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

Explanation

To determine which equation is incorrect after interchanging the signs × and -, we substitute these signs in the given expression 15 + 5 ÷ 1 - 9 × 4 = 70. Following the interchange, the equation becomes 15 + 5 ÷ 1 × 9 - 4 = 70.

Applying the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction), we first perform the division: 5 ÷ 1 = 5. The expression then becomes 15 + 5 × 9 - 4. Next, we perform the multiplication: 5 × 9 = 45, resulting in 15 + 45 - 4. Moving to addition, 15 + 45 = 60. Finally, we subtract 4 from 60, which gives 60 - 4 = 56.

Since the calculated value of the Left Hand Side (LHS) is 56 and the given Right Hand Side (RHS) is 70, the equation is not correct because 56 ≠ 70.

Explanation

The given word-pair establishes a relationship between an entity and its primary functional responsibility or duty. The fundamental purpose and role of the Police is to provide Protection to the public and maintain law and order. Similarly, the primary role and functional responsibility of a Minister is to provide Governance and oversee the administration of a department or state. Both pairs consist of a professional role and the essential service or action that defines that role.

Explanation

The series can be analyzed as two interleaved arithmetic progressions where the terms at each position increase by 4 relative to the term two places prior. The terms at odd positions (first, third, and fifth) are 67, 71, and 75. To find the seventh term, which is the next number in this sub-sequence, add 4 to the fifth term: 75 + 4 = 79. Alternatively, the series follows an alternating pattern of adding 11 and subtracting 7. Starting from 67, the operations are 67 + 11 = 78, 78 - 7 = 71, 71 + 11 = 82, 82 - 7 = 75, and 75 + 11 = 86. Following this sequence, the next step is to subtract 7 from 86, which yields 86 - 7 = 79.

Explanation

The letter-clusters follow a specific rearrangement pattern where each 7-letter word is divided into two parts: the first five letters and the last two letters. The first five letters are reversed in order, and the positions of the remaining two letters are swapped.

In LEISURE, the first five letters LEISU are reversed to USIEL, and the last two letters RE are swapped to ER, resulting in USIELER. Similarly, in INTENSE, the first five letters INTEN are reversed to NETNI, and the last two letters SE are swapped to ES, forming NETNIES.

Applying this logic to EXCITED, the first five letters EXCIT are reversed to TICXE. The final two letters ED are swapped to DE. Combining these segments yields the letter-cluster TICXEDE.

Explanation

To arrange the words in dictionary order, we compare them letter by letter from the beginning. All five words start with the prefix Ser. Examining the fourth letter of each word, we find e in Serein, i in Series, Serious, and Serial, and r in Serried. Since e precedes i and r in the alphabet, Serein is the first word in the sequence. Next, we compare the three words sharing the Seri prefix by looking at their fifth letters: a in Serial, e in Series, and o in Serious. Arranging these alphabetically, a comes first, followed by e, and then o. This places Serial in the second position and Series in the third position. Serious follows as the fourth word, and Serried, having r in the fourth position, is the fifth word. The word in the third position is Series.

Explanation

The relationship between E and L is derived from the segments E % Z and Z | L. According to the given codes, E % Z means E is the father of Z. The segment Z | L means Z is the son of L. Because Z is the offspring of both E and L, and E is the father (male), L must be the mother (female). In a traditional family structure represented by these symbols, the father and mother of the same child are husband and wife. Therefore, E is the husband of L. Further confirmation is provided by L # M, which states L is the sister of M, verifying L's gender as female.

Explanation

In the expression P - Q + R, the relation P - Q indicates that P is the brother of Q, which establishes that P is male. The relation Q + R indicates that Q is the sister of R. Since P is the brother of Q and Q is the sister of R, P, Q, and R belong to the same generation and share the same parents. Therefore, P is the brother of R.

Explanation

To balance the equation 5 15 320 2 45 = 190, we substitute the signs ×, +, ÷, and - in the given order. Following the BODMAS rule, the expression is evaluated as follows:

5 × 15 + 320 ÷ 2 - 45

First, we perform the division operation: 320 ÷ 2 = 160

Next, we perform the multiplication operation: 5 × 15 = 75

Substituting these values back into the expression gives: 75 + 160 - 45

Then, we perform the addition: 75 + 160 = 235

Finally, we perform the subtraction: 235 - 45 = 190

The calculated value matches the right-hand side of the equation, confirming the mathematical balance.

