exists a portion of the dog population that consists of bears, which confirms Conclusion II. The third premise indicates that some dogs are black, but it does not specify which dogs possess this trait. Because there is no stated requirement for the black trait to overlap with the rabbit subset, Conclusion I cannot be logically deduced from the provided information.

Explanation

Based on the given codes, we decode the relationship expression K # L | M @ N # P step by step to determine the lineage.

The segment K # L indicates that L is the son of K. The segment L | M specifies that L is the father of M. Combining these, M is the son of L, which makes M the grandson of K. The segment M @ N defines M as the husband of N, identifying N as the wife of M. Finally, the segment N # P states that P is the son of N. Since N is married to M, P is also the son of M.

By tracing the direct male lineage from K, we find that L is K's son, M is L's son (K's son's son), and P is M's son. Therefore, P is the son of the son of the son of K, which corresponds to the relationship son's son's son.

Explanation

The statements can be analyzed using set theory where the predicate All translates to a subset relationship. Statement I establishes that A ⊆ R and Statement II establishes that R ⊆ C.

Conclusion I follows through the transitive property of subsets. Since A ⊆ R and R ⊆ C, it logically necessitates that A ⊆ C, meaning all elements of A are contained within C.

Conclusion II follows from the principle of conversion. If the statement All A are R is true, it implies that the intersection of sets A and R is set A (A ∩ R = A). In categorical logic, if all members of a class A are members of class R, then at least some members of class R are members of class A. Therefore, Some R are A is a valid immediate inference from Statement I.

Explanation

The series follows a pattern where each subsequent number is obtained by adding consecutive powers of 4 to the preceding number. The logic can be expressed by the formula Tₙ₊₁ = Tₙ + 4ⁿ.

The difference between the first two terms is 33 - 29 = 4, which is 4¹. Applying the pattern for the next term, we add 4² to the second term: 33 + 4² = 33 + 16 = 49

To verify this pattern for the remaining terms in the series: 49 + 4³ = 49 + 64 = 113 113 + 4⁴ = 113 + 256 = 369

The calculations align perfectly with the given numbers in the sequence.

Explanation

To find the incorrect equation, we interchange the minus sign and the multiplication sign in the expression 7 × 2 + 27 ÷ 9 - 4 = 18 and evaluate it using the BODMAS rule. The modified expression becomes: 7 - 2 + 27 ÷ 9 × 4

Applying division first: 27 ÷ 9 = 3 The expression simplifies to 7 - 2 + 3 × 4.

Next, performing the multiplication: 3 × 4 = 12 The expression becomes 7 - 2 + 12.

Finally, performing addition and subtraction: 7 - 2 = 5 5 + 12 = 17

The calculated value is 17. Since the right-hand side of the original equation is 18, and 17 ≠ 18, the equation is not correct.

Explanation

The second conclusion follows directly from the third statement, All potatoes are fruits. In formal logic, if one set is entirely contained within another, there must be a partial overlap from the perspective of the larger set. Since the entire category of potatoes exists within the category of fruits, it is logically certain that some fruits are potatoes.

The third conclusion is derived by combining the second and third statements. The second statement establishes that there is an intersection between the set of peas and the set of potatoes. Since the third statement asserts that all potatoes are fruits, any element that belongs to the potato set must also belong to the fruit set. Consequently, the portion of peas that consists of potatoes must also consist of fruits, confirming that some peas are fruits.

The first conclusion does not follow because the statements only link tomatoes to peas and peas to potatoes. While all tomatoes are inside the pea set, the potato set only overlaps with an unspecified part of the pea set. There is no information provided to guarantee that this overlap includes any part of the tomato set.

Explanation

The series is constructed by applying a consistent arithmetic pattern to the numerical positions of the letters in each cluster. In the first position, the letters follow a pattern of -2, moving from M (13) to K (11), then to I (9), leading to G (7), and finally E (5). In the second position, the letters follow a pattern of +1, moving from B (2) to C (3), then to D (4), leading to E (5), and finally F (6). In the third position, the letters follow a pattern of -1, moving from T (20) to S (19), then to R (18), leading to Q (17), and finally P (16). In the fourth position, the letters follow a pattern of +2, moving from N (14) to P (16), then to R (18), leading to T (20), and finally V (22). Applying these operations to the third cluster IDRR results in the fourth cluster GEQT.

