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

Explanation

The coding logic involves interchanging specific letter positions within a seven-letter word. The first and third letters are swapped, and the fifth and seventh letters are swapped. The letters at the second, fourth, and sixth positions remain in their original places.

For the word TEACHER, the first letter T and third letter A swap places, while the fifth letter H and seventh letter R swap places. The second letter E, fourth letter C, and sixth letter E remain fixed. This results in the code AETCREH.

Similarly, for the word STUDENT, the first letter S and third letter U swap, and the fifth letter E and seventh letter T swap. The second letter T, fourth letter D, and sixth letter N remain unchanged. This results in the code UTSDTNE.

Applying this same logic to the word CLASSES, we identify the positions as C(1), L(2), A(3), S(4), S(5), E(6), and S(7). Swapping the first and third letters gives A at position 1 and C at position 3. Swapping the fifth and seventh letters results in S at position 5 and S at position 7. The letters at positions 2, 4, and 6 (L, S, and E) remain in their original spots. Arranging these gives the sequence ALCSSES.

Explanation

By interchanging the signs ÷ and × as suggested in option d, the given equation becomes:

81 ÷ 9 + 15 × 3 - 4 = 50

Applying the BODMAS rule, we first perform the division:

9 + 15 × 3 - 4 = 50

Next, we perform the multiplication:

9 + 45 - 4 = 50

Finally, we perform the addition and subtraction:

54 - 4 = 50 50 = 50

The equation is balanced and correct after the interchange.

Explanation

Statement I establishes that there is an intersection between set A and set W, which logically implies that Some W are A. This contradicts Conclusion III. Statement II establishes that there is an intersection between set W and set C, which logically implies that Some C are W. This contradicts Conclusion II. Regarding Conclusion I, the statements provide relationships between A and W, and W and C, but they do not provide any definitive connection between set A and set C. Since no universal relationship (All) or specific overlap is mandated between A and C by the premises, it is not possible to conclude that All A are C. Thus, none of the conclusions follow logically from the given statements.

Explanation

In the expression P × Q + R, the component P × Q signifies that P is the sister of Q based on the provided definition of the multiplication symbol. The component Q + R signifies that Q is the brother of R according to the definition of the addition symbol. Since P is the sister of Q and Q is the brother of R, P, Q, and R are siblings within the same generation. Consequently, P is the sister of R.

Explanation

The given series follows a pattern where the first, third, and fourth letters of each cluster remain constant as N, M, and E respectively. The second letter in each cluster changes according to the sequence of English vowels in alphabetical order: A, E, I, O, U. Since the first two clusters use A and E, and the last two use O and U, the missing cluster must use the vowel I in the second position, resulting in NIME.

Explanation

Substituting the signs from option a into the given equation, we get the expression: 35 × 5 ÷ 7 - 2 + 19 = 42. Following the BODMAS rule, we perform division and multiplication first. The term 35 × 5 ÷ 7 can be rewritten as 35 × ⁵⁄₇, which simplifies to 5 × 5 = 25. The equation then becomes 25 - 2 + 19 = 42. Performing addition and subtraction in sequence, 25 + 19 = 44, and 44 - 2 = 42. The left-hand side matches the right-hand side.

Explanation

The relationship between the numbers in the given sets (n₁, n₂, n₃) follows the pattern n₁ + 3 × n₂ = n₃.

In the first set (16, 7, 37), applying the formula gives 16 + (3 × 7) = 16 + 21 = 37. In the second set (28, 9, 55), applying the formula gives 28 + (3 × 9) = 28 + 27 = 55.

Applying this same logic to the option (13, 4, 25), we calculate 13 + (3 × 4) = 13 + 12 = 25, which matches the pattern exactly.

Explanation

Conclusion I follows because the statements establish an overlap between stones and cubes and place all bats within the category of cubes. Since there is no statement prohibiting an intersection between stones and bats, the possibility that some stones are bats exists within the logical framework.