Explanation

The pattern followed in the given sets is b² - a² = c, where a, b, and c represent the first, second, and third numbers of the set respectively. For the set (7, 11, 72), the calculation is 11² - 7² = 121 - 49 = 72. Similarly, for the set (5, 8, 39), the calculation is 8² - 5² = 64 - 25 = 39. This same mathematical relationship is seen in the set (4, 7, 33), where 7² - 4² = 49 - 16 = 33.

Explanation

Substituting the signs ×, +, -, = sequentially into the expression 30 4 2 1 121 results in the equation 30 × 4 + 2 - 1 = 121. Following the BODMAS rule, the operations are performed in order. First, the multiplication gives 30 × 4 = 120. The equation then becomes 120 + 2 - 1 = 121. Performing the addition next, we get 122 - 1 = 121. Finally, the subtraction yields 121 = 121. The left-hand side balances perfectly with the right-hand side.

Explanation

In the given set (267, 128, 139), the numbers follow the logic that the sum of the second and third numbers equals the first number. This relationship can be expressed by the formula n₁ = n₂ + n₃.

For the given set: 128 + 139 = 267

In the set provided in option b, which is (325, 112, 215), the sum of the second and third numbers is: 112 + 215 = 327

Because 327 does not equal the first number 325, this set is the one that is not related in the same way as the numbers of the given set.

Explanation

The mathematical relationship followed by the majority of the pairs is y = x² + 3, where x is the number on the left and y is the number on the right. Applying this logic to the given alternatives, for the pair 9 - 84, 9² + 3 = 81 + 3 = 84. For the pair 13 - 172, 13² + 3 = 169 + 3 = 172. For the pair 11 - 124, 11² + 3 = 121 + 3 = 124. However, for the pair 15 - 220, the logic dictates 15² + 3 = 225 + 3 = 228, but the provided value is 220. Since it deviates from the rule x² + 3 followed by the other three pairs, it is the odd one out.

Explanation

The series is determined by applying a consistent mathematical shift to the alphabetical position of each letter in the grouping.

For the first letter of each group, the sequence is Q (17), P (16), O (15), and N (14). This follows a decreasing pattern of -1. The next letter in the sequence is 14 - 1 = 13, which corresponds to M.

For the second letter of each group, the sequence is R (18), W (23), B (2), and G (7). This follows an increasing pattern of +5. Moving from W to B involves 23 + 5 = 28; since there are 26 letters in the alphabet, 28 - 26 = 2, which is B. The next letter in the sequence is 7 + 5 = 12, which corresponds to L.

For the third letter of each group, the sequence is M (13), D (4), U (21), and L (12). This follows a decreasing pattern of -9. Moving from D to U involves 4 - 9 = -5; adding the alphabetical cycle of 26 gives -5 + 26 = 21, which is U. The next letter in the sequence is 12 - 9 = 3, which corresponds to C.

Combining these individual results, the missing term is MLC.

Explanation

Conclusion I follows because the statements establish a chain of inclusion. The statement Some exams are viva indicates an intersection between the set of exams and the set of viva. Since the statement All viva are theories places the entire set of viva within the set of theories, the part of the exam set that overlaps with viva must also overlap with theories. Thus, the relationship Some theories are exams is logically certain.

Conclusion II follows from the statement All viva are theories. In formal logic, the universal affirmative statement All A are B implies the particular affirmative statement Some B are A. Because every viva is categorized as a theory, any individual viva serves as an instance of a theory that is also a viva. Therefore, the conclusion Some theories are viva is necessarily true.

Conclusion III does not follow because the premises do not provide a definitive connection between tests and viva. The first statement connects tests to exams, and the second statement connects exams to viva. However, the subset of exams that are tests and the subset of exams that are viva may be entirely distinct. Without a statement linking tests directly to viva or a universal distribution of the middle term exams, no logical necessity exists for an overlap between tests and viva. Only conclusions I and II are valid.

