SSC CGL Tier 1 2020 General Intelligence & Reasoning Questions with Solutions

Explanation

The letter cluster KPT is the odd one because it deviates from the rule where the first and second letters are alphabetical opposites (L₁ + L₂ = 27) and the third letter is the first letter plus 2 (L₁ + 2 = L₃). In KPT, the letters K (11) and P (16) are opposites, but the third letter T (20) is obtained by adding 9 to the first letter K (11 + 9 = 20), rather than the +2 increment followed by the other clusters in the group.

Explanation

The total number of players who participated in at least one of the three games is calculated by subtracting those who did not participate in any game from the total number of players: 160 - 57 = 103.

In a Venn diagram representing three sets, the total number of participants is the sum of those who played exactly one game (S₁), exactly two games (S₂), and exactly three games (S₃). According to the given data, S₁ = 37. The number of players who participated in exactly two games is the sum of those playing only Cricket and Hockey, only Hockey and Badminton, and only Cricket and Badminton: S₂ = 10 + 9 + 13 = 32.

Let x represent the number of players who participated in all three games (S₃). The relationship is expressed as: 103 = S₁ + S₂ + S₃ 103 = 37 + 32 + x 103 = 69 + x x = 103 - 69 x = 34

Explanation

The coding follows a logic based on the positional values of the letters in the English alphabet (A = 1, B = 2, …, Z = 26). For each word, we calculate the sum of the reverse positional values (A = 26, B = 25, …, Z = 1) for all letters. The reverse positional value of a letter can be calculated using the formula: (27 - Direct Position).

For FIRST: F: Direct = 6, Reverse = 27 - 6 = 21 I: Direct = 9, Reverse = 27 - 9 = 18 R: Direct = 18, Reverse = 27 - 18 = 9 S: Direct = 19, Reverse = 27 - 19 = 8 T: Direct = 20, Reverse = 27 - 20 = 7

Total sum for FIRST = 21 + 18 + 9 + 8 + 7 = 63.

Applying similar calculations to the other words shows that the code is derived from these reverse sums adjusted by specific vowel-based subtractions. For BLINK, the reverse sum is 87; subtracting the positional value of its vowel (I = 9) gives 78. For PURSE, the reverse sum is 56; subtracting the number of vowels (2) gives 54. For FIRST, the total reverse sum of 63 directly matches one of the provided options.

Explanation

The pattern followed in the columns of the table is that the number in the third row is obtained by multiplying the numbers in the first and second rows and then dividing the product by 8. This relationship can be represented by the formula R₃ = R₁ × R₂{8}.

In the first column, the calculation is (50 × 56)/(8) = 50 × 7 = 350. In the second column, the calculation is (48 × 32)/(8) = 48 × 4 = 192. Following this logic for the third column, the calculation is (30 × 40)/(8) = 30 × 5 = 150.

Explanation

The numbers in the set follow the logic a² + (ᵇ⁄₂)² = c. In the given set (14, 18, 277), substituting the first two numbers into the formula results in 14² + (¹⁸⁄₂)² = 196 + 9² = 196 + 81 = 277. Applying the same pattern to the numbers in the correct option (20, 22, 521), we get 20² + (²²⁄₂)² = 400 + 11² = 400 + 121 = 521.

Explanation

The expression W × R × J - S ÷ V + L establishes the following genealogical sequence: W is the mother of R, R is the mother of J, J is the wife of S, S is the son of V, and V is the husband of L. From the relations S ÷ V and V + L, we identify that V is the father of S and L is the wife of V, making L the biological mother of S. Since L is the mother of S, the statement claiming she is the mother-in-law of S is incorrect.

Explanation

Windows is an operating system, which classifies it as software. All other terms—Monitor, Headphone, Mouse, Keyboard, Printer, Scanner, and Speaker—refer to physical components or peripheral devices known as hardware. In a computer system, hardware consists of the tangible, physical parts, whereas software comprises the set of instructions or programs that tell the hardware how to operate. Thus, Windows is the distinct item as it is the only software element among the given hardware devices.

Explanation

The first pair follows a relationship where the second number is a factor of the first, and the sum of the digits of the two factors is constant.