Conclusion II follows through the transitive property of negative relationships. Given that all bats are contained within the set of cubes and the entire set of cubes is disjoint from the set of glass, it is logically impossible for any bat to be a glass.

Conclusion III is invalid because while all bats are cubes, the reverse is not necessarily true; there can be cubes that are not bats. Conclusion IV is invalid because only the stones that are cubes are restricted from being glass; stones that do not fall into the cube category have no defined relationship with glass, meaning we cannot definitively conclude that no stone is a glass.

Explanation

The relationship follows a reverse order addition pattern where the letters of the first cluster are transformed into the second cluster by adding increasing values starting from the last letter. For LAMB, the letters are L(12), A(1), M(13), and B(2). Reversing and adding yields: B+2=D(4), M+3=P(16), A+4=E(5), and L+5=Q(17), forming DPEQ.

Applying the same logic to MOTH: H(8)+2=J(10), T(20)+3=W(23), O(15)+4=S(19), and M(13)+5=R(18), which gives JWSR. Following this pattern for NERD, where the positions are N(14), E(5), R(18), and D(4), we calculate: D+2=F(6), R+3=U(21), E+4=I(9), and N+5=S(19). This results in the cluster FUIS.

Explanation

The series consists of 20 positions and is built upon a repeating five-letter block: LZXCV. Dividing the 20-character sequence into four equal segments reveals that each segment must be identical to maintain the pattern: (LZXCV) (LZXCV) (LZXCV) (LZXCV).

When the letters from the correct option are sequentially placed into the ten blanks, they complete this periodic cycle. The first blank at the very beginning of the string is filled by L. The next two blanks, located between Z and C and between C and L, are filled by X and V respectively, completing the first five-letter group. This pattern continues throughout the rest of the series, where the remaining seven letters from the option (X, V, Z, C, Z, X, and C) fill the gaps in the second, third, and fourth groups. This result aligns perfectly with the fixed letters already present in the string, such as Z at the second position and V at the twentieth position, ensuring a consistent and unbroken repetition of the LZXCV sequence.

Explanation

The statement all flowers are beautiful establishes a universal affirmative relationship where the category of flowers is a subset of the category of beautiful things. In formal logic and syllogism, a statement of the form All A are B implies the converse relationship Some B are A through the process of conversion. Since all flowers belong to the group of beautiful things, it is logically certain that there are at least some beautiful things that are flowers. Therefore, conclusion II follows directly from the first statement.

Explanation

The series follows a specific mathematical pattern for the positional shifts of each letter in the clusters based on their rank in the English alphabet.

For the first letter of each cluster: T(20) - 2 = R(18), R(18) - 2 = P(16), P(16) - 2 = N(14). Applying the same logic, the next first letter is 14 - 2 = 12, which corresponds to L.

For the second letter of each cluster: S(19) - 3 = P(16), P(16) - 3 = M(13), M(13) - 3 = J(10). Applying the same logic, the next second letter is 10 - 3 = 7, which corresponds to G.

For the third letter of each cluster: F(6) + 4 = J(10), J(10) + 4 = N(14), N(14) + 4 = R(18). Applying the same logic, the next third letter is 18 + 4 = 22, which corresponds to V.

By combining these results, the letter-cluster that replaces the question mark is LGV.

Explanation

The letter-cluster GTQ is the odd one out because it follows a different structural logic compared to the others. In the majority of the clusters, the second letter is found by moving three positions back from the first letter (L₂ = L₁ - 3), and the third letter is the alphabetical opposite of the second letter (L₂ + L₃ = 27). For example, in PMN, P(16) - 3 = M(13), and the opposite of M is N; in JGT, J(10) - 3 = G(7), and the opposite of G is T; in SPK, S(19) - 3 = P(16), and the opposite of P is K.

In the case of GTQ, this sequence of operations is shifted. Here, the first and second letters are the alphabetical opposites (G=7, T=20; 7 + 20 = 27), and the third letter is determined by moving three positions back from the second letter (Q = T - 3 = 20 - 3 = 17). Since the position of the opposite pair and the subtraction rule is distinct from the established pattern, GTQ is the different cluster.