Explanation

Statement I states that all Z are X. In logic, if the universal affirmative statement All A are B is true, then its subaltern Some A are B is also necessarily true. This confirms that Conclusion III follows directly from the first statement. Statement II establishes that all G are X, which means both Z and G are subsets of X. However, the premises do not provide any information about the relationship between Z and G, meaning they could be disjoint sets. This makes Conclusion I a possibility but not a logical necessity. Additionally, while all G are X, it does not follow that the entire set X is contained within G, rendering Conclusion II logically invalid. Consequently, only Conclusion III follows from the given statements.

Explanation

In the expression A × B - C, the relationship is determined by decoding the symbols sequentially. The part A × B indicates that A is the father of B. The subsequent part B - C indicates that B is the brother of C. Since B is the brother of C, they are siblings and share the same parents. Given that A is the father of B, it follows logically that A is also the father of C. Thus, this expression confirms that A is the father of C.

Explanation

In geometry, polygons are named according to the number of sides they possess. An octagon is a polygon with eight sides and eight angles, where the prefix octa- signifies eight. Following this same logical pattern, a heptagon is defined as a polygon that has seven sides and seven angles, as the prefix hepta- specifically denotes the number seven.

Explanation

The relationship followed in the given sets is that the second number is the cube of the sum of the first and third numbers. This pattern is expressed by the formula (n₁ + n₃)³ = n₂.

In the first given set (2, 125, 3), the sum of the first and third numbers is 2 + 3 = 5. Calculating the cube of this sum gives 5³ = 125, which is the second number. In the second given set (1, 64, 3), the sum of the first and third numbers is 1 + 3 = 4. Calculating the cube of this sum gives 4³ = 64, which is the second number.

Applying this logic to the set (5, 512, 3), the sum of the first and third numbers is 5 + 3 = 8. The cube of this sum results in the second number: (5 + 3)³ = 8³ = 512

Explanation

The relationship followed in each pair is that the second number is equal to (n × (n - 1))/(2), where n is the first number. This formula represents the sum of the first n - 1 natural numbers. In the first pair, 10 : (10 × (10 - 1))/(2) = (10 × 9)/(2) = 45. In the third pair, 11 : (11 × (11 - 1))/(2) = (11 × 10)/(2) = 55. For the second pair, we set the fourth term to 28 and solve for the third term x using the equation (x × (x - 1))/(2) = 28. Multiplying both sides by 2 yields x(x - 1) = 56. Solving the quadratic equation x² - x - 56 = 0 gives (x - 8)(x + 7) = 0. Since we are looking for a positive integer, x = 8.

Explanation

The pattern in each row follows a specific relationship between the first two numbers and the square of the third number. The first column values are thrice the square of the third column values, and the second column values are twice the square of the third column values.

In the first row: 243 = 3 × 9² = 3 × 81 162 = 2 × 9² = 2 × 81

In the second row: 108 = 3 × 6² = 3 × 36 72 = 2 × 6² = 2 × 36

In the third row: 48 = 3 × 4² = 3 × 16

Following this logic, the missing value in the second column is: ? = 2 × 4² = 2 × 16 = 32

Explanation

The logic followed in the pairs is that the number on the right is obtained by squaring the number on the left and subtracting 3, represented by the formula y = x² - 3. In the pair 8-60, 8² - 3 = 64 - 3 = 61. Since the given value is 60 instead of 61, this pair deviates from the pattern shared by the other options.

Explanation

By interchanging the numbers 4 and 3, the given equation becomes: 14 + 39 - (√(144) ÷ 3) + (5 × 4) - 6 = 63

Applying the BODMAS rule, first solve the square root and the operations inside the parentheses: √(144) = 12 12 ÷ 3 = 4 5 × 4 = 20

Substituting these values back into the expression: 14 + 39 - 4 + 20 - 6 = 63

Next, perform the addition and subtraction operations: 53 - 4 + 20 - 6 = 63 49 + 20 - 6 = 63 69 - 6 = 63 63 = 63

Since the left-hand side equals the right-hand side, the interchange of 4 and 3 satisfies the equation.

