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

Explanation

After interchanging + and - in option B, the equation becomes 20 ÷ 4 + 5 × 6 - 3. Applying the BODMAS rule, this simplifies to 5 + 30 - 3, which equals 32.

Explanation

The logic followed by the other number pairs is y = 2x + 1, where x is the first number and y is the second number. Applying this rule to the other pairs, we get 11 × 2 + 1 = 23, 25 × 2 + 1 = 51, and 13 × 2 + 1 = 27. For the pair 9-16, the rule results in 9 × 2 + 1 = 19. Because the second number provided is 16 rather than 19, this pair does not satisfy the mathematical relationship shared by the rest of the alternatives.

Explanation

The expression A%B-C+D*E implies that A is the husband of B, B is the mother of C, C is the father of D, and D is the sister of E. This makes C the father of E, and since A is the father of C, A is the father's father (paternal grandfather) of E.

Explanation

The letter-clusters in options a, c, and d follow a consistent numerical pattern based on the alphabetical positions of the letters (where A = 1, B = 2, …, Z = 26). In these groups, the second letter is the first letter plus 5, and the third letter is the second letter plus 7.

In KPW, the positions are K(11), P(16), and W(23). The differences are 11 + 5 = 16 and 16 + 7 = 23. In DIP, the positions are D(4), I(9), and P(16). The differences are 4 + 5 = 9 and 9 + 7 = 16. In SXE, the positions are S(19), X(24), and E(5). In a cyclic alphabet, 24 + 7 = 31, and 31 26 = 5, which corresponds to E.

The cluster QGM does not follow this +5, +7 pattern. Its positions are Q(17), G(7), and M(13). The change from Q to G is -10, and from G to M is +6, making it the odd one out.

Explanation

The logic followed in the given sets is b = ((a + c)²)/(2), where a, b, and c represent the first, second, and third numbers of the set respectively.

In the first set (4, 50, 6): ((4 + 6)²)/(2) = (10²)/(2) = ¹⁰⁰⁄₂ = 50

In the second set (13, 128, 3): ((13 + 3)²)/(2) = (16²)/(2) = ²⁵⁶⁄₂ = 128

Applying this rule to the set (15, 162, 3): ((15 + 3)²)/(2) = (18²)/(2) = ³²⁴⁄₂ = 162

Explanation

To arrange the words in dictionary order, we compare them letter by letter from left to right. All five words begin with the prefix Sub-. Comparing the fourth letters, l in Sublimity (2) comes before m in the other words, making it the first word in the sequence. For the remaining words starting with Subm-, we examine the fifth letters: a in Submarine (5), e in Submerge (3) and Submerse (1), and i in Submit (4). Alphabetically, a comes first, followed by e and then i. This places Submarine (5) second and Submit (4) last. To determine the order between Submerge (3) and Submerse (1), we compare the seventh letters since the first six letters Submer are identical. Because g in Submerge (3) precedes s in Submerse (1), word 3 comes before word 1. Arranging these positions gives the final sequence 2, 5, 3, 1, 4.

Explanation

The relationship followed in the given pairs is that the second term is obtained by multiplying the first term by 3 and then subtracting 2. Applying this rule to the known pairs:

For 11 : 31, we have 11 × 3 - 2 = 33 - 2 = 31. For 14 : 40, we have 14 × 3 - 2 = 42 - 2 = 40.

Applying the same logic to the middle pair where the second term is 25, let the unknown third term be x. Then, 3x - 2 = 25. Solving for x, we get 3x = 27, which gives x = 9.

Explanation

The coding pattern involves a specific rearrangement of the letter positions in each five-letter word. The first and second letters are swapped, the third letter remains fixed in its original position, and the fourth and fifth letters are swapped. For the word FACES, the pair FA becomes AF, C remains C, and ES becomes SE, resulting in AFCSE. For JEANS, the pair JE becomes EJ, A remains A, and NS becomes SN, resulting in EJASN. Applying this same rule to HANGS, the first two letters HA are swapped to AH, the third letter N stays in place, and the last two letters GS are swapped to SG. This sequence forms the code AHNSG.

