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

Explanation

The coding logic follows a pattern where adjacent pairs of letters in the given word are swapped. In ADAPTATION, the pairs AD, AP, TA, TI, and ON are reversed to become DA, PA, AT, IT, and NO. Similarly, in SKATEBOARD, the pairs SK, AT, EB, OA, and RD are reversed to become KS, TA, BE, AO, and DR.

Applying the same logic to the word LIGHTBOARD: The first pair LI is reversed to IL. The second pair GH is reversed to HG. The third pair TB is reversed to BT. The fourth pair OA is reversed to AO. The fifth pair RD is reversed to DR.

Concatenating these results gives the final coded string ILHGBTAODR.

Explanation

The coding logic involves dividing the six-letter word into two halves of three letters each. Each half is then reversed, and a constant value of 3 is added to the positional value of each letter in the English alphabet.

For the first word SHIRTS: First half: SHI. Reversed: IHS. Adding 3 to each: I(9)+3=12(L), H(8)+3=11(K), S(19)+3=22(V). Results in LKV. Second half: RTS. Reversed: STR. Adding 3 to each: S(19)+3=22(V), T(20)+3=23(W), R(18)+3=21(U). Results in VWU. Combined: LKVVWU.

For the second word KURTAS: First half: KUR. Reversed: RUK. Adding 3 to each: R(18)+3=21(U), U(21)+3=24(X), K(11)+3=14(N). Results in UXN. Second half: TAS. Reversed: SAT. Adding 3 to each: S(19)+3=22(V), A(1)+3=4(D), T(20)+3=23(W). Results in VDW. Combined: UXNVDW.

Applying this logic to FABRIC: First half: FAB. Reversed: BAF. Adding 3 to each: B(2)+3=5(E), A(1)+3=4(D), F(6)+3=9(I). Results in EDI. Second half: RIC. Reversed: CIR. Adding 3 to each: C(3)+3=6(F), I(9)+3=12(L), R(18)+3=21(U). Results in FLU. Combined: EDIFLU.

Explanation

The series follows the recursive pattern aₙ = (aₙ₋₁ × 4) + 1. Each subsequent term is derived by multiplying the preceding term by 4 and then adding 1.

Applying this rule to the provided sequence: 13 = (3 × 4) + 1 53 = (13 × 4) + 1 213 = (53 × 4) + 1

Following this logic to find the missing term: ? = (213 × 4) + 1 ? = 852 + 1 = 853

To verify, the next term in the sequence is calculated as: 3413 = (853 × 4) + 1 = 3412 + 1

The calculation confirms that 853 correctly fits the established pattern of the series.

Explanation

The pattern in the groups follows a constant common difference of 5 between consecutive numbers. In the other groups, the relation is n, n+5, n+10. For example, 137 + 5 = 142 and 142 + 5 = 147 in group a, 103 + 5 = 108 and 108 + 5 = 113 in group c, and 131 + 5 = 136 and 136 + 5 = 141 in group d. In group b, while the first increment is 117 + 5 = 122, the second increment is 122 + 7 = 129, which deviates from the established pattern of adding 5 at each step.

Explanation

The first conclusion follows through the transitive property of categorical syllogisms. Since all artists are smart and all smart individuals are rich, the entire set of artists is contained within the set of smart individuals, which in turn is contained within the set of rich individuals. Consequently, every artist is necessarily rich.

The second conclusion is valid because the statements establish an intersection between the sets of clowns and artists. Since some clowns are artists and every artist is also categorized as smart, it follows that those specific clowns who are artists must also be smart. This confirms the existence of at least some clowns who are smart.

The third conclusion does not follow because the premise only states that some clowns are artists, which does not provide enough information to claim that all clowns belong to that group. Based on the logical deduction of the provided premises, only conclusions I and II are correct.

Explanation

Dictionary order is determined by comparing words letter by letter from left to right. All five words begin with the prefix Per. Comparing the fourth letter of each word, Pernicious (3) contains n, which precedes the p found in Perpend (1), Perplex (2), Perpetrate (4), and Perpetual (5). This places Pernicious first in the sequence.