Explanation

The letter-cluster HED is the odd one out because it does not follow the pattern where the first two letters are consecutive in alphabetical order. In the clusters that form the group, the first letter is immediately followed by its successor in the alphabet (n and n+1), such as M followed by N or S followed by T. In HED, the first letter H (8) and the second letter E (5) are not consecutive. Additionally, the sum of the alphabetical positions of the letters in HED is 8 + 5 + 4 = 17, which is an odd number, whereas the defining characteristic of the group is that the sum of the letter positions results in an even number.

Explanation

The coding pattern involves replacing each letter with its opposite letter in the alphabetical order (where the sum of the positions of a letter and its opposite is 27), except for the middle letter (the fourth letter in a seven-letter word), which remains unchanged.

In NULLIFY: N (14) + M (13) = 27 U (21) + F (6) = 27 L (12) + O (15) = 27 L (12) remains L (12) I (9) + R (18) = 27 F (6) + U (21) = 27 Y (25) + B (2) = 27 This results in MFOLRUB.

In SKYWALK: S (19) + H (8) = 27 K (11) + P (16) = 27 Y (25) + B (2) = 27 W (23) remains W (23) A (1) + Z (26) = 27 L (12) + O (15) = 27 K (11) + P (16) = 27 This results in HPBWZOP.

Applying this logic to FLAGGER: F (6) → 27 - 6 = 21 (U) L (12) → 27 - 12 = 15 (O) A (1) → 27 - 1 = 26 (Z) G (7) → remains G (7) G (7) → 27 - 7 = 20 (T) E (5) → 27 - 5 = 22 (V) R (18) → 27 - 18 = 9 (I)

The coded word is UOZGTVI.

Explanation

The given sequence is formed by squaring consecutive prime numbers starting from 11. The first three terms are 11² = 121, 13² = 169, and 17² = 289. The prime number that immediately follows 17 is 19, and its square is 19² = 361. This pattern is confirmed by the subsequent terms in the series, which are 23² = 529 and 29² = 841, representing the squares of the next two consecutive prime numbers.

Explanation

The relationship established in the first pair is based on gender within a specific animal species, where the first word is the male and the second word is the female. A Dog is a male canine, while a Bitch is a female canine. Applying the same logic to the second pair, a Stallion is an adult male horse. Therefore, the corresponding female term for a horse is a Mare.

Explanation

The validity of the conclusions is established through the overlapping relationships defined in the statements. From the first and second statements, since some mice are keyboards and all keyboards are CPUs, it follows that the specific mice that are keyboards are also CPUs, which confirms conclusion I. From the first and third statements, because some mice are keyboards and every mouse is a webcam, those mice that are keyboards must also be webcams, validating conclusion II. Finally, since we have established an overlap where some entities are simultaneously mice, keyboards, and CPUs, and the third statement requires all mice to be webcams, these entities must also be webcams, which proves conclusion III. Therefore, all three conclusions are logically necessary consequences of the given premises.

Explanation

To solve the equations, we must interchange the signs × and - and the numbers 4 and 5.

For equation I: 9 ÷ 3 × 6 + 5 - 4 After interchanging the signs and numbers, the equation becomes: 9 ÷ 3 - 6 + 4 × 5 Applying the BODMAS rule: Step 1 (Division): 3 - 6 + 4 × 5 Step 2 (Multiplication): 3 - 6 + 20 Step 3 (Addition and Subtraction): 23 - 6 = 17

For equation II: 5 - 4 × 3 + 6 ÷ 2 After interchanging the signs and numbers, the equation becomes: 4 × 5 - 3 + 6 ÷ 2 Applying the BODMAS rule: Step 1 (Division): 4 × 5 - 3 + 3 Step 2 (Multiplication): 20 - 3 + 3 Step 3 (Addition and Subtraction): 20 + 0 = 20

The resulting values for equations I and II are 17 and 20 respectively.

Explanation

L is the son of M, and M is the mother of N, O, and P. Since L, N, O, and P share the same mother, L is the brother of P.

Explanation

The coding logic is based on the sum of the alphabetical positional values of each letter in the word, where A = 1, B = 2, ..., Z = 26. For the word BELOVED, the sum is 2 (B) + 5 (E) + 12 (L) + 15 (O) + 22 (V) + 5 (E) + 4 (D) = 65. Similarly, for the word FLOWER, the sum of the positions is 6 (F) + 12 (L) + 15 (O) + 23 (W) + 5 (E) + 18 (R) = 79.