Explanation

In the expression P ÷ R - Q, the relation P ÷ R indicates that P is the sister of R, which establishes that P and R are siblings belonging to the same generation. The relation R - Q indicates that R is the father of Q. Since R is a father, R is definitively male. Given that R is a male sibling of P, the expression confirms that R is the brother of P.

Explanation

To determine the word in the fourth position, compare the words alphabetically from left to right. All five words share the first three letters A-G-E. Examining the fourth letter, Ageism and Ageist contain i, while Agenda, Agency, and Agentry contain n. Since i comes before n in the alphabet, Ageism and Ageist are the first two words in the sequence. For the words starting with A-G-E-N, comparing the fifth letter reveals c in Agency, d in Agenda, and t in Agentry. The alphabetical order of these letters is c, then d, and finally t. This sequence makes Agency the third word, Agenda the fourth word, and Agentry the fifth word.

Explanation

The coding logic follows a two-step process: swapping the first and last letters of the word and then shifting every letter forward by 2 positions in the alphabetical sequence.

For the word FANCY, swapping the first letter F and the last letter Y results in YANCF. Applying a +2 shift to each letter gives: Y + 2 = A A + 2 = C N + 2 = P C + 2 = E F + 2 = H This results in the code ACPEH.

For the word TRACTOR, swapping the first letter T and the last letter R results in RRACTOT. Applying a +2 shift to each letter gives: R + 2 = T R + 2 = T A + 2 = C C + 2 = E T + 2 = V O + 2 = Q T + 2 = V This results in the code TTCEVQV.

Applying this logic to the word CARROT: Swap the first letter C and the last letter T to get TARROC. Apply a +2 shift to each letter in TARROC: T (20) + 2 = V (22) A (1) + 2 = C (3) R (18) + 2 = T (20) R (18) + 2 = T (20) O (15) + 2 = Q (17) C (3) + 2 = E (5)

The resulting code for CARROT is VCTTQE.

Explanation

The logical relationship between the categories is established through a transitive chain. The statement that all whites are pinks combined with the statement that all pinks are oranges creates a subset hierarchy where Whites ⊆ Pinks ⊆ Oranges. This directly confirms Conclusion I, as every element in the white category is necessarily contained within the orange category. Because all whites are oranges, it follows that there is an overlap between the two sets; specifically, those oranges that are whites satisfy the condition that some oranges are whites, which validates Conclusion III. Therefore, conclusions I and III are the only ones that logically result from the given premises.

Explanation

The numbers follow the formula y = x² + 10. For the first number 14, the square is 196 and adding 10 results in 14² + 10 = 206. This group is the odd one out because the second number is 208, which represents an addition of 12 to the square rather than 10.

Explanation

The relationship expression A | B # C | D @ E % F + G can be broken down as follows: A | B indicates that A is the wife of B. B # C means B is the father of C, which implies A is the mother of C. C | D establishes that C is the wife of D. Since A is the mother of C and C is married to D, A is the mother of D's wife. In kinship terms, the mother of one's spouse is defined as the mother-in-law. Therefore, A is the mother-in-law of D.

Explanation

The relationship between the first pair of words is based on antonyms. Lethargy refers to a state of drowsiness, laziness, or lack of energy, while alertness represents a state of being active, watchful, and observant. To maintain the same relationship for the second pair, the word gentle requires its opposite. Gentle describes a character or action that is mild, soft, or tender. The word harsh serves as the direct antonym because it describes something unpleasantly rough, severe, or cruel.

Explanation

The pattern followed in the given sets is that the third number is equal to the sum of half of the first number and the second number. The relationship can be expressed by the formula: n₃ = n₁{2} + n₂

Applying this logic to the provided sets: For (24, 9, 21): ²⁴⁄₂ + 9 = 12 + 9 = 21 For (34, 16, 33): ³⁴⁄₂ + 16 = 17 + 16 = 33

In option d (42, 9, 30), the same mathematical logic is satisfied: ⁴²⁄₂ + 9 = 21 + 9 = 30

Explanation

Conclusion III follows directly from Statement II through the logical rule of conversion. Statement II is a universal affirmative statement of the form All L are M. According to the rules of immediate inference, any statement in the form All A are B logically implies the existence of its converse, Some B are A. Therefore, if the entire set L is contained within the set M, it is necessarily true that at least some elements of the set M belong to the set L.