Explanation

The series follows a specific addition pattern for each corresponding letter in the triplets based on their positions in the English alphabet (A=1, B=2, ..., Z=26).

For the first letter of each group, the increment is +4: L (12) + 4 = P (16) P (16) + 4 = T (20) T (20) + 4 = X (24) X (24) + 4 = 28. In a cyclic alphabet, 28 mod 26 = 2, which is B.

For the second letter of each group, the increment is +8: M (13) + 8 = U (21) U (21) + 8 = 29 mod 26 = 3 (C) C (29) + 8 = 37 mod 26 = 11 (K) K (37) + 8 = 45 mod 26 = 19, which is S.

For the third letter of each group, the increment is +9: R (18) + 9 = 27 mod 26 = 1 (A) A (27) + 9 = 36 mod 26 = 10 (J) J (36) + 9 = 45 mod 26 = 19 (S) S (45) + 9 = 54 mod 26 = 2, which is B.

By combining these results, the next term in the series is BSB.

Explanation

The relationship between the first two words is based on a tool and its primary function; a knife is a kitchen utensil specifically designed for the purpose of cutting. Similarly, a ladle is a long-handled tool with a deep, bowl-shaped end that is primarily used for the purpose of serving liquid-based foods such as soups, stews, and sauces.

Explanation

The relationship between the words in the given pair is that of an animal and its specific dwelling or shelter. A hen is kept in a coop, which is a small cage or building used for housing poultry. Similarly, a bee lives in a hive, which is the structure used as a residence for a colony of bees. In both cases, the second word represents the primary habitat or man-made shelter specifically associated with the animal mentioned in the first word.

Explanation

The numerical relationship between the pairs is defined by a constant difference of 75. In the first pair, the second number is obtained by subtracting 75 from the first number: 687 - 75 = 612. Similarly, in the third pair, the sixth number is derived from the fifth number using the same subtraction: 621 - 75 = 546. Following this established pattern for the second pair, the missing number is calculated by subtracting 75 from 713, which results in 713 - 75 = 638.

Explanation

In the given sets of numbers, the pattern follows an arithmetic progression where each subsequent number is obtained by subtracting a constant value of 5 from the preceding number. In the other groups, the difference between the first and second number is 5, and the difference between the second and third number is also 5. For example, 405 - 400 = 5 and 400 - 395 = 5. In group c, the difference between the first two numbers is 700 - 690 = 10, while the difference between the next two numbers is 690 - 685 = 5. Because the common difference is not maintained as 5 throughout the sequence, this group is the odd one out.

Explanation

The coding pattern follows a simple logic where each digit in the code represents the total number of letters in the corresponding word of the phrase. For instance, in the phrase feel at home, the word feel has 4 letters, at has 2 letters, and home has 4 letters, resulting in the code 424. Applying this rule to the phrase the kite is flying, we count the letters in each word: the contains 3 letters, kite contains 4 letters, is contains 2 letters, and flying contains 6 letters. Combining these counts in sequence yields the code 3426.

Explanation

The equation in option C is 20 × 8 - 4 ÷ 2 + 7 = 50. By interchanging the signs - and ÷, the expression becomes 20 × 8 ÷ 4 - 2 + 7. Following the BODMAS rule, we first perform the division and multiplication from left to right: 20 × 8 = 160, then 160 ÷ 4 = 40. Substituting this value back into the expression gives 40 - 2 + 7 = 45. Since 45 is not equal to 50, this equation is not correct after the interchange. The other three equations become correct: A: 12 ÷ 4 + 11 × 3 - 8 = 3 + 33 - 8 = 28; B: 35 ÷ 5 + 8 - 4 × 3 = 7 + 8 - 12 = 3; D: 10 + 8 × 6 ÷ 4 - 2 = 10 + 12 - 2 = 20.

Explanation

The coding logic follows a specific transformation pattern for five-letter words. The first and second letters are interchanged, the third letter is shifted forward by one position in the alphabetical sequence (+1), and the fourth and fifth letters are interchanged.