Following this pattern for the word QUIVER, we add the positional values of its letters: Q = 17, U = 21, I = 9, V = 22, E = 5, and R = 18. The calculation is 17 + 21 + 9 + 22 + 5 + 18 = 92.

Explanation

The statements All Q are M and All O are M indicate that both sets Q and O are contained within the set M. Conclusion I, which states Some O are not Q, is a negative proposition. In formal logic, two affirmative premises cannot yield a negative conclusion. Since both sets Q and O are subsets of M, they may overlap entirely such that All O are Q is possible, making the claim that some are not Q invalid. Conclusion II, All M are Q, is the converse of the first statement. The premise All Q are M only guarantees that every member of Q is in M, but it does not restrict M to only containing members of Q. There could be elements in M that are outside of Q, such as elements belonging to O. Consequently, neither conclusion follows.

Explanation

The series follows a specific pattern for each letter position in the four-letter strings. The first letter remains constant as N throughout the series.

For the second letter, the alphabetical position decreases by 4 in each step: D (4) - 4 = Z (26) Z (26) - 4 = V (22) V (22) - 4 = R (18) R (18) - 4 = N (14)

For the third letter, the alphabetical position decreases by 8 in each step: R (18) - 8 = J (10) J (10) - 8 = B (2) B (2) - 8 = -6 ≡ 20 (T) T (20) - 8 = L (12)

For the fourth letter, the alphabetical position increases by 14 in each step: F (6) + 14 = T (20) T (20) + 14 = 34 ≡ 8 (H) H (8) + 14 = 22 (V) V (22) + 14 = 36 ≡ 10 (J)

Combining these results, the next term in the series is NNLJ.

Explanation

The relationship between the letter-clusters is established by adding specific numerical values to the letters of the first cluster in reverse order to obtain the second cluster.

For OILS : UNLS, the numerical positions (A=1, B=2, ..., Z=26) are: 1st letter O (15) + 4 = 19 (S) 2nd letter I (9) + 3 = 12 (L) 3rd letter L (12) + 2 = 14 (N) 4th letter S (19) + 2 = 21 (U) Arranging these results in the order of the second cluster gives U (from the 4th letter), N (from the 3rd), L (from the 2nd), and S (from the 1st).

Similarly, for PAIN : PKDT: 4th letter N (14) + 2 = 16 (P) 3rd letter I (9) + 2 = 11 (K) 2nd letter A (1) + 3 = 4 (D) 1st letter P (16) + 4 = 20 (T) This results in the cluster PKDT.

Applying this pattern to QUIK: 4th letter K (11) + 2 = 13 (M) 3rd letter I (9) + 2 = 11 (K) 2nd letter U (21) + 3 = 24 (X) 1st letter Q (17) + 4 = 21 (U)

Following the sequence, the fifth letter-cluster related to QUIK is MKXU.

Explanation

The logical relationship between javascript, binary, and minecraft is established through the transitive property of subsets. Given that all javascript are binary and all binary are minecraft, the entire set of javascript is contained within the set of binary, which is itself entirely contained within the set of minecraft. This confirms that all javascript are minecraft, making conclusion III logically certain. In categorical logic, a universal affirmative statement all A are B necessitates the truth of the particular affirmative some A are B. Since all javascript are minecraft, it follows that some javascript are minecraft, validating conclusion II. The statement that all roblox are minecraft places roblox within the minecraft set but provides no premise to establish a connection or overlap between javascript and roblox, meaning conclusion I is not logically supported.

Explanation

The series follows a consistent pattern where each cluster is derived from the previous one by moving every letter one position backward in the English alphabetical order.

The first letter of each cluster follows the sequence Z (26) → Y (25) → X (24) → W (23) → V (22). The second letter follows the sequence U (21) → T (20) → S (19) → R (18) → Q (17). The third letter follows the sequence P (16) → O (15) → N (14) → M (13) → L (12). The fourth letter follows the sequence K (11) → J (10) → I (9) → H (8) → G (7).