Conclusion I (Some M are not R) does not follow because the premise All R are M does not provide information regarding the existence of elements in M that lie outside of R; it is possible for the sets R and M to be identical. Conclusion II (Some L are R) does not follow because while both R and L are contained within the set M, the premises do not establish any specific relationship, overlap, or intersection between the sets R and L themselves. Because these sets could be entirely disjoint, the conclusion is not logically certain. Only Conclusion III is supported by the given statements.

Explanation

The relationship between the numbers follows the mathematical pattern n₂ = (n₁ ÷ 4) - 8.

In the first pair, 76 ÷ 4 = 19, and 19 - 8 = 11. In the third pair, 68 ÷ 4 = 17, and 17 - 8 = 9.

Applying this same logic to the middle pair, divide 88 by 4 to get 22. Subtracting 8 from 22 results in 14.

Explanation

To determine which equation is not correct, we apply the interchange of signs - and ÷ along with the numbers 8 and 2 into the given expressions and evaluate them using BODMAS rules.

For Equation I, 5 + 7 - 8 × 4 ÷ 2 = 9 transforms into 5 + 7 ÷ 2 × 4 - 8. Calculating the expression: 5 + (7 ÷ 2) × 4 - 8 5 + 3.5 × 4 - 8 5 + 14 - 8 = 11 Since the result 11 does not equal 9, Equation I is not correct.

For Equation II, 3 + 8 × 4 - 2 ÷ 1 = 3 transforms into 3 + 2 × 4 ÷ 8 - 1. Calculating the expression: 3 + 2 × (4 ÷ 8) - 1 3 + 2 × 0.5 - 1 3 + 1 - 1 = 3 Since the result 3 equals the given value, Equation II is correct.

Because the question asks to identify the equation that is not correct, and only Equation I fails to produce the specified result, the condition is satisfied by Equation I alone.

Explanation

The series follows a specific addition pattern for each position in the letter clusters: the first letter increases by 3 (C+3=F, F+3=I, I+3=L), the second letter increases by 2 (L+2=N, N+2=P, P+2=R), and the third and fourth letters both increase by 1 (P+1=Q, Q+1=R and M+1=N, N+1=O). Applying these increments to FNQN yields the cluster IPRO.

Explanation

The relationship in this analogy is based on geographical definitions of enclosure. A lake is a body of water that is completely surrounded by land on all sides. Following this same logic in reverse, an island is a body of land that is completely surrounded by water on all sides. The first word in each pair represents the geographical feature, while the second word represents the medium that encompasses it. Therefore, water is the surrounding medium for an island just as land is for a lake.

Explanation

By interchanging the numbers 8 and 5 and the signs - and × in the given equation 5 + 44 - 8 × 25 = 203, the modified expression becomes:

8 + 44 × 5 - 25

Applying the BODMAS rule, we first perform the multiplication: 44 × 5 = 220

The equation then becomes: 8 + 220 - 25

Next, we perform the addition: 8 + 220 = 228

Finally, we perform the subtraction: 228 - 25 = 203

The calculated value matches the right-hand side of the equation, proving that the interchange of these specific numbers and signs makes the mathematical statement correct.

Explanation

The relationship between the numbers in the given sets is defined by the formula n₁ = 2 × (n₂ × n₃), where the first number is twice the product of the second and third numbers. For the set (60, 5, 6), the calculation is 2 × (5 × 6) = 2 × 30 = 60. Similarly, for the set (48, 8, 3), the calculation is 2 × (8 × 3) = 2 × 24 = 48. Following this same pattern for the set (24, 4, 3), the product of the second and third numbers is 4 × 3 = 12, and multiplying this product by 2 results in 12 × 2 = 24, which matches the first number.

Explanation

In the given expression C # D @ E % Z | L # M - N * P, the relationship between Z and N can be traced through the following steps:

E % Z indicates that E is the father of Z. Z | L indicates that Z is the son of L. Therefore, E and L are husband and wife, making L the mother of Z.