Explanation

Substitute the given symbols into the expression based on the provided definitions where @ represents +, represents ÷, % represents ×, and # represents -. This yields the mathematical expression 29 + 128 ÷ 16 × 7 - 22. Following the BODMAS rule, the operations are performed in the sequence of division, multiplication, addition, and subtraction.

First, perform the division: 128 ÷ 16 = 8. Second, perform the multiplication: 8 × 7 = 56. Third, perform the addition: 29 + 56 = 85. Finally, perform the subtraction: 85 - 22 = 63$.

Explanation

The coding follows an incremental addition pattern where each successive letter in the word is shifted forward by an increasing number of positions in the alphabet. For the word CHHAPAK, the transformations are C + 1 = D, H + 2 = J, H + 3 = K, A + 4 = E, P + 5 = U, A + 6 = G, and K + 7 = R.

Applying this same logic to the word MALANGA: M + 1 = N A + 2 = C L + 3 = O A + 4 = E N + 5 = S G + 6 = M A + 7 = H

Combining these results gives the code NCOESMH.

Explanation

The pattern follows the logic n³ + 7 for consecutive integers. For the first pair, 223 = 6³ + 7 and 350 = 7³ + 7. In the second pair, the third number is 519 = 8³ + 7. Following the sequence, the missing number is calculated as 9³ + 7 = 729 + 7 = 736.

Explanation

To find the code for 'FARE', we first determine the sum of the positional values of the letters in the given words using the standard A=1, B=2, ..., Z=26 sequence:

For FUEL: F = 6, U = 21, E = 5, L = 12 Sum = 6 + 21 + 5 + 12 = 44 Given Code = 50 Relationship: 44 + 6 = 50

For JEER: J = 10, E = 5, E = 5, R = 18 Sum = 10 + 5 + 5 + 18 = 38 Given Code = 44 Relationship: 38 + 6 = 44

For FARE: F = 6, A = 1, R = 18, E = 5 Sum = 6 + 1 + 18 + 5 = 30

The codes for the words (50 and 44) follow a decreasing arithmetic progression with a common difference of 6 (50 - 6 = 44). Following this pattern, the code for the next word should be: 44 - 6 = 38

Explanation

The series follows an arithmetic pattern where each subsequent number is obtained by subtracting a constant value from the preceding term. By calculating the difference between consecutive terms:

237 - 196 = 41 196 - 155 = 41 155 - 114 = 41

The common difference is -41. Applying this logic to find the missing term:

114 - 41 = 73

Explanation

The code language follows a pattern where each digit represents the number of letters in the corresponding word of the sentence. In the phrase Sachin is a cricketer, the word Sachin contains 6 letters, is has 2 letters, a has 1 letter, and cricketer has 9 letters, resulting in the code 6219. Similarly, for the phrase He played from Mumbai, the word He has 2 letters, played has 6 letters, from has 4 letters, and Mumbai has 6 letters, which corresponds to the code 2646. Applying this same rule to the phrase Mumbai is very famous, the word Mumbai has 6 letters, is has 2 letters, very has 4 letters, and famous has 6 letters, yielding the code 6246.

Explanation

The series follows a mathematical pattern where each subsequent term is derived from the previous term using the formula xₙ = (xₙ₋₁ × 4) - 2.

Applying this rule step by step: The first term is 5. The second term is 5 × 4 - 2 = 18. The third term is 18 × 4 - 2 = 70. The fourth term is 70 × 4 - 2 = 278. To find the missing fifth term, multiply the fourth term by 4 and subtract 2: 278 × 4 - 2 = 1112 - 2 = 1110.

Alternatively, the pattern can be identified by looking at the differences between consecutive terms. The difference between 18 and 5 is 13. The difference between 70 and 18 is 52, which is 13 × 4. The difference between 278 and 70 is 208, which is 52 × 4. Consequently, the next difference must be 208 × 4 = 832. Adding this to the fourth term results in 278 + 832 = 1110.

