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

Explanation

The relationship between the numbers (a, b, c) in each set is defined by the formula:

c = a × (a - b)

For the first set (11, 8, 33): 11 × (11 - 8) = 11 × 3 = 33

For the second set (33, 5, 924): 33 × (33 - 5) = 33 × 28 = 924

Applying this formula to the numbers in option B (24, 15, 216): 24 × (24 - 15) = 24 × 9 = 216

Explanation

The given series of letter clusters follows a specific pattern for each letter position:

First letter: P (16) → Q (17) → R (18) → S (19) → T (20) (increases by 1)

Second letter: U (21) → T (20) → S (19) → R (18) → Q (17) (decreases by 1)

Third letter in alternating (odd-numbered) clusters: C (3) in the 1st cluster → E (5) in the 3rd cluster → G (7) in the 5th cluster (increases by 2)

Fourth letter: H (8) → G (7) → F (6) → E (5) → D (4) (decreases by 1)

Combining these determined letters in their respective positions gives TQGD.

Explanation

The symbols M, N, O, and P represent the following mathematical operations: M represents subtraction (-) N represents division (÷) O represents multiplication (×) P represents addition (+)

Substituting these operators into the given equation: (72 ÷ 9) × 4 - 26 + 97 - (36 ÷ 2)

Applying the BODMAS rule, first solve the operations inside the brackets: 72 ÷ 9 = 8 36 ÷ 2 = 18

This simplifies the expression to: 8 × 4 - 26 + 97 - 18

Next, perform the multiplication: 8 × 4 = 32

This simplifies the expression to: 32 - 26 + 97 - 18

Now, perform the addition and subtraction: 32 - 26 = 6 6 + 97 = 103 103 - 18 = 85

Explanation

The given series is based on the differences between consecutive terms, which increase by 5 at each step in an arithmetic progression.

First term = 7350 Second term = 7350 - 5 = 7345 Third term = 7345 + 0 = 7345 Fourth term = 7345 + 5 = 7350 Fifth term = 7350 + 10 = 7360 Sixth term = 7360 + 15 = 7375

The sequence of difference values is -5, 0, +5, +10, +15.

Explanation

Applying the sequence of signs from this option into the given equation: 3 × 4 × 2 + 10 = 17 × 2

Using the BODMAS rule, we simplify the Left-Hand Side (LHS): 3 × 4 × 2 + 10 = 24 + 10 = 34

Now we simplify the Right-Hand Side (RHS): 17 × 2 = 34

Since LHS = RHS (34 = 34), this combination of mathematical signs perfectly balances the equation.

Explanation

The pattern in each row is that the third number is obtained by subtracting the second number from the first number.

First number - Second number = Third number

In the first row: 162 - 91 = 71

In the second row: 218 - 126 = 92

Similarly, applying the same pattern to the third row: 194 - 79 = 115

Explanation

Replacing the asterisks with the signs in the correct order gives the following equation:

46 = 16 × 4 + 21 + 72 ÷ 4 − 57

According to the BODMAS rule, division is performed first, followed by multiplication, addition, and subtraction:

72 ÷ 4 = 18

16 × 4 = 64

Substituting these values into the equation:

46 = 64 + 21 + 18 − 57

Adding the positive terms on the right-hand side:

64 + 21 + 18 = 103

Subtracting 57 from 103:

103 − 57 = 46

This simplifies to 46 = 46, which balances the equation perfectly.

Explanation

To find the day of the week on 26 January 1950 starting from 15 August 1947, we calculate the total number of odd days between the two dates.

First, from 15 August 1947 to 15 August 1949: The year from 15 August 1947 to 15 August 1948 includes February 1948, which is a leap year, giving 2 odd days. The year from 15 August 1948 to 15 August 1949 is an ordinary year, giving 1 odd day. Odd days from 15 August 1947 to 15 August 1949 = 2 + 1 = 3 odd days.

Next, from 15 August 1949 to 26 January 1950: Remaining days in August = 16 days (2 odd days) September = 30 days (2 odd days) October = 31 days (3 odd days) November = 30 days (2 odd days) December = 31 days (3 odd days) January = 26 days (5 odd days) Total odd days for this period = 2 + 2 + 3 + 2 + 3 + 5 = 17 odd days. Converting 17 days to weeks: 17 ÷ 7 = 2 weeks and 3 odd days.