L # M indicates that L is the sister of M. M - N indicates that M is the daughter of N. Since L and M are sisters and M is the daughter of N, L is also the daughter of N.

N * P indicates that N is the wife of P, establishing N as the female head of the family.

Since L is the daughter of N and Z is the son of L, Z is the grandson of N.

Explanation

The relationship in the given sets is that the first number is the square of the sum of the second and third numbers: (b + c)² = a. In the first set (144, 9, 3), (9 + 3)² = 12² = 144. In the second set (225, 7, 8), (7 + 8)² = 15² = 225. Applying this logic to the options, only option B fits: (5 + 3)² = 8² = 64.

Explanation

Based on the syllogism rules and set theory, we analyze the statements as follows: the first statement establishes that the set of pens is a subset of plates (Pens ⊆ Plates), and the second statement establishes that the set of plates is a subset of trays (Plates ⊆ Trays). By the transitive property of subsets, if all pens are plates and all plates are trays, then all pens are trays (Pens ⊆ Trays). In logic, the statement all A are B implies the converse some B are A. Therefore, because all pens are trays, it is logically certain that some trays are pens, making conclusion II valid.

The third statement indicates an intersection between trays and boxes (Trays ∩ Boxes ≠ ∅), but it provides no specific information regarding the relationship of boxes with plates or pens. Consequently, conclusions I and III cannot be definitively concluded. Conclusion IV is directly contradicted by the statement that all plates are trays, which ensures that at least some trays are plates. Thus, only conclusion II follows.

Explanation

The coding logic follows a two-step process: first, find the reverse alphabetical position of each letter using the formula 27 - standard position, and then apply a sequential mathematical pattern of +2, -2, +2.

For CAP: C: Standard position 3, reverse is 27 - 3 = 24. Applying 24 + 2 = 26. A: Standard position 1, reverse is 27 - 1 = 26. Applying 26 - 2 = 24. P: Standard position 16, reverse is 27 - 16 = 11. Applying 11 + 2 = 13. The result is 262413.

For LOG: L: Standard position 12, reverse is 27 - 12 = 15. Applying 15 + 2 = 17. O: Standard position 15, reverse is 27 - 15 = 12. Applying 12 - 2 = 10. G: Standard position 7, reverse is 27 - 7 = 20. Applying 20 + 2 = 22. The result is 171022.

For BED: B: Standard position 2, reverse is 27 - 2 = 25. Applying 25 + 2 = 27. Since there are 26 letters in the alphabet, 27 cycles back to 1 (27 - 26 = 1). E: Standard position 5, reverse is 27 - 5 = 22. Applying 22 - 2 = 20. D: Standard position 4, reverse is 27 - 4 = 23. Applying 23 + 2 = 25. Combining these values gives the code 12025.

Explanation

For A to be the paternal uncle of C, A must be the brother of Cs father. According to the given definitions, the expression A ÷ B means A is the brother of B. Further, the expression B × C means B is the father of C. By combining these two relationships in the expression A ÷ B × C, we establish that A is the brother of B, who is the father of C. This sequence confirms that A is the paternal uncle of C.

Explanation

In the letter-cluster QLA, the first two letters Q (17) and L (12) have a positional sum of 17 + 12 = 29, which deviates from the pattern of using opposite alphabetical pairs where the sum of positions must be 27 (A=1, B=2, …, Z=26). Additionally, the third letter A (1) is 10 places ahead of the first letter Q in the cyclical alphabet (17 + 10 = 27 ≡ 1 26), whereas the structural logic of the group requires a consistent positional increment of exactly +7 from the first letter to the third. Because QLA fails to satisfy both the opposite-pairing rule for the first two letters and the +7 offset rule for the third letter, it is the outlier.

Explanation

The coding logic involves swapping the first and last letters of the word while incrementing the intermediate letters by two positions in the English alphabetical order. For the word BRIGHT, the first letter B and the last letter T are swapped. The intermediate letters R, I, G, and H are shifted by +2 as follows: R(18) + 2 = T(20), I(9) + 2 = K(11), G(7) + 2 = I(9), and H(8) + 2 = J(10). Combining these results in the code TTKIJB.