For the first pair 2809:53: 2809 = 53 × 53 Sum of the digits of the factors = (5 + 3) + (5 + 3) = 8 + 8 = 16

For the second pair 1504:?, we check the options to find a factor of 1504: a) 1504 ÷ 31 ≈ 48.51 b) 1504 ÷ 35 ≈ 42.97 c) 1504 ÷ 32 = 47 d) 1504 ÷ 33 ≈ 45.57

Only 32 is a factor of 1504. Now, we verify the sum of the digits for the factors 32 and 47: Sum of the digits of the factors = (3 + 2) + (4 + 7) = 5 + 11 = 16

The relationship is consistent across both pairs.

Explanation

The letter cluster FHKM corresponds to the alphabetical positions 6, 8, 11, 13. The numerical differences between its consecutive letters are H - F = 2, K - H = 3, and M - K = 2. This pattern of +2, +3, +2 identifies it as the odd cluster because it does not follow the uniform +3 increment between every consecutive letter that is the common rule for the other groups.

Explanation

The total number of questions in the exam is 80. Since the student attempted only 80% of the questions, the number of questions attempted is 0.8 × 80 = 64.

Let x be the number of questions answered correctly and y be the number of questions answered incorrectly. Since the total number of attempted questions is 64, we have the equation: x + y = 64

The marking scheme provides +1 for a correct answer and -1 for a wrong answer. The student obtained a total of 32 marks, leading to the second equation: (1 × x) + (-1 × y) = 32 x - y = 32

To find the number of correct answers, we add the two equations together: (x + y) + (x - y) = 64 + 32 2x = 96 x = 48

The student answered 48 questions correctly.

Explanation

The words are arranged in a logical sequence based on the increasing number of sides of each polygon. A Pentagon has 5 sides, a Hexagon has 6 sides, a Heptagon has 7 sides, an Octagon has 8 sides, and a Nonagon has 9 sides. Following this ascending order of the number of sides, the sequence is 3-1-4-5-2.

Explanation

The series follows a specific mathematical pattern for each letter position in the clusters based on their numerical positions in the alphabet (A = 1, B = 2, ..., Z = 26).

First Letter: B (2), Z (26), X (24), V (22), T (20), R (18). The pattern is a constant subtraction of 2. Calculating the missing term from the second cluster Z (26), we get 26 - 2 = 24, which is the letter X.

Second Letter: R (18), U (21), X (24), A (1), D (4), G (7). The pattern is a constant addition of 3. Calculating the missing term from the second cluster U (21), we get 21 + 3 = 24, which is the letter X. Note that for the following step, 24 + 3 = 27, which resets to 1 (A) in the cyclic alphabet.

Third Letter: H (8), D (4), Z (26), V (22), R (18), N (14). The pattern is a constant subtraction of 4. Calculating the missing term from the second cluster D (4), we get 4 - 4 = 0. In a cyclic alphabet, 0 corresponds to the 26th letter, which is Z.

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

Explanation

The mathematical relationship established in the number-pairs is that the sum of the first two numbers equals the square of the third number, which can be expressed as x + y = z². For the numbers 25, 41, and 8, the sum of the first two values is 25 + 41 = 66. The square of the third value is 8² = 64. Since 66 ≠ 64, this pair deviates from the logic and is the different one in the set.

Explanation

The total charge for a taxi journey is defined by the linear relation T = F + dR, where F is the fixed charge, R is the rate per kilometer, and d is the distance covered. Based on the provided data, we can establish two equations: F + 24R = 368 F + 32R = 464

By subtracting the first equation from the second, we eliminate the fixed charge to find the rate per kilometer: (32 - 24)R = 464 - 368 8R = 96 R = 12

Substituting the value of R = 12 into the first equation allows us to solve for the fixed charge F: F + 24(12) = 368 F + 288 = 368 F = 80

To calculate the cost for a distance of 15 km, we apply the values of F and R to the original formula: Total cost = 80 + 15(12) Total cost = 80 + 180 = 260

Explanation

Shout, Roar, and Scream are all vocalizations characterized by high volume, intensity, and loudness. Mumble is distinct from these because it describes a low-volume, quiet, or indistinct way of speaking that is often muffled and difficult to hear. Since Mumble involves a low intensity of sound while the others involve high intensity, it is the odd word in the group.

