SSC CGL Tier 1 2021 General Intelligence & Reasoning Questions with Solutions

Explanation

The coding logic follows an alternating pattern based on the position of the letters in the word. For letters at odd positions (1st, 3rd, and 5th), the code uses the reverse or opposite letter in the English alphabet, where the sum of the numerical positions of the original letter and its opposite is 27. For letters at even positions (2nd, 4th, and 6th), the code subtracts 7 from the numerical position of the letter.

Applying this logic to FLOWER: The 1st letter F (6) is at an odd position, so its opposite letter is 27 - 6 = 21, which is U. The 2nd letter L (12) is at an even position, so subtracting 7 gives 12 - 7 = 5, which is E. The 3rd letter O (15) is at an odd position, so its opposite letter is 27 - 15 = 12, which is L. The 4th letter W (23) is at an even position, so subtracting 7 gives 23 - 7 = 16, which is P. The 5th letter E (5) is at an odd position, so its opposite letter is 27 - 5 = 22, which is V. The 6th letter R (18) is at an even position, so subtracting 7 gives 18 - 7 = 11, which is K.

Combining these letters yields the word UELPVK.

Explanation

Mohammad Azharuddin is the only individual among the given options who has served as an elected Member of Parliament (MP). He was elected to the 15th Lok Sabha in 2009 from the Moradabad constituency in Uttar Pradesh. While all four individuals are celebrated Indian cricketers and have held various roles in the sport, Rahul Dravid, Ajay Jadeja, and Saurav Ganguly have not been elected to the Indian Parliament. This distinction in their professional careers after or during their time in cricket makes Mohammad Azharuddin the odd one out.

Explanation

The coding logic involves reversing the string and then applying a pattern of alternating subtraction and addition of two to the alphabetical positions of the letters. For the word INHALE, reversing it results in ELAHNI. Applying the pattern of -2 and +2 yields: E - 2 = C, L + 2 = N, A - 2 = Y, H + 2 = J, N - 2 = L, and I + 2 = K, which forms the code CNYJLK.

Applying this same logic to GUILTY: First, reverse the word to get YTLIUG. Then, apply the -2, +2 alternating shifts: Y - 2 = W T + 2 = V L - 2 = J I + 2 = K U - 2 = S G + 2 = I The resulting code is WVJKSI.

Explanation

The pattern followed in the given set (3, 2, 3) involves two operations. The second number is determined by squaring the first number and subtracting 7, while the third number is calculated by multiplying the second number by 1.5.

For the set (3, 2, 3): n₂ = 3² - 7 = 9 - 7 = 2 n₃ = 2 × 1.5 = 3

Applying this same logic to the set (5, 18, 27): n₂ = 5² - 7 = 25 - 7 = 18 n₃ = 18 × 1.5 = 27

The numbers in option d satisfy both mathematical conditions established by the original set.

Explanation

The letters in the clusters are arranged according to their numerical positions in the English alphabet. The common rule followed is an increase of 2 between the first and second letters, and an increase of 3 between the second and third letters. For the cluster JLP, the alphabetical positions are J = 10, L = 12, and P = 16. While the first gap is 12 - 10 = 2, the second gap is 16 - 12 = 4. This +2, +4 progression differs from the +2, +3 progression found in the other clusters.

Explanation

The relationship between the numbers is defined by the logic x × (ˣ⁄₂ + 1). In the first pair 14:112, the first number 14 is divided by 2 to get 7, and 1 is added to this quotient to get 8. Multiplying the original number 14 by 8 gives 112. Applying this same mathematical pattern to the third number 18, we divide 18 by 2 to get 9, and add 1 to get 10. Multiplying the original number 18 by 10 results in 180. This logic can also be represented as (x²)/(2) + x, where calculating for 18 gives (18²)/(2) + 18 = ³²⁴⁄₂ + 18 = 162 + 18 = 180.

Explanation

Pint is a unit of volume or liquid capacity used in the imperial and United States customary systems. It is the odd one out because the other terms in the group are all units of currency used for financial transactions in various countries or regions. While the others denote monetary value, a pint is a physical measurement of quantity.

Explanation

The relationship between the words in the given pair is that of energy source and the machine that consumes it. A television is an electronic device that requires electricity to function and operate. Similarly, a car is a mechanical vehicle that requires petrol as a fuel source to provide the necessary energy for its engine to run.