Explanation

Dictionary order is determined by comparing the letters of each word from left to right. All five words share the identical eight-letter prefix Petition. According to alphabetical rules, the shortest word that serves as the base, Petition (3), appears first. Among the remaining words, the character following the shared prefix determines the sequence. Petitionary (1) comes next because the letter a is the first in the alphabet. Comparing the words where the ninth letter is e, Petitioned (5) precedes Petitioners (4) because the tenth letter d comes before r. Finally, Petitioning (2) is placed last because its ninth letter i follows a and e in the alphabetical sequence. This logic establishes the correct dictionary order as 3, 1, 5, 4, 2.

Explanation

Let the cost of one pen be p and the cost of one notebook be n. Based on the purchases made by Mohit and Sudesh, we can form the following linear equations:

3p + 6n = 180 (Equation 1) 5p + 2n = 116 (Equation 2)

To find the amount Mohit spent on notebooks, we need to calculate the value of 6n. First, simplify Equation 1 by dividing the entire equation by 3, which gives p + 2n = 60. From this, we can express 2n as 60 - p.

Substitute the value of 2n into Equation 2: 5p + (60 - p) = 116 4p + 60 = 116 4p = 56 p = 14

The cost of one pen is ₹14. Now, substitute p = 14 back into Equation 1 to find the total cost of the notebooks Mohit bought: 3(14) + 6n = 180 42 + 6n = 180 6n = 180 - 42 6n = 138

Explanation

Since the house faces North, the backdoor is located on the South side. Walking straight out of the backdoor means Gaurav initially travels 25 m South. His first left turn while facing South leads him 36 m East. From there, a second left turn while facing East directs him 47 m North. Finally, a third left turn while facing North takes him 36 m West.

To find his final position relative to the house, we calculate the net displacement in both directions. In the East-West direction, the movements of 36 m East and 36 m West cancel each other out, meaning he is back on the same vertical axis as his house. In the North-South direction, his displacement is 47 m (North) - 25 m (South) = 22 m. Because the Northward distance is greater than the Southward distance, he is exactly 22 m North of his starting point.

Explanation

Substituting the signs from option b into the equation gives 60 + 48 ÷ 36 × 6 - 15 = 53. Applying the BODMAS rule, the division and multiplication operations are performed first. The expression 48 ÷ 36 × 6 can be calculated as ⁴⁸⁄₃₆ × 6. Simplifying the fraction ⁴⁸⁄₃₆ results in ⁴⁄₃. Multiplying this by 6 gives ⁴⁄₃ × 6 = 4 × 2 = 8. The equation then simplifies to 60 + 8 - 15 = 53. Following the order of operations, the addition and subtraction result in 68 - 15 = 53, which simplifies to 53 = 53. This sequence of mathematical signs perfectly balances the equation.

Explanation

By interchanging the numbers 6 and 20 and the signs × and ÷ in the expression 729 × 81 ÷ 20 + 16 - 6 = 50, the equation becomes:

729 ÷ 81 × 6 + 16 - 20 = 50

Applying the BODMAS rule to the left-hand side:

Perform division first: 729 ÷ 81 = 9. The equation is now: 9 × 6 + 16 - 20 = 50.

Perform multiplication next: 9 × 6 = 54. The equation is now: 54 + 16 - 20 = 50.

Perform addition: 54 + 16 = 70. The equation is now: 70 - 20 = 50.

Perform subtraction: 70 - 20 = 50.

The calculation results in 50 = 50, which satisfies the equation.

Explanation

The coding logic follows two specific rules applied to the letters of the word written in reverse order. First, consonants are coded using their reverse alphabetical rank, calculated as 27 - rank. Second, vowels are coded using their direct alphabetical rank.

For the word FRUGAL, the letters in reverse order are L, A, G, U, R, and F.