Among the remaining words starting with Perp, comparing the fifth letter shows that e in Perpend (1), Perpetrate (4), and Perpetual (5) comes before l in Perplex (2), making Perplex the final word in the list. To arrange the words starting with Perpe, we look at the sixth letter: n in Perpend (1) precedes t in Perpetrate (4) and Perpetual (5), placing Perpend second. Finally, comparing the seventh letters of the remaining two words, r in Perpetrate (4) comes before u in Perpetual (5). Arranging these observations yields the sequence 3, 1, 4, 5, 2.

Explanation

In the letter-cluster XFWE, the relationship between alternating letters follows a subtraction of one. The first and third letters satisfy the relation X - 1 = W (24 - 1 = 23), and the second and fourth letters satisfy the relation F - 1 = E (6 - 1 = 5). This pattern of (-1, -1) for alternating pairs differs from the rule governing the rest of the group, where the first and third letters have an alphabetical difference of +2 and the second and fourth letters have an alphabetical difference of -1.

Explanation

The series follows a specific arithmetic progression for each letter position within the triplets. For the first letter of each term, the sequence is N, Q, T, W. Converting these to their positions in the English alphabet (A=1, B=2, ...), we get 14, 17, 20, 23. This is an increasing series with a constant difference of +3. The next value is 23 + 3 = 26, which corresponds to the letter Z.

For the second letter, the sequence is M, F, Y, R, which corresponds to 13, 6, 25, 18. This follows a constant subtraction of -7. Note that 6 - 7 = -1, and in a cyclic alphabet of 26 letters, -1 is equivalent to 25 (Y). Following this pattern, the next value is 18 - 7 = 11, which corresponds to the letter K.

For the third letter, the sequence is R, Z, H, P, which corresponds to 18, 26, 8, 16. This is an increasing series with a constant difference of +8. Note that 26 + 8 = 34, and 34 - 26 = 8 (H). Applying the same logic, the next value is 16 + 8 = 24, which corresponds to the letter X. Combining these results, the next term is ZKX.

Explanation

The expression S | T % R @ P # Q can be decoded step-by-step to determine the relationship between S and P. S | T indicates that S is the wife of T, which also implies T is the husband. T % R means T is the father of R. Combining these, S is the mother of R. R @ P establishes that R is the husband of P, making P the wife of R. Since S is the mother of R and R is the husband of P, S is the mother of P's husband. In family relations, the mother of one's husband is defined as the mother-in-law.

Explanation

The relationship in this analogy is based on an animal and its specific dwelling or shelter. A horse is housed in a stable, which is a building specifically designed to provide shelter and care for horses. Following the same logic, a hen is typically kept in a coop, which is a small enclosure or building used to house poultry and protect them from predators and weather.

Explanation

The numerical relationship in the given sets follows the logic that the third number is the square of the difference between the first and second numbers. The mathematical pattern can be expressed as:

(First Number - Second Number)² = Third Number

In the first set (76, 75, 1): (76 - 75)² = 1² = 1

In the second set (90, 87, 9): (90 - 87)² = 3² = 9

Applying this same logic to the numbers in option b, we find: (56 - 48)² = 8² = 64

Explanation

The logic followed in the given series is based on the pattern x³ - 13 = y, where x is the first term of a pair and y is the second term.

For the first pair 7:330, calculating 7³ - 13 gives 343 - 13 = 330. For the third pair 9:716, calculating 9³ - 13 gives 729 - 13 = 716.

Applying the same logic to the middle pair ? : 203, let the unknown term be x. x³ - 13 = 203 x³ = 203 + 13 x³ = 216 x = ³√(216) x = 6

Explanation

The given expression P - Q % R | S + T defines the family structure as follows: P - Q signifies that P is the mother of Q. The relation Q % R indicates that Q is the brother of R, which implies that P is also the mother of R. Further, R | S denotes that R is the son of S. Since P is the mother of R, and S is the parent of R who is not P, S must be the father of R and the husband of P. Finally, S + T establishes that S is the father of T. Because P and S are husband and wife, any child of S is also a child of P. Consequently, P is the mother of T.