Explanation

The given series is a geometric progression where each term is twice the value of the previous term. This relationship is defined by a constant multiplier of 2, often referred to as the common ratio in a geometric sequence. Starting with the first term, the second term is calculated as 13 × 2 = 26. Continuing this consistent multiplication pattern, the third term is 26 × 2 = 52, and the fourth term is 52 × 2 = 104. To find the value that replaces the question mark, we apply the same rule of doubling the preceding value. By calculating 104 × 2, we arrive at 208.

Explanation

Let the amounts with Priya, Kavya, Gaurvi, and Shalini be P, K, G, and S respectively. From the problem, we have the following equations:

1. S + K + G = 840
2. S + K = 550
3. P + 88 = G
4. G + 25 = K

By substituting the second equation into the first, we can find the amount Gaurvi has: (S + K) + G = 840 550 + G = 840 G = 840 - 550 = 290

Now, using the third equation which relates Priya's and Gaurvi's amounts: P + 88 = G P + 88 = 290 P = 290 - 88 = 202

Thus, Priya has ₹202. While the fourth equation can be used to find K = 315 and then S = 235, these steps are not required to determine the amount with Priya.

Explanation

The pattern in the given matrix is established by a vertical relationship between the numbers in the second and third rows. Each number in the third row is calculated by multiplying the corresponding number in the second row by 4 and then subtracting 2.

For the first column: 5 × 4 - 2 = 20 - 2 = 18

For the third column: 60 × 4 - 2 = 240 - 2 = 238

Following the same logic for the second column, let the missing number be x: 32 × 4 - 2 = x 128 - 2 = 126

Explanation

The words are arranged by comparing each letter from left to right according to the English alphabet. All five words begin with the prefix Ill. Comparing the fifth letter of each word, Illegality (2), Illegible (5), and Illegitimate (1) start with the letter g, which precedes i in Illiterate (4) and u in Illuminate (3). Within the first group, Illegality (2) comes first because its sixth letter is a, which precedes the letter i found in both Illegible and Illegitimate. Between Illegible (5) and Illegitimate (1), the eighth letter b in Illegible comes before the eighth letter t in Illegitimate, establishing the sequence 2, 5, 1. Finally, comparing Illiterate (4) and Illuminate (3), the fifth letter i in Illiterate precedes the fifth letter u in Illuminate. This results in the complete dictionary order 2, 5, 1, 4, 3.

Explanation

The relationship can be decoded by breaking down the statement from Anuj's perspective. Anuj's mother is Vinita. The expression mother's father's son refers to Vinita's brother. The brother of this son is also Vinita's brother. Sumit is identified as the son of this brother. Since Sumit is the son of Vinita's brother, Vinita is the sister of Sumit's father. This establishes that Vinita is Sumit's father's sister.

Explanation

The relationship established in the first pair is gender-based, where a Hen is the female bird and a Rooster is the corresponding male bird. Applying this same logic to the second pair, a Duck refers to the female of the species, while a Drake is the specific term for the adult male duck.

Explanation

The relationship followed by the similar pairs is y = 3x - 10, where x is the first number and y is the second number. In the pair 68:196, the calculation 68 × 3 - 10 = 194 does not yield 196. Instead, this pair follows the logic 68 × 3 - 8 = 196, making it different from the others which consistently subtract 10 from three times the first number.

Explanation

The series progresses by incrementing pairs of consecutive letters by one position in the English alphabet (+1), moving from left to right through the word. In the first step, the first and second letters (C and U) of CUPBOARD are changed to D and V, resulting in DVPBOARD. In the second step, the third and fourth letters (P and B) of DVPBOARD are changed to Q and C, resulting in DVQCOARD. To find the missing term, the pattern is applied to the fifth and sixth letters of DVQCOARD. Incrementing O and A by one position yields P and B, while the other characters remain unchanged, resulting in DVQCPBRD. This logic is confirmed by the final transition where the seventh and eighth letters (R and D) are incremented to S and E to arrive at the term DVQCPBSE.

Explanation

The statement All extroverts are ambiverts establishes that the set of extroverts is a subset of the set of ambiverts. In formal logic, a universal affirmative statement (All A are B) can be converted into a particular affirmative statement (Some B are A). This ensures that the intersection between ambiverts and extroverts is non-empty, making conclusion III logically valid.