In the word EAGER, interchanging the first two letters E and A gives AE. The third letter G is incremented by one to become H. Interchanging the last two letters E and R results in RE. Combining these yields AEHRE.

In the word GIRLS, interchanging G and I gives IG. The third letter R is incremented by one to become S. Interchanging the last two letters L and S results in SL. Combining these yields IGSSL.

Applying this same logic to ISSUE, the first two letters I and S are interchanged to form SI. The third letter S is incremented by one to become T. The last two letters U and E are interchanged to form EU. Concatenating these segments results in the code SITEU.

Explanation

The pattern in each row follows the mathematical logic where the third number is calculated as Third Number = (Second Number × 5) - First Number. In the first row, substituting the numbers into the formula gives 9 × 5 - 18 = 45 - 18 = 27. In the second row, the operation is 36 × 5 - 40 = 180 - 40 = 140. Applying this consistent logic to the third row, the missing number is calculated as 13 × 5 - 40 = 65 - 40 = 25.

Explanation

To arrange the words in alphabetical order, they are compared letter by letter from left to right. All five words share the initial prefix Kin. At the fourth letter, Kinglet, Kingship, Kingdom, and Kingly all have g, while Kinsfolk has s. Because g appears before s in the alphabet, Kinsfolk (4) is placed at the end of the list. Next, comparing the fifth letter of the words starting with King, Kingdom has d, Kinglet and Kingly have l, and Kingship has s. Alphabetical order dictates that d comes first, followed by l, and then s, which places Kingdom (3) at the start and Kingship (2) in the fourth position. Finally, to distinguish between Kinglet (1) and Kingly (5), the sixth letters are compared; e in Kinglet precedes y in Kingly. This analysis results in the dictionary sequence 3, 1, 5, 2, 4.

Explanation

The letter clusters are categorized based on the numerical positions of their letters in the English alphabet. The clusters MKI, YWU, and SQO follow a uniform pattern where each letter decreases by exactly 2 positions from the preceding one. Specifically, MKI corresponds to the positions 13, 11, 9; YWU corresponds to 25, 23, 21; and SQO corresponds to 19, 17, 15. In each of these cases, the common difference is -2. The cluster GED is different because it deviates from this pattern. The alphabetical positions for GED are G(7), E(5), and D(4). While the gap between G and E is 2, the gap between E and D is only 1. This inconsistency in the letter intervals makes GED the odd cluster among the group.

Explanation

In the expression P × Q ÷ R, the symbol × indicates that the first person is the father of the second, and ÷ indicates that the first person is the brother of the second. Breaking down the expression, P × Q establishes that P is the father of Q. The next part, Q ÷ R, establishes that Q is the brother of R. Because Q and R are siblings (specifically, Q is the brother of R), any parent of Q is also the parent of R. Given that P is the father of Q, P must also be the father of R.

Explanation

The logic followed in the given sets is that the third number is the sum of the cubes of the first and second numbers. The formula is a³ + b³ = c.

In the first set (3, 2, 35): 3³ + 2³ = 27 + 8 = 35

In the second set (1, 4, 65): 1³ + 4³ = 1 + 64 = 65

Applying the same logic to the set (7, 2, 351): 7³ + 2³ = 343 + 8 = 351

Explanation

The coding language follows a pattern where each letter of the word is shifted forward by three positions in the English alphabetical sequence (Letter + 3).

For the word MOBILE: M (13) + 3 = P (16) O (15) + 3 = R (18) B (2) + 3 = E (5) I (9) + 3 = L (12) L (12) + 3 = O (15) E (5) + 3 = H (8)

For the word SILENT: S (19) + 3 = V (22) I (9) + 3 = L (12) L (12) + 3 = O (15) E (5) + 3 = H (8) N (14) + 3 = Q (17) T (20) + 3 = W (23)

Applying the same +3 shift logic to the word PAINTING: P (16) + 3 = S (19) A (1) + 3 = D (4) I (9) + 3 = L (12) N (14) + 3 = Q (17) T (20) + 3 = W (23) I (9) + 3 = L (12) N (14) + 3 = Q (17) G (7) + 3 = J (10)

Following this systematic alphabetical increment, the letters transform to produce the corresponding code.