L is the 12th letter and a consonant, so it is coded as 27 - 12 = 15. A is the 1st letter and a vowel, so it is coded as 1. G is the 7th letter and a consonant, so it is coded as 27 - 7 = 20. U is the 21st letter and a vowel, so it is coded as 21. R is the 18th letter and a consonant, so it is coded as 27 - 18 = 9. F is the 6th letter and a consonant, so it is coded as 27 - 6 = 21.

Combining these values in the reversed sequence 15, 1, 20, 21, 9, and 21 results in the code 1512021921.

Explanation

Nirupama is the mother of Deepak, and Ankit is married to Nirupama, which makes Ankit the father of Deepak. The problem states that Kartik is the paternal grandfather of Deepak. By definition, a paternal grandfather is the father of one's father. Since Ankit is the father of Deepak, Kartik must be the father of Ankit. This is further supported by the information that Saloni is the daughter of Kartik's only son, identifying Ankit as that only son.

Explanation

The coding logic follows a pattern based on the type of letter: consonants are shifted three places forward (+3), while vowels are shifted three places backward (-3) in the English alphabetical order.

Applying this to BACTERIA: B (Consonant) + 3 = E A (Vowel) - 3 = X C (Consonant) + 3 = F T (Consonant) + 3 = W E (Vowel) - 3 = B R (Consonant) + 3 = U I (Vowel) - 3 = F A (Vowel) - 3 = X This results in the term EXFWBUFX.

Applying the same logic to WOUNDS: W (Consonant) + 3 = Z O (Vowel) - 3 = L U (Vowel) - 3 = R N (Consonant) + 3 = Q D (Consonant) + 3 = G S (Consonant) + 3 = V The resulting code is ZLRQGV.

Explanation

The pattern in the third row follows a specific arithmetic relationship between the numbers in that row and the number in the second column of the following row:

In the third row (45, 15, 21), dividing the first number by the second number and then multiplying by the middle number of the fourth row yields the third number: ⁴⁵⁄₁₅ × 7 = 3 × 7 = 21

Similarly, looking at the relationship between the first and second columns across the rows: The middle number of the third row is derived from the difference of the first two numbers in the first row: 63 - 48 = 15

The third number of the second row is derived from the difference between the third and first numbers of the first row: 56 - 48 = 8

Substituting these values into the pattern, the number 21 correctly completes the logical sequence for the third row.

Explanation

The series follows a fixed addition pattern for each corresponding letter position in the character groups. For the first letter, the sequence increases by +4 in alphabetical order: R(18) + 4 = V(22), V(22) + 4 = Z(26), Z(26) + 4 = D(30 ≡ 4), and D(4) + 4 = H(8). For the second letter, the sequence increases by +6: T(20) + 6 = Z(26), Z(26) + 6 = F(32 ≡ 6), F(6) + 6 = L(12), and L(12) + 6 = R(18). For the third letter, the sequence increases by +11: M(13) + 11 = X(24), X(24) + 11 = I(35 ≡ 9), I(9) + 11 = T(20), and T(20) + 11 = E(31 ≡ 5). Following this consistent pattern of adding 4, 6, and 11 respectively to the last given term DLT, the next term in the series is HRE.

Explanation

The logic applied to the groups follows the pattern (n, n², n² - 5), where the second number is the square of the first number and the third number is 5 less than the second number. For the first number 15, the second number should be 15² = 225 and the third number should be 225 - 5 = 220. The group (15, 220, 215) is the odd one out because it deviates from this pattern. In this set, the second number is 220 instead of 225, and the third number is 215 instead of 220, thus failing to satisfy the square relationship between the first and second terms.

Explanation

Akun and Nikita are a married couple with two daughters and no son. Their sons-in-law are Uday and Vanmay. Vanmay is married to one daughter, Yamini, and they have three children: Tina, Smita, and a son. Uday is married to the second daughter, and they have two children: a son and a daughter.