Conclusions I and II do not follow because the statements only exclude introverts from the extrovert group; they do not provide information regarding the relationship between introverts and the larger category of ambiverts. An introvert cannot be an extrovert, but there is no information preventing an introvert from being an ambivert. Conclusion IV is invalid because the universal relationship is one-way; while all extroverts are ambiverts, the statements do not establish that every ambivert must be an extrovert. Therefore, only conclusion III is a necessary consequence of the given statements.

Explanation

The coding logic follows two specific steps. First, the letters of the given word are arranged in ascending alphabetical order. Second, numerical transformations are applied based on whether a letter is a vowel or a consonant.

For vowels (A, E, I, O, U), the code is the reverse alphabetical positional value, calculated as 27 - original position. For consonants, the code is double the alphabetical positional value, calculated as 2 × original position.

In the word LIBERTY, the alphabetical arrangement is B, E, I, L, R, T, Y. B (Consonant, position 2): 2 × 2 = 4 E (Vowel, position 5): 27 - 5 = 22 I (Vowel, position 9): 27 - 9 = 18 L (Consonant, position 12): 2 × 12 = 24 R (Consonant, position 18): 2 × 18 = 36 T (Consonant, position 20): 2 × 20 = 40 Y (Consonant, position 25): 2 × 25 = 50 Combining these results in the code 4221824364050.

Applying this logic to the word SLAVERY, the alphabetical order is A, E, L, R, S, V, Y. A (Vowel, position 1): 27 - 1 = 26 E (Vowel, position 5): 27 - 5 = 22 L (Consonant, position 12): 2 × 12 = 24 R (Consonant, position 18): 2 × 18 = 36 S (Consonant, position 19): 2 × 19 = 38 V (Consonant, position 22): 2 × 22 = 44 Y (Consonant, position 25): 2 × 25 = 50

Concatenating these values results in the final code 26222436384450.

Explanation

The series is composed of 21 characters, which can be divided into three equal groups of 7 characters each. By placing the letters c, m, k, b, d, e, d sequentially into the blanks, the series follows a specific structural pattern:

Group 1: b c e m d k k Group 2: c e m b k k b Group 3: d c e m d k k

In this arrangement, the triplet c-e-m and the doublet k-k act as fixed anchors within each group. The first and third groups follow a similar structure where the triplet c-e-m is preceded by a variable letter (b in Group 1, d in Group 3) and followed by the letter d and the doublet k-k. The second group rearranges these elements, placing the triplet c-e-m at the beginning, followed by b, the doublet k-k, and ending with b. This creates a rhythmic repetition of the letter clusters across the 21-character sequence.

Explanation

The given condition is expressed by the equation 0.03A + 0.06B = ⅘ (0.04A + 0.06B). Multiplying the entire equation by 100 to simplify the percentages results in 3A + 6B = ⅘ (4A + 6B). To eliminate the fraction, multiply both sides by 5, yielding 15A + 30B = 16A + 24B.

By rearranging the terms, we subtract 15A from both sides and 24B from both sides: 30B - 24B = 16A - 15A 6B = A

The ratio of A to B is therefore 6:1. Using this relationship, the required ratio of A + B to A - B is calculated by substituting A = 6B: (A + B)/(A - B) = (6B + B)/(6B - B) = (7B)/(5B) = ⁷⁄₅ This results in the ratio 7:5.

Explanation

The relationship in the first pair is based on a tool and the surface or object it is used upon. Toothpaste is a substance used for cleaning and maintaining teeth. Similarly, a broom is a tool specifically designed for sweeping and cleaning the floor. The second word in each pair represents the physical surface that the first word acts upon.

Explanation

The series follows a consistent pattern for each position of the letters within the clusters based on their numerical values in the English alphabet (A=1, B=2, ..., Z=26).

For the first letter of each cluster, there is an increment of 1: P (16) + 1 = Q (17), Q (17) + 1 = R (18), R (18) + 1 = S (19). The next letter is S (19) + 1 = T (20).

For the second letter of each cluster, there is a decrement of 3: N (14) - 3 = K (11), K (11) - 3 = H (8), H (8) - 3 = E (5). The next letter is E (5) - 3 = B (2).

For the third letter of each cluster, there is an increment of 5: D (4) + 5 = I (9), I (9) + 5 = N (14), N (14) + 5 = S (19). The next letter is S (19) + 5 = X (24).

Combining these results, the next cluster in the series is TBX.