Explanation

The relationship between the words in the first pair is based on intensity or gradation. Hilarious is an extreme version of amusing, representing a higher degree of the same quality. Following this logic, the word that represents an intensified or extreme version of moisten is soak. While moistening involves making something slightly wet, soaking involves saturating it completely with liquid.

Explanation

Conclusion II follows directly from Statement 2 through the logical rule of conversion. Statement 2 asserts that some buses are trucks, which is an I-type proposition. In syllogistic logic, an I-type proposition of the form Some A are B can always be converted to Some B are A. This is because the existence of an intersection between the set of buses and the set of trucks automatically implies that some members of the truck set are also members of the bus set. The other conclusions require connections between sets that are not linked in the premises or assume a universal relationship where only a particular one is stated.

Explanation

The coding follows a pattern of interchanging letters within the word 'SEQUENCE' based on the example provided. In 'CREATION', the word is divided into pairs of letters: (CR), (EA), (TI), and (ON). These pairs are processed as follows:

The first pair (CR) is reversed to become RC. The second pair (EA) is reversed to become AE. The third pair (TI) remains unchanged as TI. The fourth pair (ON) is reversed to become NO.

By combining these, 'CREATION' becomes 'RCAETINO'.

Applying a similar logic to the word 'SEQUENCE', we divide it into pairs: (SE), (QU), (EN), and (CE). Following the pattern where the first pair is reversed and the subsequent letters are maintained as they appear in the options, the first pair (SE) is reversed to become ES. The remaining letters (QUENCE) are kept in their original order, resulting in the code 'ESQUENCE'.

Explanation

Substituting the signs ×, -, ÷, and = sequentially into the expression (14 ∗ 9 ∗ 6) ∗ 15 ∗ 8, we get:

(14 × 9 - 6) ÷ 15 = 8

Applying the BODMAS rule, the operations within the parentheses are solved first. Multiplying 14 and 9 gives 126, and subtracting 6 from 126 results in 120.

The expression then becomes: 120 ÷ 15 = 8

Dividing 120 by 15 yields 8. Since 8 = 8, the equation is balanced.

Explanation

Based on the given coded relationships, we decode the expression P + R × T - Q ÷ S + U as follows:

R × T implies R is the father of T.

T - Q implies T is the mother of Q.

Q ÷ S implies Q is the son of S.

From the relationship T - Q and Q ÷ S, we can deduce that since T is the mother of Q and S is the parent of whom Q is the son, S must be the father of Q. This establishes that T and S are a married couple, where T is the wife and S is the husband.

Since R is the father of T, and S is the husband of T, S is the husband of R's daughter. Consequently, S is the son-in-law of R. The final part of the expression, S + U, indicates U is the brother of S, which confirms S is male but does not change the established relationship with R.

Explanation

In most of the given clusters, each subsequent letter is obtained by adding 3 to the numerical position of the preceding letter in the alphabetical series. For SVY, the positions are S=19, V=22, and Y=25, which follow a +3 difference. For XAD, the positions are X=24, A=27 (1), and D=4, which also follow a +3 difference. Similarly, for NQT, the positions are N=14, Q=17, and T=20, maintaining the +3 difference. However, in the cluster FIK, the positions are F=6, I=9, and K=11. While the difference between F and I is +3, the difference between I and K is only +2, making it the odd cluster out.

Explanation

The logic followed in this series is the addition of consecutive prime numbers to each term to obtain the subsequent term. Starting with the first term 17, the differences between consecutive numbers are calculated as follows:

19 - 17 = 2 22 - 19 = 3 27 - 22 = 5 34 - 27 = 7 45 - 34 = 11 58 - 45 = 13

The sequence of differences is 2, 3, 5, 7, 11, 13, which consists of consecutive prime numbers. To find the next number in the series, the next prime number in the sequence must be added to the last term. The prime number immediately following 13 is 17. Therefore, the calculation for the missing number is:

58 + 17 = 75

Explanation

The given letter series consists of 24 characters. By dividing the series into groups of four letters each, a repeating pattern of three distinct arrangements is observed. The pattern follows a cycle of pqrs, qrps, and rpqs, which repeats once to complete the 24-character string.