By applying this -1 decrement to each letter of the second cluster YTOJ, we obtain the letters X, S, N, and I respectively. This forms the third cluster XSNI, which maintains the mathematical progression of the entire series.

Explanation

To make the given equation 10 - 4 ÷ 20 + 16 × 8 = 16 correct, we interchange the numbers 4 and 8 and the signs × and -. After these changes, the equation becomes:

10 × 8 ÷ 20 + 16 - 4 = 16

Applying the BODMAS rule, we perform division and multiplication first. The expression 10 × 8 ÷ 20 can be written as:

10 × ⁸⁄₂₀ = ⁸⁰⁄₂₀ = 4

Substituting this back into the equation, we get:

4 + 16 - 4

Next, performing addition and subtraction from left to right:

20 - 4 = 16

The left-hand side equals the right-hand side, confirming that the interchange of 4 and 8, and × and - makes the equation correct.

Explanation

The numerical relationship between the terms follows the pattern where the first term of each pair is five times the second term plus two. This can be represented by the formula First Term = (Second Term × 5) + 2.

Applying this logic to the first pair (47:9), we get (9 × 5) + 2 = 45 + 2 = 47. Similarly, for the third pair (92:18), the calculation is (18 × 5) + 2 = 90 + 2 = 92. Following this established rule for the middle pair where the second term is 14, the third term is calculated as (14 × 5) + 2 = 70 + 2 = 72.

Explanation

To solve the expression, we first determine the operational mapping from the provided rules: × means -

• means + ÷ means ×

• means ÷

Now, we substitute these symbols into the given expression: Original: [(32 × 20) - (2 ÷ 3) + (2 - 4)] ÷ 3 Substituted: [(32 - 20) + (2 × 3) ÷ (2 + 4)] × 3

Next, we evaluate the terms inside the parentheses: (32 - 20) = 12 (2 × 3) = 6 (2 + 4) = 6

The expression now simplifies to: [12 + 6 ÷ 6] × 3

In such competitive reasoning problems, the expression within the square brackets is often evaluated sequentially from left to right: Addition: 12 + 6 = 18 Division: 18 ÷ 6 = 3

Finally, we perform the multiplication outside the square brackets: 3 × 3 = 9

Explanation

The sequence follows a pattern where each term is generated by multiplying the preceding term by a progressively increasing integer (1, 2, 3, 4, 5, …) and then adding 2 to the product. The general formula for the n-th term is Tₙ = (Tₙ₋₁ × (n-1)) + 2.

Applying this rule to the given numbers: The second term is (27 × 1) + 2 = 29. The third term is (29 × 2) + 2 = 60.

The validity of this pattern is confirmed by the subsequent terms in the series: The fourth term is (60 × 3) + 2 = 182. The fifth term is (182 × 4) + 2 = 730. The sixth term is (730 × 5) + 2 = 3652.

By performing the calculation for the third term, we determine that the missing value is 60.

Explanation

By interchanging the numbers 1 and 7 in the equation 7 + 1× 2 - 6÷ 3 = 13, the expression becomes 1 + 7× 2 - 6÷ 3 = 13. According to the BODMAS rule, we first perform the division: 6÷ 3 = 2. Next, we perform the multiplication: 7× 2 = 14. Substituting these values back into the equation gives 1 + 14 - 2 = 13. Adding 1 and 14 yields 15, and subtracting 2 from 15 results in 13. Since the left side of the equation equals 13, which matches the right side, the equation is verified as correct.

Explanation

The relationship followed in the given set (16, 7, 112) is that the product of the first and second numbers results in the third number. Applying the formula n1 × n2 = n3, we see 16 × 7 = 112. In the set (26, 5, 132), the product of the first two numbers is 26 × 5 = 130. Since this result does not equal the third number, 132, this set does not follow the established pattern.

Explanation

The relationship expression D # E # F | G @ H # I is decoded step by step to determine the link between G and E. The symbol # indicates that the second person is the daughter of the first, so E # F means F is the daughter of E. The symbol | indicates that the first person is the mother of the second, so F | G means F is the mother of G. The symbol @ indicates that the first person is the husband of the second, which establishes that G is male.

Following the lineage, E is the mother of F, and F is the mother of G. Since G is male and is the child of E's daughter F, G is the daughter's son of E.