Explanation

The equation provided in option c is 8× 4 + 6 - 2÷ 1 = 6. By interchanging the numbers 8 and 2, the left-hand side of the equation becomes 2× 4 + 6 - 8÷ 1. Following the BODMAS rule, we first perform the division: 8÷ 1 = 8. Next, we perform the multiplication: 2× 4 = 8. The expression now simplifies to 8 + 6 - 8. Carrying out the addition and subtraction, we get 14 - 8 = 6. Since the result of the calculation matches the value on the right-hand side, the equation is correct after the interchange.

Explanation

To make the equation correct, we interchange the numbers 6 and 4. Applying the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, and Subtraction), we evaluate the expression as follows:

Original Equation: 18 + (12 × 6) + (63 ÷ 7) × 4 + ³√(27) - 11 = 112

Interchanging 6 and 4, the equation becomes: 18 + (12 × 4) + (63 ÷ 7) × 6 + ³√(27) - 11 = 112

Step 1: Solve the brackets and the cube root. (12 × 4) = 48 (63 ÷ 7) = 9 ³√(27) = 3

Step 2: Substitute these values back into the equation and perform multiplication. 18 + 48 + (9 × 6) + 3 - 11 18 + 48 + 54 + 3 - 11

Step 3: Perform addition and subtraction from left to right. 66 + 54 + 3 - 11 120 + 3 - 11 123 - 11 = 112

The result matches the Right Hand Side (112), confirming that interchanging 6 and 4 makes the equation correct.

Explanation

The series follows a specific numerical pattern for each letter position in the cluster based on alphabetical order where A = 1, B = 2, ..., Z = 26.

The first letters of the clusters are O, R, X, G. Converting these to their numerical positions, we get 15, 18, 24, and 7 (or 33 in the cyclic alphabet sequence). The differences between these consecutive terms are 18 - 15 = 3, 24 - 18 = 6, and 33 - 24 = 9. This shows an increasing increment pattern where the difference itself increases by 3 each time. Following this logic, the next increment is 9 + 3 = 12. Adding 12 to the position of G (7) results in 19, which corresponds to the letter S.

The second letters of the clusters are G, L, Q, V. Their numerical positions are 7, 12, 17, and 22. The difference between each consecutive letter is a constant +5. Following this pattern, the next second letter is 22 + 5 = 27. In a cyclic 26-letter system, 27 is equivalent to 27 - 26 = 1, which corresponds to the letter A.

Combining these results, the next letter cluster in the series is SA.

Explanation

To arrange the words in alphabetical order as they appear in a dictionary, we compare them letter by letter from left to right. The words Historian (2), Historical (4), and History (1) all begin with the sequence H-i-s-t-o-r-i. Comparing the eighth letter of these words, Historian has a, Historical has c, and History has o. Since a comes before c, and c comes before o in the alphabet, the sequence for these three words is 2, 4, 1. Next, we examine the words starting with H-o, which are Hobnail (3) and Hobnob (5). Both share the prefix H-o-b-n. Comparing their fifth letters, a in Hobnail precedes o in Hobnob. Therefore, Hobnail (3) comes before Hobnob (5). Combining these two groups, the complete dictionary order is 2, 4, 1, 3, 5.

Explanation

The relationship in the first pair is based on a substance and its standard unit of measurement. Milk is a liquid, and its quantity is typically measured in Litres. Following the same logic, Sugar is a solid substance whose quantity is measured by weight. The standard metric unit for measuring the mass or weight of solid commodities like sugar is the Kilogram.