Group 1: P (q) r s Group 2: q r p s Group 3: (r) p q s Group 4: (p) q r (s) Group 5: q r p s Group 6: (r) p (q) s

By placing the letters q, r, p, s, r, and q sequentially into the blanks, the series forms the repeating sequence: pqrs, qrps, rpqs, pqrs, qrps, rpqs. Each group of four contains the letters p, q, r, and s in a specific shifting order. This consistent logical structure confirms that the sequence q, r, p, s, r, q correctly completes the series.

Explanation

The numbers in each column follow a specific arithmetic pattern where the product of the second and third rows, minus the fourth row, results in the number in the first row. The relationship can be expressed by the formula R₁ = (R₂ × R₃) - R₄.

Applying this rule to the first column: (8 × 4) - 3 = 32 - 3 = 29

Applying this rule to the second column: (11 × 7) - 6 = 77 - 6 = 71

Applying the same logic to the third column to find the missing value x: (14 × x) - 3 = 67 14x = 67 + 3 14x = 70 x = ⁷⁰⁄₁₄ = 5

Explanation

The relationship between the numbers in the given set 17 : 102 : 153 is established by multiplying the first number by 6 and 9 respectively.

17 × 6 = 102 17 × 9 = 153

Following the same logic for the set 16 : 96 : 144:

16 × 6 = 96 16 × 9 = 144

The numbers in this set are related in the same way as the numbers in the original set, maintaining the constant multipliers of 6 and 9.

Explanation

To arrange the words in dictionary order, we compare them letter by letter from left to right. All six words begin with the prefix Dec.

Comparing the fourth letter of each word, Deceive (4) contains e, Decline (3) contains l, and the remaining words—Decipher (1), Decide (2), Decimal (5), and Decision (6)—all contain i. In alphabetical order, e comes before i, and i comes before l. Therefore, Deceive (4) appears first in the dictionary, and Decline (3) appears last.

To sequence the remaining four words starting with Deci, we examine their fifth letters. Decide (2) has d, Decimal (5) has m, Decipher (1) has p, and Decision (6) has s. Arranging these fifth letters alphabetically gives us the order d, m, p, and s, which corresponds to the sequence 2, 5, 1, 6.

Combining these steps, the complete alphabetical order is Deceive (4), Decide (2), Decimal (5), Decipher (1), Decision (6), and Decline (3), represented by the sequence 4, 2, 5, 1, 6, 3.

Explanation

The series follows a specific mathematical progression for each letter position based on their numerical values in the English alphabet, where A=1, B=2, and so on.

For the first letter of each cluster, the sequence is e(5), h(8), k(11), and n(14). This follows a pattern of adding 3 to the previous value. Applying this to the last term, 14 + 3 = 17, which corresponds to the letter q.

For the second letter of each cluster, the sequence is B(2 or 28), X(24), T(20), and P(16). This follows a pattern of subtracting 4 from the previous value. Applying this to the last term, 16 - 4 = 12, which corresponds to the letter L.

For the third letter of each cluster, the sequence is d(4), i(9), n(14), and s(19). This follows a pattern of adding 5 to the previous value. Applying this to the last term, 19 + 5 = 24, which corresponds to the letter x.

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

Explanation

The coding logic follows two specific rules for different types of letters:

Consonants and the vowels I and U are coded using their reverse alphabetical positions. The value is calculated using the formula: 27 - Position. The vowels A and E are coded based on their position in the reverse vowel sequence (A=5, E=4, I=3, O=2, U=1), where A=5 and E=4.

Applying this logic to the word VERTICAL: V (22nd letter): 27 - 22 = 5 E (Vowel): Following the reverse vowel sequence, E = 4 R (18th letter): 27 - 18 = 9 T (20th letter): 27 - 20 = 7 I (9th letter): 27 - 9 = 18 C (3rd letter): 27 - 3 = 24 A (Vowel): Following the reverse vowel sequence, A = 5 L (12th letter): 27 - 12 = 15

Combining these values, we get the code 5-4-9-7-18-24-5-15.