Similarly, for the word ROAST, the letters R and T are swapped, and the intermediate letters O, A, and S are shifted: O(15) + 2 = Q(17), A(1) + 2 = C(3), and S(19) + 2 = U(21), resulting in TQCUR. Applying this pattern to AROUND, the first letter A and the last letter D are swapped to positions six and one, respectively. The intermediate letters R, O, U, and N are then incremented: R(18) + 2 = T(20), O(15) + 2 = Q(17), U(21) + 2 = W(23), and N(14) + 2 = P(16). Placing these between the swapped letters D and A yields the final code DTQWPA.

Explanation

The relationship established in the first pair of words is based on synonymy, as Commence and Begin are synonymous terms meaning to start or initiate. Applying the same logic to the second pair, a Doctrine refers to a set of principles, dogmas, or a system of tenets held and taught by a specific group, such as a religion or political party. Among the choices, Belief is the synonym that corresponds to the meaning of Doctrine.

Explanation

By interchanging the signs - and × in the equation 4 × 5 - 36 ÷ 6 + 10 = 10, the modified expression becomes 4 - 5 × 36 ÷ 6 + 10. To evaluate this, we follow the BODMAS rule. First, perform the division: 36 ÷ 6 = 6, which changes the expression to 4 - 5 × 6 + 10. Next, perform the multiplication: 5 × 6 = 30, leading to 4 - 30 + 10. Finally, performing the addition and subtraction results in 14 - 30 = -16. Since the calculated value -16 does not equal the right-hand side value of 10, this equation is not correct.

Explanation

To solve the equation 686 - 14 × 49 + 400 ÷ 5 = 596, we interchange the numbers 5 and 49 and the signs ÷ and -. Substituting these changes into the original expression, the equation transforms as follows:

686 ÷ 14 × 5 + 400 - 49 = 596

Applying the BODMAS rule, we first perform the division: 686 ÷ 14 = 49

Next, we perform the multiplication: 49 × 5 = 245

Finally, we perform the addition and subtraction: 245 + 400 - 49 = 645 - 49 = 596

The resulting value matches the right-hand side of the equation, confirming that the specified interchanges satisfy the mathematical statement.

Explanation

To determine the dictionary order, we compare the letters of each word from left to right. All five words share the same first four letters, Devo. We then examine the fifth letter of each word: c in Devocalize, l in Devolution, t in Devotement, t in Devotional, and u in Devoutness. Arranging these alphabetically, c appears first, followed by l, then the words starting with t, and finally u. Since u is the alphabetically last character among the fifth letters provided, Devoutness naturally falls into the fifth position. For the words sharing the fifth letter t, Devotement precedes Devotional because the sixth letter e comes before i. Consequently, the complete sequence is Devocalize, Devolution, Devotement, Devotional, and Devoutness.

Explanation

The numbers in each set follow an arithmetic progression where the sum of the first and third numbers is equal to twice the middle number, defined by the relation a + c = 2b.

For the set (34, 23, 12): 34 + 12 = 46 2 × 23 = 46

For the set (71, 37, 3): 71 + 3 = 74 2 × 37 = 74

For the set (19, 55, 91): 19 + 91 = 110 2 × 55 = 110

The relationship holds because the common difference between consecutive terms in this set is 36, just as the previous sets maintained a constant difference between their respective terms.

Explanation

The pattern followed by the other three pairs is x : (x² - 1). In these pairs, the number on the right is one less than the square of the number on the left. Specifically, 9² - 1 = 80, 5² - 1 = 24, and 11² - 1 = 120. In the case of 7- 52, the calculation 7² - 1 results in 48, not 52, which makes it the odd pair that does not conform to the established rule.

Explanation

The series follows a specific addition and subtraction pattern for each corresponding letter position in the strings. By converting letters to their numerical positions in the alphabet (A=1, B=2, ..., Z=26), we can determine the next term.

For the first letter, the pattern is T (20), W (23), Z (26), C (3), where 3 is added to the previous value. Following this, 3 + 3 = 6, which corresponds to the letter F.