Explanation

The alphabetical positions of the letters in the cluster GIEY are G(7), I(9), E(5), and Y(25). The common logic for these clusters follows a sequential pattern of +2, -4, and +6. In GIEY, the transitions are 7 + 2 = 9 and 9 - 4 = 5. However, the final transition in this cluster is 5 + 20 = 25, whereas the consistent pattern requires 5 + 6 = 11, which corresponds to the letter K.

Explanation

The coding logic involves adding 3 and 2 alternately to the positional values of the letters in the English alphabet.

For the word PAWAN: P (16) + 3 = S (19) A (1) + 2 = C (3) W (23) + 3 = Z (26) A (1) + 2 = C (3) N (14) + 3 = Q (17)

For the word SOHAM: S (19) + 3 = V (22) O (15) + 2 = Q (17) H (8) + 3 = K (11) A (1) + 2 = C (3) M (13) + 3 = P (16)

Applying the same +3, +2, +3, +2, +3 pattern to KIRAN: K (11) + 3 = N (14) I (9) + 2 = K (11) R (18) + 3 = U (21) A (1) + 2 = C (3) N (14) + 3 = Q (17)

This gives the sequence NKUCQ.

Explanation

The series follows a pattern based on adding specific values to each preceding term. The differences between consecutive terms are as follows:

13 - 11 = 2 19 - 13 = 6 49 - 19 = 30 109 - 49 = 60 239 - 109 = 130

The logic for these differences is n³ + n for odd positions and n³ - n for even positions in the difference sequence:

1³ + 1 = 2 2³ - 2 = 6 3³ + 3 = 30 4³ - 4 = 60 5³ + 5 = 130

Following this pattern, the next difference is 6³ - 6, which equals 216 - 6 = 210. Adding this difference to the last term of the series, we get 239 + 210 = 449.

Explanation

By substituting the signs sequentially into the given equation, the expression becomes 25 × 7 + 40 - 20 ÷ 4 = 210. Applying the BODMAS rule, which dictates the order of operations as Division, Multiplication, Addition, and Subtraction, the calculation is performed as follows:

First, perform the division operation: 20 ÷ 4 = 5. The equation is now 25 × 7 + 40 - 5 = 210.

Next, perform the multiplication: 25 × 7 = 175. The equation becomes 175 + 40 - 5 = 210.

Then, perform the addition: 175 + 40 = 215. The equation becomes 215 - 5 = 210.

Finally, perform the subtraction: 215 - 5 = 210.

This results in 210 = 210, confirming that the combination of signs in option (a) correctly balances the equation.

Explanation

The numbers in the given set (63, 76, 46) follow a specific arithmetic pattern where the difference between the second and first number is 13 (76 - 63 = 13) and the difference between the second and third number is 30 (76 - 46 = 30). In option c, the set (69, 84, 52) fails to maintain this relationship. Calculating the differences for this set yields 84 - 69 = 15 and 84 - 52 = 32. Since these differences are 15 and 32 respectively, rather than the required 13 and 30, this set does not share the same logic as the original group.

Explanation

To arrange words in dictionary order, they must be compared letter by letter from left to right. All five words begin with the prefix Se. Comparing the third letters, Sensational, Sensitize, Sentiment, and Sentence contain n, whereas September contains p. As n precedes p in the alphabet, September (4) is the final word in the sequence.

Among the words starting with Sen, the fourth letters are s for Sensational (1) and Sensitize (2), and t for Sentiment (3) and Sentence (5). Since s precedes t, words 1 and 2 must come before 3 and 5. Comparing the fifth letters of Sensational (a) and Sensitize (i) shows that a comes before i, placing Sensational (1) first and Sensitize (2) second.

Next, comparing the fifth letters of Sentence (e) and Sentiment (i), e appears before i in the alphabet, meaning Sentence (5) comes before Sentiment (3). Combining these steps, the complete dictionary order is 1, 2, 5, 3, 4.

Explanation

The given series contains 20 elements. To find the underlying pattern, the series can be divided into four groups of five letters each. By observing the recurring letters, it is evident that the pattern consists of the five-letter sequence GPCTD repeating four times.

The series is structured as follows: G _ C T _ / G P _ T _ / G P C _ D / _ P C _ D

When the letters from the sequence P, D, C, D, T, G, T are placed sequentially into the blanks: The first group G _ C T _ becomes GPCTD by filling P and D. The second group G P _ T _ becomes GPCTD by filling C and D. The third group G P C _ D becomes GPCTD by filling T. The fourth group _ P C _ D becomes GPCTD by filling G and T.