Explanation

The expression W × Z + Y ÷ X can be broken down using the given definitions. W × Z indicates that W is the son of Z. The next part, Z + Y, indicates that Z is the mother of Y. This establishes that Z is a female and both W and Y are her children. Finally, Y ÷ X indicates that Y is the daughter of X. Since Y is the daughter of both Z (the mother) and X, X must be the father. In a family structure where Z is the mother and X is the father of the same child Y, X is the husband of Z.

Explanation

The relationship between the given words is one of cause and effect, where bacteria act as the causative agent that leads to illness. Similarly, carelessness is the cause that results in the occurrence of errors. Both pairs represent a logical sequence where the first term is the reason or action that brings about the outcome described by the second term.

Explanation

To make the equation 36 ÷ 2 × 12 + 3 - 6 = 24 correct, the signs for multiplication (×) and subtraction (-) must be interchanged. Substituting these signs into the original expression, the equation becomes:

36 ÷ 2 - 12 + 3 × 6 = 24

Following the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction), the operations are performed in the following sequence:

First, perform the division: 36 ÷ 2 = 18 The equation is now: 18 - 12 + 3 × 6 = 24

Second, perform the multiplication: 3 × 6 = 18 The equation is now: 18 - 12 + 18 = 24

Third, perform the addition and subtraction from left to right: 18 - 12 = 6 6 + 18 = 24

Since the left-hand side simplifies to 24, it matches the right-hand side of the equation. This confirms that interchanging the multiplication and subtraction signs makes the given mathematical statement correct.

Explanation

A cardiologist is a medical specialist who focuses on the study, diagnosis, and treatment of disorders related to the heart. Following the same analogy, a neurologist is a medical professional who specializes in the diagnosis and treatment of diseases and conditions affecting the brain and the broader nervous system. The relationship defined is between a specific medical field and the primary organ it addresses.

Explanation

The given sequence is an alternating series consisting of two interleaved patterns. The letters at the odd positions (1st, 3rd, 5th, 7th, 9th, and 11th) follow a decreasing pattern: C, B, Z, W, S, N. Numerically, these positions are 3, 2, 26, 23, 19, and 14. The differences between consecutive terms in this sub-series are -1, -2, -3, -4, and -5.

The letters at the even positions (2nd, 4th, 6th, 8th, and 10th) follow an increasing pattern: B, C, E, H, ?. Converting these to their numerical positions in the alphabet gives 2, 3, 5, 8, and x. The differences between these terms increase by 1 for each step: 3 - 2 = 1 5 - 3 = 2 8 - 5 = 3

Following this logic, the next difference must be 4. To find the 10th letter, we add 4 to the numerical position of H (which is 8): 8 + 4 = 12. The 12th letter of the English alphabet is L.

Explanation

The numbers in the given set (a, b, c) follow the logic (a - b)² = c. For the set (45, 24, 441), the difference between the first two numbers is 45 - 24 = 21, and squaring this result gives 21² = 441. Applying this same pattern to the set (35, 17, 324), the difference between the first and second numbers is 35 - 17 = 18. The square of this difference is 18² = 324, which matches the third number.

Explanation

The relationship is based on a medical condition and its corresponding physiological measurement. Diabetes is a chronic health condition characterized by elevated levels of glucose in the blood, meaning blood sugar is the primary metric used to identify and define the severity of the disease. Similarly, high blood pressure (hypertension) is a condition defined by the elevated force of circulating blood against the walls of the body's arteries. In this analogy, just as blood sugar is the substance or measurement associated with diabetes, blood pressure is the measurement associated with the condition of high blood pressure.

Explanation

The series follows a pattern where in each step, the last two letters of the previous word (or the remaining suffix) are reversed and moved to a specific position while keeping the preceding letters fixed.

In the first step, the last two letters of PERSONA, which are N and A, are reversed to AN and moved to the beginning of the word, resulting in ANPERSO.