For the second letter, the pattern is M (13), G (7), A (1), U (21), where 6 is subtracted from the previous value. Subtracting 6 from U (21) results in 15, which corresponds to the letter O.

For the third letter, the pattern is T (20), C (3), L (12), U (21), where 9 is added to the previous value. Adding 9 to U (21) results in 30; since there are 26 letters in the alphabet, 30 - 26 = 4, which corresponds to the letter D.

For the fourth letter, the pattern is Q (17), E (5), S (19), G (7), where 14 is added to the previous value. Adding 14 to G (7) results in 21, which corresponds to the letter U.

Combining these letters results in the term FODU.

Explanation

The relationship between the words in the given pair is that of a finished structure and its primary building material. Concrete is a core material used in the construction of a Road. Similarly, a Brick is the fundamental unit or material used to build a Wall. In both cases, the second word represents the physical substance required to create the object mentioned in the first word.

Explanation

In syllogism, no definite negative conclusion can be derived from a set of purely affirmative statements. Statement I (Some Z are F) and Statement II (All G are Z) are both affirmative. Consequently, Conclusion I (No F is G), Conclusion II (Some G are not F), and Conclusion III (No F is Z) are all negative propositions and cannot logically follow. Specifically, Conclusion III is a direct contradiction of Statement I, which confirms that an intersection exists between Z and F. For Conclusions I and II, although G is contained within Z and F overlaps with Z, there is no information provided to establish a definite relationship—either of inclusion or exclusion—between G and F. Therefore, none of the proposed conclusions are logically certain.

Explanation

Applying the sequence of signs -, ÷, +, ×, = to the given expression 59 ∗ 12 ∗ 6 ∗ 24 ∗ 2 ∗ 105 results in the equation: 59 - 12 ÷ 6 + 24 × 2 = 105

According to the BODMAS rule, the operations must be performed in the order of Division, Multiplication, Addition, and then Subtraction.

Step 1: Perform the division. 12 ÷ 6 = 2 The equation becomes: 59 - 2 + 24 × 2 = 105

Step 2: Perform the multiplication. 24 × 2 = 48 The equation becomes: 59 - 2 + 48 = 105

Step 3: Perform addition and subtraction from left to right. 57 + 48 = 105 105 = 105

The calculation results in 105 on the left side, which matches the value on the right side, thereby balancing the equation.

Explanation

The relationship sequence in the expression U + V × K - B is interpreted as follows: U + V establishes that U is the husband of V, which also means V is the wife of U. The next part, V × K, states that V is the mother of K. Since U is the husband of V, U must be the father of K. Finally, K - B signifies that K is the father of B. Thus, U is the father of K, and K is the father of B. A person who is the father of one's father is known as the paternal grandfather.

Explanation

The series is determined by observing the alphabetical progression of each letter position across the terms.

For the first letter of each triplet, the pattern follows a decreasing sequence: L (12), K (11), J (10), I (9), and H (8). Each letter shifts one position backward in the alphabet. This establishes J as the first letter of the missing term.

For the third letter of each triplet, the pattern follows an increasing sequence: C (3), D (4), E (5), F (6), and G (7). Each letter shifts one position forward in the alphabet. This establishes E as the third letter of the missing term.

For the middle letter, the pattern follows an increasing sequence with an increment of two: K (11), M (13), O (15), Q (17), and S (19). Starting from the first term and applying the constant addition of two, the middle letter of the third term is identified as O.

Combining these results into a single triplet produces the term JOE.

Explanation

The coding language follows a pattern based on the distinction between vowels and consonants. Vowels (A, E, I, O, U) are shifted backward by one position in the alphabet (n - 1), while consonants are shifted forward by three positions (n + 3).

For the word ABASE, the calculation is: A (vowel) 1 - 1 = 26 (Z); B (consonant) 2 + 3 = 5 (E); A (vowel) 1 - 1 = 26 (Z); S (consonant) 19 + 3 = 22 (V); E (vowel) 5 - 1 = 4 (D). This results in ZEZVD.

For the word BANDS, the calculation is: B (consonant) 2 + 3 = 5 (E); A (vowel) 1 - 1 = 26 (Z); N (consonant) 14 + 3 = 17 (Q); D (consonant) 4 + 3 = 7 (G); S (consonant) 19 + 3 = 22 (V). This results in EZQGV.