Total odd days from 15 August 1947 to 26 January 1950 = 3 + 3 = 6 odd days.

Adding 6 odd days to Friday gives Thursday.

Explanation

The series follows a specific addition pattern for each letter position based on their numerical alphabetical values (A = 1, B = 2, ..., Z = 26).

For the first letter of each cluster, the value increases by 5: T (20) + 5 = Y (25) Y (25) + 5 = D (30, which is 4) D (4) + 5 = I (9) I (9) + 5 = N (14)

For the second letter, the value increases by 7: C (3) + 7 = J (10) J (10) + 7 = Q (17) Q (17) + 7 = X (24) X (24) + 7 = E (31, which is 5)

For the third letter, the value increases by 9: I (9) + 9 = R (18) R (18) + 9 = A (27, which is 1) A (1) + 9 = J (10) J (10) + 9 = S (19)

For the fourth letter, the value increases by 11: D (4) + 11 = O (15) O (15) + 11 = Z (26) Z (26) + 11 = K (37, which is 11) K (11) + 11 = V (22)

Applying these addition rules to the second cluster YJRO gives the third cluster DQAZ.

Explanation

From the statement "All stones are bricks", the entire set of stones is contained within the set of bricks.

From the statement "Some marbles are stones", there is a common overlapping region between the set of marbles and the set of stones.

Since all stones are bricks, the marbles that are stones must also be bricks. This means there is a guaranteed overlap between the set of bricks and the set of marbles, which directly validates conclusion I, "Some bricks are marbles".

Additionally, since no cement is a brick and all stones are bricks, there can be no overlap between cement and stones, making conclusion II incorrect. Since some marbles must be bricks, conclusion III is also incorrect.

Explanation

The coding pattern involves reversing the letters of the given word and then applying a specific rule based on the position of each letter in the reversed sequence.

For letters at odd positions (1st, 3rd, 5th, etc.) in the reversed word, they are replaced by their corresponding alphabetical positional values (A = 1, B = 2, ..., Z = 26).

For letters at even positions (2nd, 4th, 6th, etc.) in the reversed word, they are written in lowercase.

Applying this pattern to the word SCREEN: Reversing the word gives N - E - E - R - C - S. 1st letter N (odd position) is replaced by its positional value 14. 2nd letter E (even position) is converted to lowercase e. 3rd letter E (odd position) is replaced by its positional value 5. 4th letter R (even position) is converted to lowercase r. 5th letter C (odd position) is replaced by its positional value 3. 6th letter S (even position) is converted to lowercase s. This results in the code 14e5r3s.

Applying this pattern to the word CODE: Reversing the word gives E - D - O - C. 1st letter E (odd position) is replaced by its positional value 5. 2nd letter D (even position) is converted to lowercase d. 3rd letter O (odd position) is replaced by its positional value 15. 4th letter C (even position) is converted to lowercase c. This results in the code 5d15c.

Explanation

The letters of the given words are rearranged according to a specific position pattern. By numbering the positions of the letters in the original six-letter word from 1 to 6, the coded word is formed by rearranging these positions into the order 6, 3, 4, 2, 1, 5.

Applying this to the word ABROAD: 1: A, 2: B, 3: R, 4: O, 5: A, 6: D Rearranging to 6, 3, 4, 2, 1, 5 gives D, R, O, B, A, A, which is DROBAA.

Applying this to the word ACTIVE: 1: A, 2: C, 3: T, 4: I, 5: V, 6: E Rearranging to 6, 3, 4, 2, 1, 5 gives E, T, I, C, A, V, which is ETICAV.

Applying this same pattern to the word BISHOP: 1: B, 2: I, 3: S, 4: H, 5: O, 6: P Rearranging to 6, 3, 4, 2, 1, 5 gives P, S, H, I, B, O, which is PSHIBO.

Explanation

The relationship between the terms follows the mathematical pattern x³ − 2x, where the second number in each pair is obtained by subtracting twice the first number from its cube.