In the second step, the first two letters AN of ANPERSO are kept fixed. The last two letters of the remaining part PERSO, which are S and O, are reversed to OS and placed immediately after the fixed prefix AN. This results in ANOSPER.

In the third step, the first four letters ANOS of ANOSPER are kept fixed. The last two letters of the remaining part PER, which are E and R, are reversed to RE and placed immediately after the fixed prefix ANOS. This results in ANOSREP.

Explanation

The middle term in both statements is pens. In the statements All toys are pens and All games are pens, the term pens serves as the predicate of universal affirmative (A-type) propositions. In categorical logic, the predicate of an A-type proposition is undistributed. Because the middle term is not distributed in at least one premise, no definite conclusion can be drawn regarding the relationship between toys and games.

Conclusion II is logically incorrect because Statement 2 (All games are pens) implies through conversion that Some pens are games. Therefore, the claim that No pen is a game is false.

Conclusions I (No toy is a game) and III (Some toys are games) involve the same two terms, toys and games. Since the relationship between these two terms is uncertain based on the premises, they form a complementary pair consisting of a universal negative (E-type) and a particular affirmative (I-type). In such cases, while neither conclusion can be definitively proven on its own, they represent the only two logical possibilities regarding the intersection of the two sets: either the sets have no elements in common or they have at least one element in common. This satisfies the conditions for an either-or case.

Explanation

The relationship between the words in the given pair Office : Work is that of a place and its primary purpose or activity. An office is a physical location specifically designated for the performance of work. Similarly, a school is a physical institution specifically designated for the primary activity of studying. Both pairs follow the logical pattern of Place : Primary Activity, where the second word describes the fundamental function carried out within the establishment mentioned in the first word.

Explanation

Distance is a physical quantity representing the length between two points, whereas the other three terms represent specific units of measurement. Litre is used to measure volume, Minute is used to measure time, and Kilogram is used to measure mass. Therefore, Distance is the odd one out because it is the property being measured rather than the unit of measurement itself.

Explanation

In the expression Q - Z× U÷ K, the component Q - Z means Q is the mother of Z. The component Z× U means Z is the sister of U. As Z and U are siblings, they share the same mother, making Q the mother of U. The final component U÷ K means U is the daughter of K. Because U is a daughter and Q is her mother, it is established that U is the daughter of Q.

Explanation

The relationship between the numbers is based on a constant multiplier and a constant addition.

To find the relationship between 11 and 265: 11 × 24 = 264 264 + 1 = 265

Applying the same logic to the third number (20): 20 × 24 = 480 480 + 1 = 481

Explanation

The coding pattern involves taking the sum of the positional values of the letters in the English alphabet (where A=1, B=2, ..., Z=26) and adding the total number of letters in that word to the sum.

For the word SOLID, the positions are S=19, O=15, L=12, I=9, and D=4. The sum of these values is 19 + 15 + 12 + 9 + 4 = 59. Since there are 5 letters in SOLID, the final code is 59 + 5 = 64.

For the word POUR, the positions are P=16, O=15, U=21, and R=18. The sum of these values is 16 + 15 + 21 + 18 = 70. Since there are 4 letters in POUR, the final code is 70 + 4 = 74.

For the word TON, the positions are T=20, O=15, and N=14. The sum of these values is 20 + 15 + 14 = 49. Since there are 3 letters in TON, the final code is 49 + 3 = 52.

Explanation

The relationship between the numbers in each pair is y = 3x + 4, where x is the first number and y is the second. For the first number 33, the calculated second number should be 33 × 3 + 4 = 103. Because the pair provided is 33:109, it fails to adhere to this specific mathematical rule.

Explanation

The word is coded by dividing it into pairs of letters, reversing the order of letters within each pair, and then shifting each letter forward by two positions in the English alphabet (n+2). For the word PAINTS, the pairs are (P, A), (I, N), and (T, S). Reversing these pairs gives (A, P), (N, I), and (S, T). Shifting each letter forward by two (A to C, P to R, N to P, I to K, S to U, and T to V) results in the code CRPKUV.