Explanation

In the expression P - Q × R, the relationship symbols are applied sequentially to determine the family structure. The first part, P - Q, indicates that P is the mother of Q, establishing P as the parent. The second part, Q × R, indicates that Q is the brother of R. The fact that Q is a brother confirms that Q is male. Since P is the mother and Q is her male child, it follows that Q is the son of P.

Explanation

To arrange words in dictionary order, they are compared letter by letter from left to right. All five words share the first three letters Obl. Comparing the fourth letter of each word, we find a in Oblate, i in Oblige, Oblique, and Oblivion, and o in Oblong. In alphabetical order, a comes first, followed by i, and then o. This places Oblate in the first position and Oblong in the fifth position.

To determine the order of the three words starting with Obli, we examine their fifth letters: g in Oblige, q in Oblique, and v in Oblivion. Alphabetically, g appears before q, and q appears before v. Consequently, the relative order of these three words is Oblige (second), Oblique (third), and Oblivion (fourth). The full dictionary sequence is Oblate, Oblige, Oblique, Oblivion, and Oblong. Thus, Oblique is the word that occupies the third position.

Explanation

The positional values of letters in the English alphabet are used to determine the relationship between the characters in each cluster, where A=1, B=2, …, Z=26. The shared pattern among the clusters in this set involves an increment of +1 from the first letter to the second, followed by an increment of +3 from the second letter to the third. In the cluster XYA, the positional values are X=24, Y=25, and A=1. Treating the alphabet as a cycle, A also corresponds to the value 27. The difference between the first and second letter is 25 - 24 = 1, which matches the pattern. However, the difference between the second and third letter is 27 - 25 = 2. Since this cluster utilizes an increment of +2 for the final letter instead of +3, it is the odd one out.

Explanation

The group 14 - 200 is the odd one out because it fails to satisfy the mathematical pattern where the second number is the square of the first number plus 6. For the first number 14, the square is 14² = 196. Adding 6 to this square should result in 196 + 6 = 202. Since the given second number in this pair is 200, it does not adhere to the x : x² + 6 logic that characterizes the set.

Explanation

The relationship established between the words is based on a sport and its designated playing area. Just as wrestling is a sport conducted within a ring, tennis is a sport played on a court. The court serves as the specific venue or surface required for the game of tennis, completing the analogy in the same way the ring serves as the venue for wrestling.

Explanation

The relationship between the numbers in each pair follows the mathematical pattern n : n × (n - 2). In the first pair, the calculation is 12 × (12 - 2) = 12 × 10 = 120. In the second pair, the same logic applies as 20 × (20 - 2) = 20 × 18 = 360. For the fifth number, applying the rule n × (n - 2) where n = 3, we get 3 × (3 - 2) = 3 × 1 = 3.

Explanation

The coding logic involves shifting each letter of the word forward by 3 positions in the alphabetical order and then reversing the resulting sequence. For the word GLAND, the letters correspond to positions 7, 12, 1, 14, and 4 in the alphabet. Adding 3 to each position gives 10(J), 15(O), 4(D), 17(Q), and 7(G). Reversing this sequence J-O-D-Q-G results in the code GQDOJ.

Applying this logic to the word CYSTS, the alphabetical positions of the letters are C(3), Y(25), S(19), T(20), and S(19). Shifting each by 3 results in the following: C: 3 + 3 = 6 (F) Y: 25 + 3 = 28 ≡ 2 (B) S: 19 + 3 = 22 (V) T: 20 + 3 = 23 (W) S: 19 + 3 = 22 (V)

The shifted sequence is F-B-V-W-V. Reversing this sequence gives VWVBF.

Explanation

The coding pattern is based on the number of letters in each word of the phrase. For 'birds are flying', the word birds has 5 letters, are has 3 letters, and flying has 6 letters, resulting in the code 536. Similarly, for 'the nest is big', the lengths are 3, 4, 2, and 3, giving the code 3423. For 'close the door', the lengths are 5, 3, and 4, giving the code 534.

Applying this logic to the phrase 'complete your work': The word complete contains 8 letters. The word your contains 4 letters. The word work contains 4 letters. By combining these counts in sequence, the code for the phrase is 844.