This results in the completed uniform series: GPCTD GPCTD GPCTD GPCTD. The sequence of letters inserted into the blanks is P, D, C, D, T, G, T.

Explanation

The relationship between S and N is determined by decoding the symbols in the expression H > R S @ T > N. According to the given definitions, S @ T means that S is the son of T. Furthermore, the notation T > N means that T is the daughter of N. By combining these two relations, S is identified as the son of T, and T is identified as the daughter of N. Since S is the son of N's daughter, S is the grandson of N.

Explanation

The numbers in the set (a, b, c) follow the logic b = 2 × (a² + c³).

For the given set (4, 282, 5): a = 4 c = 5 b = 2 × (4² + 5³) b = 2 × (16 + 125) b = 2 × 141 = 282

Similarly, for option a) (7, 152, 3): a = 7 c = 3 b = 2 × (7² + 3³) b = 2 × (49 + 27) b = 2 × 76 = 152

Explanation

The relationship between the words Help and Hinder is that of antonyms, as helping involves assisting or making an action easier, while hindering involves creating an obstacle or delay. Similarly, Indigent and Rich are antonyms. Indigent refers to a person who is extremely poor or lacking necessities, which is the direct opposite of Rich, which describes someone possessing great wealth or resources.

Explanation

The relationship between the numbers is based on the ratio 3:7. In the first pair, the numbers are multiples of 13, where 39 = 13 × 3 and 91 = 13 × 7. Applying this same logic to the third number, 51 is 17 × 3. Therefore, the missing number must be 17 × 7, which equals 119.

Explanation

The logic followed by the similar number pairs is that the second number is calculated by multiplying the first number by 4 and then subtracting 8. Using the formula y = (x × 4) - 8, where x represents the first number and y represents the second number, the calculations for the other pairs are (19 × 4) - 8 = 76 - 8 = 68, (17 × 4) - 8 = 68 - 8 = 60, and (23 × 4) - 8 = 92 - 8 = 84.

The pair 13:90 is different because it does not satisfy this arithmetic pattern. When the same formula is applied to the first number 13, the result is (13 × 4) - 8 = 52 - 8 = 44, which does not equal 90. Therefore, this pair deviates from the consistent mathematical relationship shared by the others.

Explanation

The coding logic follows a two-step process: first, calculate the sum of the reverse positional values of the letters (where A=26, B=25, ..., Z=1), and then multiply this sum by the number of consonants in the word.

For LOWER: Reverse positional values: L=15, O=12, W=4, E=22, R=9 Sum = 15 + 12 + 4 + 22 + 9 = 62 Number of consonants (L, W, R) = 3 Code = 62 × 3 = 186

For MULISH: Reverse positional values: M=14, U=6, L=15, I=18, S=8, H=19 Sum = 14 + 6 + 15 + 18 + 8 + 19 = 80 Number of consonants (M, L, S, H) = 4 Code = 80 × 4 = 320

Applying the same logic to OPTIONAL: Reverse positional values: O=12, P=11, T=7, I=18, O=12, N=13, A=26, L=15 Sum = 12 + 11 + 7 + 18 + 12 + 13 + 26 + 15 = 114 Number of consonants (P, T, N, L) = 4 Code = 114 × 4 = 456

Explanation

The coding logic follows a specific pattern of adding values to the numerical position of each letter in the alphabet (A=1, B=2, ..., Z=26).

For LOAD: L (12) + 15 = 27 O (15) + 9 = 24 A (1) + 15 = 16 D (4) + 9 = 13 Pattern: The letters are coded by alternating between adding 15 and 9 to their respective alphabetical positions.

For CLEAN: C (3) + 24 = 27 L (12) + 13 = 25 E (5) + 18 = 23 A (1) + 15 = 16 N (14) + 0 = 14 Pattern: The letters are coded by adding specific values that result in the sequence 27, 25, 23, 16, 14.

For STRIKE: Applying the identified numerical values for each letter: S is the 19th letter. 19 + 4 = 23 T is the 20th letter. 20 - 1 = 19 R is the 18th letter. 18 - 1 = 17 I is the 9th letter. 9 + 1 = 10 K is the 11th letter. 11 - 2 = 9 E is the 5th letter. 5 + 3 = 8

Combining these results gives the code 2319171098.