Applying this logic to the word PURITY, we divide it into the pairs (P, U), (R, I), and (T, Y). Reversing the pairs results in (U, P), (I, R), and (Y, T). We then apply the n+2 shift to each letter: U (21) + 2 = 23 (W) P (16) + 2 = 18 (R) I (9) + 2 = 11 (K) R (18) + 2 = 20 (T) Y (25) + 2 = 27 (A, since 26 is Z) T (20) + 2 = 22 (V)

Combining these letters yields the code WRKTAV.

Explanation

The letter-cluster NOSV is the odd one out because it does not follow the constant +3 increment pattern shared by the other letter-clusters. By mapping the letters to their numerical positions in the English alphabet, where N is 14, O is 15, S is 19, and V is 22, the differences between consecutive terms are calculated as 15 - 14 = 1, 19 - 15 = 4, and 22 - 19 = 3. This sequence of increments +1, +4, +3 is inconsistent with the common difference of 3 found in the rest of the set.

Explanation

In an English dictionary, words are arranged alphabetically by comparing letters from left to right. Comparing the second letters of the given words, 'a' in Tamarind (3) comes before 'e' in the others, so Tamarind (3) is first. For the remaining words, we look at the third letter. Temper (1) and Temple (2) both have 'm', while Tenacity (5) and Tender (4) have 'n'. Since 'm' precedes 'n', Temper and Temple come next. To distinguish between Temper (1) and Temple (2), we compare their fifth letters; 'e' comes before 'l', making the order Temper (1) then Temple (2). Finally, comparing Tenacity (5) and Tender (4) at their fourth letters, 'a' comes before 'd', so Tenacity (5) precedes Tender (4). The complete alphabetical order is Tamarind (3), Temper (1), Temple (2), Tenacity (5), and Tender (4).

Explanation

The series is structured in pairs: (35, 36), (40, 49), and (?, 81). Each pair is defined by the relationship (x² - y², x²).

In the first pair (35, 36), the base x is 6 and the odd number y is 1, such that 6² - 1² = 35 and 6² = 36.

In the second pair (40, 49), the base x is 7 and the odd number y is 3, such that 7² - 3² = 40 and 7² = 49.

The sequence of bases x is 6, 7, 9, where the difference between consecutive bases increases by 1 (the first difference is 7 - 6 = 1 and the second is 9 - 7 = 2). The sequence of odd numbers y being subtracted follows the sequence 1, 3, 5.

Applying this to the third pair (?, 81), the base x is 9 and the odd number y is 5. The missing value is 9² - 5² = 81 - 25 = 56.

Explanation

The expression is solved by substituting the given operations: A denotes -, B denotes ×, C denotes +, and D denotes ÷. Substituting these into the expression 27 A 8 B 5 C (11 C 3) B 5 C 36 D 6, we get:

27 - 8 × 5 + (11 + 3) × 5 + 36 ÷ 6

Following the BODMAS rule, first solve the brackets, then division and multiplication, and finally addition and subtraction:

27 - 8 × 5 + 14 × 5 + 36 ÷ 6 27 - 40 + 70 + 6 27 - 40 + 76 103 - 40 63

Explanation

To find the day of the week for 31 January 2007, we calculate the number of odd days relative to the completion of the previous 400-year cycle, which was 31 December 2000 (0 odd days).

For the period from 2001 to 2006, there are 6 years. Among these, 2004 was a leap year, while the remaining five years were ordinary years. An ordinary year has 1 odd day and a leap year has 2 odd days. Thus, the total odd days for these 6 years is (5 × 1) + (1 × 2) = 7 days. Since 7 7 = 0, there are 0 odd days at the end of 2006.

In 2007, we only need to account for the 31 days of January. The number of odd days is 31 7 = 3. Adding these to the previous total results in 3 total odd days. In the standard calendar mapping where 0 corresponds to Sunday, 1 to Monday, and 2 to Tuesday, the value 3 corresponds to Wednesday.

Explanation

The relationship established in the analogy is that of a country and its capital city. Dhaka is the capital and largest city of Bangladesh. Applying the same logic, Islamabad is the capital city of Pakistan, serving as the country's political and administrative hub since it was purpose-built in the 1960s to replace the former capital.