Explanation

Based on Statement I (All R are H), set R is a subset of set H, but this does not imply that set H is a subset of set R; thus, Conclusion I is not necessarily true. Statement II (Some T are R) establishes that there is a non-empty intersection between set T and set R. Because all elements of R are contained within H, the elements in the intersection of T and R must also be in H, leading to the valid deduction that Some T are H. However, this provides no logical basis to assert that All T are H as stated in Conclusion II. Finally, since Statement II confirms that some elements are both T and R, Conclusion III (No R is T) is directly contradicted. Since none of the proposed conclusions are logically certain, the result is that no conclusion follows.

Explanation

The coding logic uses the opposite letter pairs of the English alphabet, where the sum of the numerical positions of the original letter and its coded letter is 27. For the word KNIGHT, the pairs are K(11)+P(16)=27, N(14)+M(13)=27, I(9)+R(18)=27, G(7)+T(20)=27, H(8)+S(19)=27, and T(20)+G(7)=27. Similarly, for FELLOW, the pairs are F(6)+U(21)=27, E(5)+V(22)=27, L(12)+O(15)=27, L(12)+O(15)=27, O(15)+L(12)=27, and W(23)+D(4)=27.

Applying this rule to DECENT: D is 4th, so 27 - 4 = 23 (W) E is 5th, so 27 - 5 = 22 (V) C is 3rd, so 27 - 3 = 24 (X) E is 5th, so 27 - 5 = 22 (V) N is 14th, so 27 - 14 = 13 (M) T is 20th, so 27 - 20 = 7 (G)

The resulting code for DECENT is WVXVMG.

Explanation

Based on the given symbol meanings, the expression G # H | I @ J | K can be decoded to determine the relationship between H and J. The segment H | I indicates that H is the mother of I. The segment I @ J indicates that I is the husband of J. If H is the mother of I and I is the husband of J, then H is the mother of J's husband. By definition, the mother of an individual's spouse is their mother-in-law. Therefore, H is the mother-in-law of J.

Explanation

The coding logic involves two steps: first, reversing the order of the letters in the word, and second, applying specific numerical shifts to their alphabetical positions. The pattern for the shifts applied to the reversed letters is +2 for the first and last letters, and +1 for the two middle letters.

For the word FUND, the letters are F(6), U(21), N(14), and D(4). Reversing them gives D(4), N(14), U(21), and F(6). Applying the shifts: 4 + 2 = 6 (F) 14 + 1 = 15 (O) 21 + 1 = 22 (V) 6 + 2 = 8 (H) This results in the code FOVH.

For the word SEND, reversing S(19), E(5), N(14), D(4) gives D(4), N(14), E(5), S(19). Applying the shifts: 4 + 2 = 6 (F) 14 + 1 = 15 (O) 5 + 1 = 6 (F) 19 + 2 = 21 (U) This results in the code FOFU.

Applying this logic to GIFT: the letters are G(7), I(9), F(6), and T(20). Reversing them gives T(20), F(6), I(9), and G(7). Applying the shifts: T(20) + 2 = 22 (V) F(6) + 1 = 7 (G) I(9) + 1 = 10 (J) G(7) + 2 = 9 (I) The final coded word is VGJI.

Explanation

The expression P × Q ÷ R is analyzed by applying the given definitions to each operator. The part P × Q indicates that P is the brother of Q, which confirms that P and Q are siblings belonging to the same generation. The subsequent part Q ÷ R indicates that Q is the mother of R, which defines the gender of Q as female. Since Q is a female sibling of P, she is the sister of P.

Explanation

The relationship in the given pair is between a physical quantity and its standard unit of measurement in the International System of Units (SI). Length is a physical dimension, and the metre is the base SI unit used to quantify it. Similarly, electric current is a fundamental physical quantity, and the ampere is the official SI unit used for its measurement.

Explanation

In the letter-clusters XYZ, ABC, and IJK, the letters follow a consecutive alphabetical sequence where each subsequent letter is the immediate successor of the previous one. Specifically, the pattern of their positional values in the English alphabet is n, n+1, n+2. For example, X(24), Y(25), and Z(26) are consecutive, as are A(1), B(2), and C(3), and I(9), J(10), and K(11). In contrast, the cluster LNM consists of the letters L(12), N(14), and M(13). This arrangement follows a +2 and -1 pattern rather than a continuous +1 increment, making it the odd one out.