Pamila and Rahul are siblings and grandchildren of Akun, meaning they are the children of one of the two daughters. Since Rahul is the cousin of Kamal, they must belong to different nuclear families within the extended family. To satisfy the relationship where Yamini is the aunt of Rahul, Rahul and Pamila must be the children of Uday and the second daughter. In this family structure, Yamini is the sister of Rahul's mother, which identifies her as Rahul's maternal aunt.

Explanation

The statement "All reds are yellows" indicates that the set of reds is a subset of the set of yellows (R ⊆ Y). The statement "No pink is yellow" (P ∩ Y = ∅) establishes that the set of pinks and yellows are completely disjoint. Since all reds are contained within the yellow set, and the yellow set has no intersection with the pink set, it logically follows that no red can be pink, validating Conclusion I. Similarly, the statement "No yellow is white" (Y ∩ W = ∅) means there is no overlap between yellows and whites. Because all reds are part of the yellow set, they are also excluded from the white set, confirming Conclusion II (R ∩ W = ∅). Conclusion III is a direct logical conversion of the second statement; if no yellow is white, then it is inherently true that no white is yellow. Therefore, all three conclusions follow from the premises.

Explanation

The letter-cluster series follows a specific mathematical pattern for each position of the letters in the clusters.

First letter series: K -5 F -5 A -5 V -5 Q -5 L. The position values are 11, 6, 1, 22 (27-5), 17, 12. Subtracting 5 from V (22) gives 17, which corresponds to Q.

Second letter series: Y -5 T -5 O -5 J -5 E -5 Z. The position values are 25, 20, 15, 10, 5, 26 (0). Subtracting 5 from J (10) gives 5, which corresponds to E.

Third letter series: B +3 E +3 H +3 K +3 N +3 Q. The position values are 2, 5, 8, 11, 14, 17. Adding 3 to K (11) gives 14, which corresponds to N.

Fourth letter series: A, E, I, O, U, A. This position follows the sequential order of English vowels. After O, the next vowel is U.

By combining these derived letters, the cluster that replaces the question mark is QENU.

Explanation

The coding logic follows a pattern where the numerical position of each letter in the English alphabetical series (A=1, B=2, …, Z=26) is multiplied by 2.

For the word RAKHI, the positions are R=18, A=1, K=11, H=8, I=9. Multiplying each by 2 gives 18 × 2 = 36, 1 × 2 = 2, 11 × 2 = 22, 8 × 2 = 16, and 9 × 2 = 18, resulting in the code 36-2-22-16-18.

For the word SHALU, the positions are S=19, H=8, A=1, L=12, U=21. Multiplying each by 2 gives 19 × 2 = 38, 8 × 2 = 16, 1 × 2 = 2, 12 × 2 = 24, and 21 × 2 = 42, resulting in the code 38-16-2-24-42.

Applying this logic to MANJU: M = 13 ⟹ 13 × 2 = 26 A = 1 ⟹ 1 × 2 = 2 N = 14 ⟹ 14 × 2 = 28 J = 10 ⟹ 10 × 2 = 20 U = 21 ⟹ 21 × 2 = 42

Following these calculations, the code for MANJU is 26-2-28-20-42.

Explanation

The relationship between the numbers follows the pattern (n - 2)², where n is the given number. In the first pair, subtracting 2 from 23 gives 21, and the square of 21 is 21 × 21 = 441. Applying this logic to the third number, subtracting 2 from 28 gives 26. Squaring 26 results in 26 × 26 = 676.

Explanation

The coding logic involves shifting each letter of the word forward by 3 positions in the English alphabetical order. In the word MONEY, the transformations are M (13) + 3 = P (16), O (15) + 3 = R (18), N (14) + 3 = Q (17), E (5) + 3 = H (8), and Y (25) + 3 = B (2, considering the cyclic nature of the alphabet). Applying the same +3 increment to the letters of CREDIT, we obtain C (3) + 3 = F (6), R (18) + 3 = U (21), E (5) + 3 = H (8), D (4) + 3 = G (7), I (9) + 3 = L (12), and T (20) + 3 = W (23). Combining these results gives the code FUHGLW.