For the first pair: 11³ − 2 × 11 = 1331 − 22 = 1309

For the second pair: 15³ − 2 × 15 = 3375 − 30 = 3345

Applying this pattern to the third pair: 7³ − 2 × 7 = 343 − 14 = 329

Explanation

The pattern in the given series is based on adding 3 to the alphabetical position of each letter in the clusters.

For the first letter of each cluster: F (6) + 3 → I (9) + 3 → L (12) + 3 → O (15) + 3 → R (18)

For the second letter of each cluster: D (4) + 3 → G (7) + 3 → J (10) + 3 → M (13) + 3 → P (16)

For the third letter of each cluster: H (8) + 3 → K (11) + 3 → N (14) + 3 → Q (17) + 3 → T (20)

Combining these letters results in the cluster RPT.

Explanation

The terms in the given series follow the pattern of n³ - n² for decreasing consecutive integers starting from n = 9.

Substituting the values of n from 9 down to 4 gives the terms of the series:

For n = 9: 9³ - 9² = 729 - 81 = 648 For n = 8: 8³ - 8² = 512 - 64 = 448 For n = 7: 7³ - 7² = 343 - 49 = 294 For n = 6: 6³ - 6² = 216 - 36 = 180 For n = 5: 5³ - 5² = 125 - 25 = 100

Following this pattern, the next term for n = 4 is: 4³ - 4² = 64 - 16 = 48

Explanation

Substituting the signs from option C (+, ×, =, +) into the given equation 60 19 4 94 42 yields:

60 + 19 × 4 = 94 + 42

By applying the BODMAS rule to evaluate the Left Hand Side (LHS): LHS = 60 + 19 × 4 LHS = 60 + 76 LHS = 136

Evaluating the Right Hand Side (RHS): RHS = 94 + 42 RHS = 136

Since both the LHS and RHS evaluate to 136, the mathematical equation is correctly balanced.

Explanation

To find the day of the week on 28 February 2025 starting from 14 January 2022:

First, calculate the number of odd days between 14 January 2022 and 14 January 2025. The number of years is 3. Since 2024 is a leap year, it contributes 2 odd days, while 2022 and 2023 contribute 1 odd day each. Total odd days from 14 January 2022 to 14 January 2025 = 1 + 1 + 2 = 4 odd days. So, the day on 14 January 2025 is Friday + 4 days = Tuesday.

Next, find the number of days from 14 January 2025 to 28 February 2025: Remaining days in January 2025 = 31 - 14 = 17 days Days in February 2025 = 28 days Total days = 17 + 28 = 45 days

Find the odd days in 45 days: 45 ÷ 7 = 6 weeks and 3 odd days.

Add these 3 odd days to Tuesday: Tuesday + 3 days = Friday.

Thus, 28 February 2025 is a Friday.

Explanation

The relationship between the numbers in each pair is that the digits of the first number are rearranged in descending order to form the second number.

In the first pair, the digits of 5372 are 5, 3, 7, and 2. Arranging them in descending order gives 7532.

In the second pair, the digits of 4928 are 4, 9, 2, and 8. Arranging them in descending order gives 9842.

Applying the same logic to the third pair, the digits of 9284 are 9, 2, 8, and 4. Arranging them in descending order gives 9842.

Explanation

Let the seven positions of friends from tallest (1) to shortest (7) be represented as 1, 2, 3, 4, 5, 6, 7.

Since A is the shortest among all, A is at position 7.

Only four people are taller than C, which means C is at position 5.

Since C is taller than D, and position 7 is already occupied by A, D must be at position 6.

The remaining four positions (1, 2, 3, 4) must be occupied by B, F, E, and G.

We are given that E is taller than G but shorter than F (F > E > G), and F is not the tallest. Since F cannot be at position 1, the only possible positions for F, E, and G to maintain the order F > E > G within the top four spots are positions 2, 3, and 4 respectively.

This leaves the tallest position 1 for B.

The final arrangement from tallest to shortest is: 1: B 2: F 3: E 4: G 5: C 6: D 7: A

The people between B (position 1) and G (position 4) are F and E. Thus, there are 2 people between the heights of B and G.