Explanation

The numbers in the sets follow the mathematical logic where the sum of half of the first number and the second number results in the third number. This can be expressed by the formula: (First Number)/(2) + Second Number = Third Number

Applying this logic to the provided sets: In the first set (56, 6, 34): ⁵⁶⁄₂ + 6 = 28 + 6 = 34

In the second set (102, 27, 78): ¹⁰²⁄₂ + 27 = 51 + 27 = 78

Similarly, for the set in option b (76, 34, 72): ⁷⁶⁄₂ + 34 = 38 + 34 = 72

Explanation

By interchanging the numbers 5 and 9 in the equation 9× 4 + 5 - 8÷ 2 = 25, the expression becomes 5× 4 + 9 - 8÷ 2. Applying the BODMAS rule, the division is performed first, giving 8÷ 2 = 4. Next, the multiplication results in 5× 4 = 20. The equation then simplifies to 20 + 9 - 4. Adding 20 and 9 yields 29, and subtracting 4 results in 25, which matches the right-hand side of the equation.

Explanation

Conclusion II follows directly from the third statement through the logical principle of conversion. The statement No vegetable is healthy is a universal negative proposition (E-type), which allows for a valid conversion where the subject and predicate are interchanged. Therefore, the statement No healthy is vegetable is a direct logical consequence of the given premise.

Conclusion III is derived by combining the first and second statements. The first statement establishes that Some apples are fruits, and the second statement asserts that All fruits are vegetables. Using the rules of syllogism, if a portion of apples belongs to the category of fruits, and every member of the fruit category is also a vegetable, then that same portion of apples must be vegetables. This leads to the conclusion Some apples are vegetables. The converse of a particular affirmative statement (I-type) is also valid, meaning that Some vegetables are apples is a necessary logical result.

Conclusion I does not follow because the premises only establish that the specific apples which are vegetables cannot be healthy. This results in the particular negative conclusion Some apples are not healthy. In formal logic, this specific observation does not provide enough evidence to support the universal negative claim No apple is healthy, as there may be apples that are not vegetables and could potentially be healthy. Since only conclusions II and III are supported by the statements, the logical choice is the one specifying those two.

Explanation

The pair 28-56 is the odd one out because it follows the mathematical relation y = 2x, whereas the consistently applied pattern in the question is y = 2x + 1. Calculating the value for this specific pair using the logic of doubling the first number and adding one yields 28 × 2 + 1 = 57. Because the second number provided is 56 instead of 57, it fails to match the required incrementing rule, which distinguishes it as the outlier.

Explanation

The series follows a fixed addition pattern for each letter position across the terms in the sequence.

For the first letter, the pattern is an increment of +4: S(19) + 4 = W(23), W(23) + 4 = A(27 ≡ 1), A(1) + 4 = E(5), and E(5) + 4 = I(9).

For the second letter, the pattern is an increment of +8: M(13) + 8 = U(21), U(21) + 8 = C(29 ≡ 3), C(3) + 8 = K(11), and K(11) + 8 = S(19).

For the third letter, the pattern is an increment of +9: Q(17) + 9 = Z(26), Z(26) + 9 = I(35 ≡ 9), I(9) + 9 = R(18), and R(18) + 9 = A(27 ≡ 1).

Following these increments from the term EKR, the resulting letters are I, S, and A.

Explanation

The numbers in the given sets follow the mathematical logic where the third number is the sum of the first number and thrice the second number.

Pattern: First Number + (3 × Second Number) = Third Number

Applying this to the provided sets: Set 1: 40 + (3 × 120) = 40 + 360 = 400 Set 2: 18 + (3 × 20) = 18 + 60 = 78

Following the same logic for the set in option a: 29 + (3 × 23) = 29 + 69 = 98

Explanation

Statement I is an I-type proposition which states that Some white are car. In syllogism, an I-type proposition (Some A are B) can be logically converted into its converse (Some B are A). Therefore, if Some white are car is true, then Some car are white is also logically true. This directly validates Conclusion II. Conclusion I does not follow because the statements provide no information to establish a universal positive relationship between trucks and white; the second statement only confirms that no truck is a car.