Explanation

To find the code for the word okay, we compare the given sentences to identify common words and their corresponding digits. Comparing her father is okay (6583) and my father is well (5137), the common words are father and is, which correspond to the common digits 5 and 3. Next, comparing her father is okay (6583) and her arm is injured (2839), the common words are her and is, which correspond to the common digits 8 and 3. Since the word is appears in all three phrases and the digit 3 is the only digit present in all three codes (6583, 5137, 2839), we determine that is is 3. From the previous comparisons, we can then deduce that father is 5 and her is 8. In the first phrase her father is okay, which is coded as 6583, the digits for her (8), father (5), and is (3) are already accounted for. The only remaining word is okay and the only remaining digit in that set is 6.

Explanation

The words are arranged in a logical sequence based on the increasing order of their physical size and body mass. The starfish (1) is the smallest organism in the list, followed by the penguin (5). The giant tortoise (4) is larger and heavier than a penguin but smaller than a shark (3), which can reach several meters in length. The blue whale (2) is the largest animal on Earth, completing the progression from the smallest to the largest creature.

Explanation

Based on the given conditions for five persons sitting in a row facing north, we determine their positions from left to right. Since a weak person is sitting to the immediate left of the extrovert, the extrovert cannot be at the left extreme; therefore, the extrovert must be at the right extreme (position 5) and the introvert must be at the left extreme (position 1). The weak person occupies position 4.

The intelligent person is sitting exactly between the introvert and the thin persons. For the intelligent person to be between position 1 (introvert) and another person, they must occupy position 2, placing the thin person at position 3. This arrangement is further confirmed by the condition that the thin person is to the immediate right of the intelligent person. Thus, the sequence from left to right is: Introvert, Intelligent, Thin, Weak, and Extrovert. The person in the third position, which is the centre of the five-person row, is the thin person.

Explanation

The pattern among the letter-clusters is based on the incremental addition to the alphabetical position of each consecutive letter. In the clusters NQUZF, LOSXD, and FIMRX, the gap between letters follows the sequence +3, +4, +5, and +6. Specifically, for NQUZF, the positions are 14, 17, 21, 26, 6, which corresponds to 14+3=17, 17+4=21, 21+5=26, and 26+6=32 (or 6 in a 26-letter cycle).

In the cluster ZCGLS, the positional values are Z(26), C(3), G(7), L(12), and S(19). Calculating the differences: 26 + 3 = 3 (C), 3 + 4 = 7 (G), 7 + 5 = 12 (L), and 12 + 7 = 19 (S). Because the final increment is +7 instead of the +6 required by the established pattern, this cluster is the odd one out.

Explanation

The series follows an alternating pattern of two operations. The first operation is adding 4 to the current term to get the next term, and the second operation is multiplying the current term by 2 and adding 3 to get the next term.

The steps are: 10 + 4 = 14 (14 × 2) + 3 = 31 31 + 4 = 35 (35 × 2) + 3 = 73 73 + 4 = 77

Following this logic, the next step requires the second operation: (77 × 2) + 3 = 154 + 3 = 157

Explanation

To make the equation 384 ÷ 16 - 72 + 9 × 10 = 2 correct, we interchange the digits 7 and 9. This transformation changes 72 into 92 and 9 into 7. Substituting these new values into the expression, we get 384 ÷ 16 - 92 + 7 × 10. Following the BODMAS rule, we first perform the division 384 ÷ 16 = 24. Then, we perform the multiplication 7 × 10 = 70. The expression simplifies to 24 - 92 + 70. Adding the positive terms together gives 24 + 70 = 94. Finally, subtracting 92 from 94 results in 94 - 92 = 2. This satisfies the equation.

Explanation

The relationship between the terms is based on a two-step transformation. First, each letter of the word is shifted forward by one position in the alphabet (+1). Second, the resulting sequence is divided into pairs of adjacent letters, and the positions of the letters within each pair are swapped.