Explanation

The letter-clusters in the series follow a specific mathematical pattern based on the alphabetical positions of their constituents.

For the first letter of each cluster, there is a constant subtraction of 2: Z(26) - 2 = X(24); X(24) - 2 = V(22); V(22) - 2 = T(20); T(20) - 2 = R(18). The next letter in the sequence is 18 - 2 = 16, which is P.

For the second letter, there is a constant subtraction of 4: V(22) - 4 = R(18); R(18) - 4 = N(14); N(14) - 4 = J(10); J(10) - 4 = F(6). The next letter in the sequence is 6 - 4 = 2, which is B.

For the third letter, there is a constant addition of 2: G(7) + 2 = I(9); I(9) + 2 = K(11); K(11) + 2 = M(13); M(13) + 2 = O(15). The next letter in the sequence is 15 + 2 = 17, which is Q.

Assembling these components, the cluster that replaces the question mark is PBQ.

Explanation

Hariprasad Chaurasiya is an internationally acclaimed Indian classical flautist who plays the Bansuri, a side-blown bamboo flute. Much like Zakir Hussain is a preeminent maestro and virtuoso of the Tabla, Pandit Hariprasad Chaurasiya is the most prominent figure associated with the flute in the Hindustani classical music tradition, having received prestigious honors such as the Padma Vibhushan for his contributions to the arts.

Explanation

The relationship between the sets can be understood through logical containment. Since all pilots are ministers and all ministers are politicians, the set of pilots is a subset of ministers, which is in turn a subset of politicians (Pilots ⊂ Ministers ⊂ Politicians). Conclusion I is valid because the statement all pilots are ministers implies that the intersection of ministers and pilots contains at least the pilots themselves, meaning some ministers are pilots.

The third statement specifies that no engineer is a politician, meaning the sets of engineers and politicians are disjoint. Since the set of ministers is entirely contained within the set of politicians, and no engineer is a politician, it follows that no engineer can be a minister, validating Conclusion II. Furthermore, because the set of pilots is entirely contained within the set of ministers, the exclusion of engineers from ministers necessitates that no engineer is a pilot, validating Conclusion III. Thus, all conclusions follow logically from the premises.

Explanation

The series follows a pattern where each term is derived from the previous term using the formula Tₙ = Tₙ₋₁{2} + k, where the value of k decreases by 1 for every subsequent step.

For the second term: ²⁸⁄₂ + 4 = 14 + 4 = 18

For the third term: ¹⁸⁄₂ + 3 = 9 + 3 = 12

For the fourth term: ¹²⁄₂ + 2 = 6 + 2 = 8

To find the missing number, we continue the pattern by dividing the fourth term by 2 and adding the next constant in the decreasing sequence, which is 1. The calculation is ⁸⁄₂ + 1 = 4 + 1 = 5.

Explanation

By applying the signs from option a in the sequence provided, the expression follows the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction):

252 ÷ 14 × 8 - 100 + 16 = 60

First, perform the division: 252 ÷ 14 = 18

Next, perform the multiplication: 18 × 8 = 144

Then, perform the addition and subtraction: 144 - 100 + 16 = 44 + 16 = 60

Since the left-hand side equals the right-hand side (60 = 60), the equation is balanced.

Explanation

Gallop is a term used to describe a specific mode of animal locomotion or a fast gait, most commonly associated with horses. While the other three words represent the characteristic vocalizations or sounds emitted by various animals, gallop refers to the physical action of movement.

Explanation

The numbers in the set (3, 6, 63) follow the mathematical logic a³ + b² = c, where a is the first number, b is the second number, and c is the third number. Substituting the values from the given set, we get 3³ + 6² = 27 + 36 = 63.

Applying this same relationship to the set in option d, which consists of (4, 5, 89), we use the first two numbers as a and b to calculate the third number: 4³ + 5² = 64 + 25 = 89. The result matches the third number of the set, confirming that it follows the same pattern as the original set.

Explanation

The relationship in the given analogy is based on collective nouns for groups of animals. Just as a group of bats is called a colony, the standard term used to describe a social group of lions is a pride. This collective term specifically identifies their unique social structure, which typically consists of several related females, their dependent offspring, and a small number of adult males.