Explanation

The relationship between the numbers follows the logic n : n × (n + 11).

For the first pair, 24 : 840, the calculation is 24 × (24 + 11) = 24 × 35 = 840.

For the third pair, 33 : 1452, the calculation is 33 × (33 + 11) = 33 × 44 = 1452.

Applying this same logic to the second pair where the third term is 27: 27 × (27 + 11) = 27 × 38 = 1026.

Explanation

In the provided letter-clusters, the standard pattern follows an increment of +3 between the first and second letters and an increment of +4 between the second and third letters in the alphabetical sequence. DGI consists of D at position 4, G at position 7, and I at position 9. While the first gap is 7 - 4 = 3, the second gap is 9 - 7 = 2. This deviation in the second increment makes DGI the different cluster in the set.

Explanation

The coding language follows a positional transformation pattern. To find the code for a seven-letter word, divide the word into three segments: the first three letters, the fourth letter, and the last three letters.

The transformation rule is: Reverse the order of the first three letters (positions 1, 2, and 3 become 3, 2, and 1). Keep the fourth letter in its original position. Reverse the order of the last three letters (positions 5, 6, and 7 become 7, 6, and 5).

Applying this logic to BABYSIT: The first three letters BAB reversed remain BAB. The fourth letter Y remains Y. The last three letters SIT reversed become TIS. Combining these segments results in BABYTIS.

Applying the same logic to AFFABLE: The first three letters AFF reversed become FFA. The fourth letter A remains A. The last three letters BLE reversed become ELB. Combining these segments results in FFAAELB.

Explanation

The coding logic involves a two-step process: first, swapping the positions of the first and last letters of the word; second, applying a numerical shift to each letter based on whether it is a consonant or a vowel. Consonants are shifted forward by 3 positions (+3), while vowels are shifted backward by 1 position (-1).

For the word FLOAT: Swap the first (F) and last (T) letters: T L O A F. Apply the shifts: T (consonant) +3 = W L (consonant) +3 = O O (vowel) -1 = N A (vowel) -1 = Z F (consonant) +3 = I The resulting code is WONZI.

For the word TRIBE: Swap the first (T) and last (E) letters: E R I B T. Apply the shifts: E (vowel) -1 = D R (consonant) +3 = U I (vowel) -1 = H B (consonant) +3 = E T (consonant) +3 = W The resulting code is DUHEW.

Following the same logic for GARDEN: Swap the first (G) and last (N) letters: N A R D E G. Apply the shifts: N (consonant) +3 = Q A (vowel) -1 = Z R (consonant) +3 = U D (consonant) +3 = G E (vowel) -1 = D G (consonant) +3 = J The resulting code is QZUGDJ.

Explanation

The logic followed in the given sets is that the sum of all three numbers in the set is a constant value of 85.

For the set (21, 33, 31): 21 + 33 + 31 = 85

For the set (42, 17, 26): 42 + 17 + 26 = 85

Following this relationship, the sum of the numbers in the set (36, 14, 35) is: 36 + 14 + 35 = 85

This set satisfies the condition where the sum of the whole numbers equals 85, matching the pattern established by the provided sets.

Explanation

The equation is validated by interchanging the signs + and - and the numbers 6 and 3. Applying these changes to the left-hand side of the expression 8 + 4 × 6 ÷ 3 - 9:

LHS = 8 - 4 × 3 ÷ 6 + 9

Following the BODMAS rule for the order of operations: Division: 3 ÷ 6 = 0.5 Multiplication: 4 × 0.5 = 2 Addition and Subtraction: 8 - 2 + 9 = 15

The resulting value of 15 matches the right-hand side of the equation.