Explanation

An Automated Teller Machine (ATM) is a service utility that is operated by and fundamentally associated with a Bank. Similarly, an Ambulance is a specialized vehicle operated by and functionally associated with a Hospital to provide emergency medical transportation and care. This establishes a direct analogy between a service tool or utility and its parent institution.

Explanation

The code is obtained by dividing the eight-letter word into four consecutive pairs of letters. For each pair, every letter is incremented by one (+1) in alphabetical order, and then the position of the two letters in that pair is reversed.

Applying this logic to MULTIPLY:

Pair 1: MU. Incrementing by one gives NV, and reversing NV gives VN.

Pair 2: LT. Incrementing by one gives MU, and reversing MU gives UM.

Pair 3: IP. Incrementing by one gives JQ, and reversing JQ gives QJ.

Pair 4: LY. Incrementing by one gives MZ, and reversing MZ gives ZM.

Combining these pairs in order yields VNUMQJZM.

Explanation

The given words are arranged in a descending order of their geographical size and hierarchy, progressing from the largest region to the smallest locality:

Asia represents the continent. South-East Asia represents the sub-continental region. India represents the country located within this broader region. Kerala represents a state within India. Haripad represents a town within Kerala.

This hierarchical progression from the largest geographical entity to the smallest yields the sequence 5, 3, 2, 4, 1.

Explanation

To arrange the given words in alphabetical order as they appear in an English dictionary, they are compared letter by letter from left to right. All five words begin with the letters As. Comparing their third letters: c in Ascertain (5) comes first, followed by p in Aspirations (4), and then s in Assertive (1).

For the remaining two words, Astringent (2) and Astronomy (3), both begin with the letters Astr. Comparing their fifth letters, i in Astringent comes before o in Astronomy, placing Astringent (2) before Astronomy (3).

Explanation

The given number series follows an alternating pattern of multiplication and subtraction using consecutive integers:

First term: 9 Second term: 9 × 2 = 18 Third term: 18 - 3 = 15 Fourth term: 15 × 4 = 60 Fifth term: 60 - 5 = 55 Sixth term: 55 × 6 = 330

Explanation

By substituting the letters with their respective mathematical operations: I represents ÷ J represents × K represents − L represents +

The given equation is: (18 ÷ 9) × 12 + 22 − 41 + (36 × 2) − 2 × 8

Following the BODMAS rule, solve the brackets first: 18 ÷ 9 = 2 36 × 2 = 72

This gives: 2 × 12 + 22 − 41 + 72 − 2 × 8

Next, perform the multiplication operations: 2 × 12 = 24 2 × 8 = 16

The equation becomes: 24 + 22 − 41 + 72 − 16

Finally, perform the addition and subtraction: 24 + 22 + 72 = 118 118 − 41 − 16 = 61

Explanation

The series is formed by applying a specific mathematical pattern to each letter position in the clusters from one term to the next.

First letter of each cluster increases by 5: R (18) + 5 = W (23) W (23) + 5 = B (28 or 2) B (2) + 5 = G (7) G (7) + 5 = L (12)

Second letter of each cluster increases by 11: S (19) + 11 = D (30 or 4) D (4) + 11 = O (15) O (15) + 11 = Z (26) Z (26) + 11 = K (37 or 11)

Third letter of each cluster increases by 17 (or decreases by 9): D (4) + 17 = U (21) U (21) + 17 = L (38 or 12) L (12) + 17 = C (29 or 3) C (3) + 17 = T (20)

Fourth letter of each cluster decreases by 3: A (27 or 1) - 3 = X (24) X (24) - 3 = U (21) U (21) - 3 = R (18) R (18) - 3 = O (15)

Applying these shifts to the second term WDUX yields the cluster BOLU.

Explanation

The given number series follows an alternating pattern of multiplication and addition with decreasing integers starting from 6.