Applying this logic to CABIN: C (consonant) is shifted by +3 to become F (6). A (vowel) is shifted by -1 to become Z (26). B (consonant) is shifted by +3 to become E (5). I (vowel) is shifted by -1 to become H (8). N (consonant) is shifted by +3 to become Q (17).

The final coded word is FZEHQ.

Explanation

The numerical series follows a specific growth pattern where each subsequent term is derived by multiplying the previous term by an incrementing natural number and then adding a constant of 2. The general formula for the sequence is Tₙ₊₁ = (Tₙ × n) + 2, where Tₙ represents the term at position n.

Starting with the first term T₁ = 37, the second term is calculated as (37 × 1) + 2 = 39. Following this logic, the missing third term is found by applying the next multiplier, which is 2, to the second term and adding 2, resulting in (39 × 2) + 2 = 80. The validity of this logic is confirmed by calculating the remaining terms in the series: the fourth term is (80 × 3) + 2 = 242, the fifth term is (242 × 4) + 2 = 970, and the sixth term is (970 × 5) + 2 = 4852.

Explanation

The numbers in the given sets follow the logic that the third number is equal to half the square of the sum of the first and second numbers. The formula can be expressed as:

n₃ = ((n₁ + n₂)²)/(2)

In the first set (2, 4, 18): ((2 + 4)²)/(2) = (6²)/(2) = ³⁶⁄₂ = 18

In the second set (1, 9, 50): ((1 + 9)²)/(2) = (10²)/(2) = ¹⁰⁰⁄₂ = 50

Following the same logic for the set (3, 5, 32): ((3 + 5)²)/(2) = (8²)/(2) = ⁶⁴⁄₂ = 32

The pattern is consistently applied to yield the third number from the sum of the first two numbers.

Explanation

The series follows a pattern for each letter position: the first letter increases by 2 (E, G, I, K, M), the second letter decreases by 1 (G, F, E, D, C), the third letter increases by 2 (J, L, N, P, R), and the fourth letter increases by 1 (M, N, O, P, Q). Applying these patterns to the fourth cluster results in KDPP.

Explanation

Conclusion I is a logically valid possibility because the statements establish that some floors are plates and all gardens are plates. This places both floors and gardens within the same overarching category of plates. Since there is no negative constraint or exclusion provided between the set of floors and the set of gardens, a scenario where they intersect is entirely possible.

Conclusion II follows directly through the principle of deduction. Since all gardens are contained within the set of plates and it is explicitly stated that no plate is a sofa, no element that is a garden can be a sofa. Because the set of gardens is a subset of plates, and the set of plates has no intersection with the set of sofas, it is certain that no garden is a sofa.

Explanation

In the expression P - Q × R, the symbol - represents the father relationship and × represents the sister relationship. Decoding the components of the expression, P - Q implies that P is the father of Q. The second part, Q × R, implies that Q is the sister of R. Because Q is the sister of R, they are siblings. Therefore, if P is the father of Q, he is necessarily the father of Q's sibling, R. This confirms that the expression P - Q × R successfully establishes P as the father of R.

Explanation

The second statement establishes that all B are contained within the set Q. The first statement specifies that no P is Q, meaning the sets P and Q are completely disjoint and have no intersection. Since B is entirely inside Q, and Q has no overlap with P, it logically follows that B cannot have any overlap with P, which validates conclusion I (No P is B). Furthermore, the statement No P is Q implies its converse, No Q is P. In formal logic, a universal negative statement (No Q is P) always implies its particular negative form (Some Q are not P). Therefore, conclusion II is also logically valid. Conclusion III directly contradicts the second statement, which asserts that every B is a Q, making it impossible for some B to not be Q.

Explanation

The relationship between the numbers in the given sets follows the logic that the product of the first and the third numbers equals the second number.

In the first set (5, 35, 7): 5 × 7 = 35

In the second set (8, 32, 4): 8 × 4 = 32

Following the same logic for the set (3, 27, 9): 3 × 9 = 27