Explanation

The relationship between the words in the first pair is based on intensity or degree. Agony represents an extreme or intense form of pain. Following the same logic for the second pair, rage is the word that represents an extreme or intense level of anger. Therefore, the second word in each pair serves as an intensified synonym of the first.

Explanation

The groups of numbers follow a pattern where the difference between the third number and the second number is a constant value of 20. This can be expressed by the formula n₃ - n₂ = 20. In this group, the third number is 49 and the second number is 25. Calculating the difference gives 49 - 25 = 24. Because this difference is 24 rather than the required 20, the group does not follow the mathematical logic shared by the others.

Explanation

By interchanging the numbers 1 and 9 in the equation 9× 3 - 4÷ 2 + 1 = 10, the expression is rewritten as:

1× 3 - 4÷ 2 + 9 = 10

To verify the correctness of this equation, apply the BODMAS rule, which dictates the order of operations as Division, Multiplication, Addition, and then Subtraction.

First, perform the division: 4÷ 2 = 2 The equation becomes: 1× 3 - 2 + 9 = 10

Second, perform the multiplication: 1× 3 = 3 The equation becomes: 3 - 2 + 9 = 10

Third, perform the addition and subtraction from left to right: 3 - 2 = 1 1 + 9 = 10

The resulting value 10 matches the Right Hand Side of the equation, confirming its correctness after the interchange.

Explanation

The repetition of a calendar year depends on the accumulation of odd days. For a calendar to repeat, the sum of odd days starting from the given year must be a multiple of 7, and the repeating year must be of the same type (ordinary or leap) as the original year. A standard shortcut rule states that if a year is a (Leap Year + 1), the calendar repeats every 6 years.

The year 2009 follows the leap year 2008. Since 2009 = 2008 + 1, we apply the 6-year repetition rule: 2009 + 6 = 2015.

This can be verified by counting odd days from 2009 until the sum is divisible by 7. An ordinary year has 1 odd day (365 7) and a leap year has 2 odd days (366 7). 2009 (Ordinary): 1 odd day 2010 (Ordinary): 1 odd day 2011 (Ordinary): 1 odd day 2012 (Leap): 2 odd days 2013 (Ordinary): 1 odd day 2014 (Ordinary): 1 odd day Sum of odd days = 1 + 1 + 1 + 2 + 1 + 1 = 7.

Since the total number of odd days is 7 (which is 0 7), the next year, 2015, will start on the same day of the week as 2009. Because both 2009 and 2015 are ordinary years, their calendars are identical.

Explanation

The logic followed in the given letter-clusters is a repeating addition pattern of +2 and +1 to the positional values of the letters. For the first pair BEAR to DFCS, B + 2 = D, E + 1 = F, A + 2 = C, and R + 1 = S. This confirms the pattern is +2, +1, +2, +1.

Checking the second pair FEEL to HFGM, the same logic applies where F + 2 = H, E + 1 = F, E + 2 = G, and L + 1 = M. Applying this specific transformation to the fifth letter-cluster MANY, we calculate M + 2 = O, A + 1 = B, N + 2 = P, and Y + 1 = Z. Following this sequence, the resulting cluster is OBPZ.

Explanation

The logical validity of the conclusions is determined by the overlap between the sets of watches, projectors, lamps, and heaters. From the statements, we know that all projectors are contained within the set of lamps and that there is an overlap between watches and projectors. This implies that some watches are lamps, but it does not justify the conclusion that all watches are lamps, so conclusion III does not follow.

Furthermore, while some heaters are watches, there is no statement that links heaters to projectors or lamps. The portion of watches that overlaps with heaters may be entirely separate from the portion of watches that overlaps with projectors and lamps. Without a defined connection or a universal quantifier linking these specific sets, conclusion I (heaters and projectors) and conclusion II (lamps and heaters) are not logically necessary. Since none of the conclusions are guaranteed by the premises, none of them follow.

Explanation

The expression A % B | C # D @ E describes the following relationships: A is the mother of B (A % B), B is the wife of C (B | C), C is the brother of D (C # D), and D is the son of E (D @ E).