Applying this pattern step-by-step: First step: 5 × 6 = 30 Second step: 30 + 5 = 35 Third step: 35 × 4 = 140 Fourth step: 140 + 3 = 143 Fifth step: 143 × 2 = 286

Explanation

The series progresses by applying a specific letter-shifting pattern to each of the four positions. The first letter in each term increases by 1 step (W to X to Y to Z to A). The second letter in each term decreases by 1 step (X to W to V to U to T). The third letter in each term increases by 1 step (Y to Z to A to B to C). The fourth letter in each term decreases by 1 step (Z to Y to X to W to V). Applying this systematic pattern of (+1, -1, +1, -1) to the third cluster, YVAX, yields ZUBW.

Explanation

The relationship between the numbers in each set (A, B, C) follows the logic where the third number is equal to the product of the first number and the difference between the first and second numbers, which can be expressed as C = A × (A - B).

In the first set (45, 37, 360), this is demonstrated by 45 × (45 - 37) = 45 × 8 = 360.

In the second set (17, 14, 51), this is demonstrated by 17 × (17 - 14) = 17 × 3 = 51.

Applying this logic to the set (34, 26, 272) in option D, we get 34 × (34 - 26) = 34 × 8 = 272.

Explanation

The difference between consecutive terms in the series forms a sequence of consecutive multiples of 9:

45 - 36 = 9 63 - 45 = 18 90 - 63 = 27 126 - 90 = 36 171 - 126 = 45

Following this pattern, the next difference must be 54 (which is 9 × 6).

The next term in the series is calculated as: 171 + 54 = 225

Explanation

The letters of the word are rearranged according to their position indices from left to right. Let the letters of a four-letter word be indexed as 1, 2, 3, and 4.

In the word CODE, C is 1, O is 2, D is 3, and E is 4. The coded form DCEO is represented by the index pattern 3, 1, 4, 2.

Similarly, in the word MAKE, M is 1, A is 2, K is 3, and E is 4. Rearranging these letters in the same pattern of 3, 1, 4, 2 yields KMEA.

Applying this identical pattern to the word HEAD, where H is 1, E is 2, A is 3, and D is 4, rearranging them in the order 3, 1, 4, 2 gives AHDE.

Explanation

Interchanging the numbers 7 and 9 in the given equation transforms the expression on the left-hand side.

Original equation: (17 × 4) - (7)² + (63 ÷ 9) × 6 + 83 - 41 = 83

After interchanging 7 and 9, the equation becomes: (17 × 4) - (9)² + (63 ÷ 7) × 6 + 83 - 41 = 83

Solving the left-hand side using the BODMAS rule: First, solve the operations inside the parentheses and the exponent: 17 × 4 = 68 9² = 81 63 ÷ 7 = 9

Substitute these values back into the equation: 68 - 81 + 9 × 6 + 83 - 41

Next, perform the multiplication: 9 × 6 = 54

Now, substitute the multiplication result and perform the addition and subtraction from left to right: 68 - 81 + 54 + 83 - 41 = -13 + 54 + 83 - 41 = 41 + 83 - 41 = 124 - 41 = 83

This matches the right-hand side of the equation.

Explanation

Using the mathematical signs in option D (where the first operator represents division, ÷):

25 ÷ 5 + 10 × 2 - 4 = 21

Applying the BODMAS rule:

First, solve the division part: 25 ÷ 5 = 5

Next, solve the multiplication part: 10 × 2 = 20

Now, perform the addition: 5 + 20 = 25

Finally, perform the subtraction: 25 - 4 = 21

This balances the equation as LHS = RHS = 21.

Explanation

The relationship between the numbers in each pair follows the mathematical formula where the second term is equal to the square of the first term plus 7:

Second term = (First term)² + 7

For the first pair (6 : 43): 6² + 7 = 36 + 7 = 43

For the third pair (20 : 407): 20² + 7 = 400 + 7 = 407

To find the missing first term (x) in the second pair (x : 203): x² + 7 = 203 x² = 203 - 7 x² = 196 x = √196 x = 14

Explanation

The letters in the series are positioned in decreasing order of their alphabetical values. Substituting each letter with its corresponding position in the English alphabet:

V = 22 S = 19 O = 15 L = 12 E = 5

The differences between consecutive terms follow an alternating pattern of subtracting 3 and subtracting 4:

22 - 3 = 19 (S) 19 - 4 = 15 (O) 15 - 3 = 12 (L)

Following this pattern, the next step requires subtracting 4 from the position of L (12):

12 - 4 = 8

The 8th letter of the alphabet is H.