In the case of PATELS, shifting each letter by +1 gives the sequence Q (P+1), B (A+1), U (T+1), F (E+1), M (L+1), and T (S+1). Arranging these into pairs results in (Q, B), (U, F), and (M, T). Swapping the characters within each pair produces BQ, FU, and TM, which combines to form BQFUTM.

Applying the same logic to NECTAR, shifting each letter by +1 results in O (N+1), F (E+1), D (C+1), U (T+1), B (A+1), and S (R+1). Grouping these into pairs yields (O, F), (D, U), and (B, S). Swapping the characters within these pairs results in FO, UD, and SB. Concatenating these pairs results in the final string FOUDSB.

Explanation

The series follows a pattern where each term is calculated by multiplying the preceding term by an increasing integer and then adding 1. The multiplier starts at 2 and increments by 1 for each step.

The calculation for each term is as follows: 16 × 2 + 1 = 33 33 × 3 + 1 = 100 100 × 4 + 1 = 401

To find the missing number, the previous term 401 is multiplied by the next integer in the sequence, which is 5, and then 1 is added: 401 × 5 + 1 = 2005 + 1 = 2006

Explanation

By interchanging the numbers 12 and 16 and the signs × and ÷, the equation transforms from 24 ÷ 16 - 96 + 48 × 12 = 195 to 24 × 12 - 96 + 48 ÷ 16 = 195. Following the BODMAS rule, the calculation proceeds as follows:

First, perform the division: 48 ÷ 16 = 3. Next, perform the multiplication: 24 × 12 = 288. The equation now reads: 288 - 96 + 3 = 195. Finally, perform the addition and subtraction: 291 - 96 = 195. Since 195 = 195, the equation is balanced.

Explanation

The total area of the park including the garden is determined by the side length of the outermost square boundary. According to the problem, the side of the larger square-shaped development is 24 m. The formula for the area of a square is Area = side × side. By substituting the given side length, the calculation is 24 m × 24 m = 576 m². Since the garden is developed around the original park, this outer measurement represents the combined area of both the park and the garden.

Explanation

The series is formed by the continuous repetition of the five-letter unit ULHEN. By dividing the given series into four groups of five letters each, the pattern becomes clear:

First group: (U) L H (E) (N) Second group: U (L) H (E) (N) Third group: U (L) H (E) N Fourth group: U (L) (H) E N

The fixed letters in the series (L and H at positions 2 and 3; U and H at positions 6 and 8; U and H at positions 11 and 13; N and U at positions 15 and 16; E and N at positions 19 and 20) align perfectly with the repeated ULHEN sequence. Sequentially placing the letters from option a (U, E, N, L, E, N, L, E, L, H) into the ten available blanks completes the four-unit cycle.

Explanation

To make the equation 32 + 24 × 4 ÷ 16 - 64 = 90 correct, the signs + and - are interchanged. The modified expression becomes:

32 - 24 × 4 ÷ 16 + 64

Following the BODMAS rule, first perform the division operation: 4 ÷ 16 = ¼

The equation now stands as: 32 - 24 × ¼ + 64

Next, perform the multiplication: 24 × ¼ = 6

The equation simplifies to: 32 - 6 + 64

Finally, solve the addition and subtraction from left to right: 26 + 64 = 90

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

Explanation

The letter-clusters follow a logic where each letter is determined by adding 11 to the numerical position of the preceding letter. This relation is defined as Pₙ₊₁ = (Pₙ + 11) 26, where P represents the position of the letter in the alphabet (A=1, B=2, ..., Z=26). In the cluster YJB, the transition from the first letter Y (25) to the second letter J (10) follows this rule because 25 + 11 = 36, and 36 26 = 10. However, the transition from J (10) to the third letter B (2) violates the pattern. According to the formula, the third letter should be 10 + 11 = 21, which corresponds to U. Because the cluster contains B instead of U, it is the odd one out.