Since D is the son of E and C is the brother of D, C is also the son of E. Because B is the wife of C, she is the wife of E's son. In a family hierarchy, the wife of one's son is referred to as a daughter-in-law. Thus, B is the daughter-in-law of E.

Explanation

The series follows a pattern of decreasing differences between consecutive terms. By subtracting consecutive integers starting from 11, we get:

15 - 11 = 4 4 - 12 = -8 -8 - 13 = -21 -21 - 14 = -35

The common difference between these subtrahends is 1. Therefore, the next number to be subtracted from the current term is 15. The calculation for the missing number is:

-35 - 15 = -50

Explanation

The series follows a specific arithmetic progression for each letter position based on their alphabetical values, where A=1, B=2, and so on up to Z=26.

For the first letter, the pattern is +4: A (1) + 4 = E (5); E (5) + 4 = I (9); I (9) + 4 = M (13). The next letter in the sequence is 13 + 4 = 17, which is Q.

For the second letter, the pattern is -6: B (2) - 6 = V (22); V (22) - 6 = P (16); P (16) - 6 = J (10). In a cyclic alphabet, subtracting 6 from 2 yields 22. The next letter is 10 - 6 = 4, which is D.

For the third letter, the pattern is +8: C (3) + 8 = K (11); K (11) + 8 = S (19); S (19) + 8 = 27, which wraps around to A (1). The next letter is 1 + 8 = 9, which is I.

For the fourth letter, the pattern is +16: D (4) + 16 = T (20); T (20) + 16 = 36, which wraps around to J (10); J (10) + 16 = 26 (Z). The next letter is 26 + 16 = 42, which corresponds to 42 - 26 = 16, which is P.

Combining these four results yields the next term in the series: QDIP.

Explanation

The numbers in the sets follow the mathematical relationship where the third number is the sum of three times the first number and the second number. The pattern is defined by the formula 3 × Number₁ + Number₂ = Number₃.

In the first given set (4, 21, 33): 3 × 4 + 21 = 12 + 21 = 33

In the second given set (10, 111, 141): 3 × 10 + 111 = 30 + 111 = 141

Applying this logic to the set (25, 53, 128): 3 × 25 + 53 = 75 + 53 = 128

Explanation

The series follows a specific mathematical pattern for each letter position in the clusters. For the first letter of each cluster, the sequence is A, E, J, P. Converting these to their numerical positions in the alphabet gives 1, 5, 10, and 16. The differences between consecutive terms are 5 - 1 = 4, 10 - 5 = 5, and 16 - 10 = 6. This indicates an increasing increment pattern of +4, +5, and +6. The next increment must be +7, resulting in 16 + 7 = 23, which corresponds to the letter W.

For the second letter of each cluster, the sequence is R, P, N, L. Their numerical positions are 18, 16, 14, and 12. This sequence follows a constant subtraction of 2. Applying this to the last term, 12 - 2 = 10, which corresponds to the letter J.

For the third letter of each cluster, the sequence is C, F, I, L. Their numerical positions are 3, 6, 9, and 12. This sequence follows a constant addition of 3. Applying this to the last term, 12 + 3 = 15, which corresponds to the letter O. Combining the resulting letters W, J, and O gives the next cluster in the series.

Explanation

The letter-clusters are analyzed by the numerical positions of their constituent letters in the English alphabet, where A = 1, B = 2, …, Z = 26. In the clusters DOL, ARI, and NEV, the difference between the positional value of the third letter and the first letter is constant at 8. Specifically, for DOL, the first letter D is 4 and the third letter L is 12, giving 12 - 4 = 8. For ARI, the first letter A is 1 and the third letter I is 9, giving 9 - 1 = 8. For NEV, the first letter N is 14 and the third letter V is 22, giving 22 - 14 = 8. However, in the cluster MIP, the first letter M is 13 and the third letter P is 16, resulting in a difference of 16 - 13 = 3. Since MIP does not follow the +8 difference pattern between the first and third letters shared by the other clusters, it is the odd one out.