Explanation

Dictionary order is determined by comparing letters of each word sequentially from left to right. All words start with S. Comparing the second letters, i in Singular (3) and Sinuous (1) precedes o in the remaining words. Between Singular and Sinuous, both share the prefix Sin, but g in Singular comes before u in Sinuous, making the order 3, 1. Next, comparing the words starting with So, namely Solemnity (2), Solvable (4), and Sorting (5), the third letters l in Solemnity and Solvable precede r in Sorting. Between Solemnity and Solvable, the fourth letter e in Solemnity precedes v in Solvable, placing them in the order 2, 4. Finally, Sorting (5) follows because r comes after l. This yields the complete sequence 3, 1, 2, 4, 5.

Explanation

The coding logic follows a pattern where the letters of the word are divided into pairs, the positions of the letters within each pair are swapped, and then each letter is moved forward by one position in the English alphabetical series.

For the word TRAVEL: The pairs are (T, R), (A, V), and (E, L). Swapping the first pair (T, R) gives (R, T). Adding 1 to each: R + 1 = S, T + 1 = U. Swapping the second pair (A, V) gives (V, A). Adding 1 to each: V + 1 = W, A + 1 = B. Swapping the third pair (E, L) gives (L, E). Adding 1 to each: L + 1 = M, E + 1 = F. Combining these results gives the code SUWBMF.

Applying the same logic to the word FROZEN: The pairs are (F, R), (O, Z), and (E, N). Swapping the first pair (F, R) gives (R, F). Adding 1 to each: R + 1 = S, F + 1 = G. Swapping the second pair (O, Z) gives (Z, O). Adding 1 to each: Z + 1 = A, O + 1 = P. Swapping the third pair (E, N) gives (N, E). Adding 1 to each: N + 1 = O, E + 1 = F. Combining these results gives the code SGAPOF.

Explanation

The numbers in the given set (4, 532, 10) follow the logic where the second number is half the sum of the cubes of the first and third numbers. The relationship is defined by the formula b = (a³ + c³)/(2). Substituting the values a = 4 and c = 10 from the set results in:

b = (4³ + 10³)/(2) = (64 + 1000)/(2) = ¹⁰⁶⁴⁄₂ = 532

Applying this same logic to the set (4, 140, 6), where a = 4 and c = 6, we get:

b = (4³ + 6³)/(2) = (64 + 216)/(2) = ²⁸⁰⁄₂ = 140

The calculation yields 140, which is the middle term of the set.

Explanation

The age of the 9th person, who is the overlapping individual in both subgroups, is determined by calculating the difference between the combined sum of the subgroups and the total sum of the entire group.

Total sum of ages of 17 persons = 17 × 39 = 663 years. Sum of ages of the first 9 persons = 9 × 35 = 315 years. Sum of ages of the last 9 persons = 9 × 44 = 396 years.

Since the 9th person is counted twice in the subgroup sums, their age is: Age of 9th person = (Sum of first 9 + Sum of last 9) - Total sum of 17 persons Age of 9th person = (315 + 396) - 663 = 711 - 663 = 48 years.

Using the deviation method, the first 9 persons have a deviation of -4 each from the total average (35 - 39), and the last 9 persons have a deviation of +5 each (44 - 39). The net deviation is 9 × (-4) + 9 × 5 = -36 + 45 = +9. Adding this net deviation to the group average yields 39 + 9 = 48 years.

Explanation

The letter-cluster WYBY is different because it fails to satisfy the uniform pattern applied to the others. The consistent logic involves three steps: the second letter is two positions ahead of the first (L₂ = L₁ + 2), the second and third letters are alphabetical opposites whose numerical positions sum to 27, and the fourth letter is five positions behind the third (L₄ = L₃ - 5).

In WYBY, the first letter W (23) increases by 2 to reach Y (25), and Y (25) correctly pairs with its alphabetical opposite B (2). However, the final transition from the third letter B (which can be treated as 28 in a cyclic sequence) to the fourth letter Y (25) involves a subtraction of only 3 (28 - 25 = 3). Following the established rule of subtracting 5, the fourth letter should have been W (23), making this cluster the odd one out.

Explanation

The numerical relationship followed in the other pairs is that the second number is exactly twice the square of the first number, represented by the formula y = 2x². For the pair 19:622, substituting x = 19 into the formula yields y = 2 × 19² = 2 × 361 = 722. Since the second number provided in this pair is 622 rather than 722, it does not satisfy the mathematical logic shared by the remaining sets, where 2 × 12² = 288, 2 × 14² = 392, and 2 × 11² = 242.