To verify, subtracting 3 from 8 gives 5, which corresponds to the final letter E. Therefore, the missing letter is H.

Explanation

The relationship among the numbers in each set follows the logic: (First term + Third term) = (3 × Second term) + 8

This can be verified as follows:

For the set (41, 24, 39): 41 + 39 = (3 × 24) + 8 80 = 72 + 8 80 = 80

For the set (10, 5, 13): 10 + 13 = (3 × 5) + 8 23 = 15 + 8 23 = 23

Applying the same logic to the set (22, 17, 37): 22 + 37 = (3 × 17) + 8 59 = 51 + 8 59 = 59

Explanation

The coding pattern involves dividing the word into pairs of consecutive letters and reversing the order of letters within each pair.

In the word ISLAND, the letters are paired as IS, LA, and ND. Reversing each pair gives SI, AL, and DN, which combines to form SIALDN.

In the word LAWYER, the letters are paired as LA, WY, and ER. Reversing each pair gives AL, YW, and RE, which combines to form ALYWRE.

Applying this same rule to the word LAUNCH, the letters are paired as LA, UN, and CH. Reversing each pair gives AL, NU, and HC, which combines to form ALNUHC.

Explanation

The relationship between the terms in each pair follows the pattern: (First term)² - 18 = Second term

Using this logic for the known pairs: 5² - 18 = 25 - 18 = 7 22² - 18 = 484 - 18 = 466

Applying the same pattern to find the third term, let the term be x: x² - 18 = 271 x² = 289 x = √289 x = 17

Explanation

The series follows an alternating pattern of multiplication and addition, with the numbers used in the operations decreasing by 1 at each successive step.

The mathematical operations applied to the sequence are: 7 × 6 = 42 42 + 5 = 47 47 × 4 = 188 188 + 3 = 191 191 × 2 = 382

Following this pattern, multiplying 47 by 4 yields the missing number, 188.

Explanation

The pattern followed in the given pairs is that the second term is obtained by subtracting 5 from the square of the first term.

First pair: 12² - 5 = 144 - 5 = 139

Third pair: 18² - 5 = 324 - 5 = 319

Applying the same logic to the second pair: 7² - 5 = 49 - 5 = 44

Explanation

By decoding the letters with their respective mathematical operators, A represents +, B represents ×, C represents -, and D represents ÷.

Substituting these operators into the given equation: 92 + (121 ÷ 11) - (6 × 3) ÷ 2 + 7 × 8

Solving the terms inside the parentheses first according to BODMAS rule: 92 + 11 - 18 ÷ 2 + 7 × 8

Next, performing the division: 92 + 11 - 9 + 7 × 8

Next, performing the multiplication: 92 + 11 - 9 + 56

Finally, solving the addition and subtraction: 103 - 9 + 56 = 94 + 56 = 150

Explanation

To find the next term in the series, we look at the positional value of each letter in the alphabetical order where A = 1, B = 2, and so on up to Z = 26.

For the first letters of each cluster, the pattern is subtracting 6 at each step: H (8) - 6 = B (2) B (2) - 6 = V (22) V (22) - 6 = P (16)

For the second letters, the pattern is subtracting 4 at each step: M (13) - 4 = I (9) I (9) - 4 = E (5) E (5) - 4 = A (1)

For the third letters, the pattern is subtracting 3 at each step: S (19) - 3 = P (16) P (16) - 3 = M (13) M (13) - 3 = J (10)

For the fourth letters, the pattern is subtracting 2 at each step: E (5) - 2 = C (3) C (3) - 2 = A (1) A (1) - 2 = Y (25)

By combining these resulting letters, we get the next cluster in the series, which is PAJY.

Explanation

The phrase his son's mother refers to the man's wife.

The phrase my son's sister's sister translates to Radhika's son's sister, who is Radhika's daughter, and her sister is also Radhika's daughter.

By equating the two expressions, the man's wife is Radhika's daughter. Since the man is married to Radhika's daughter, he is Radhika's son-in-law.

Explanation

In this code language, each letter of the word is represented by its corresponding numerical position in the English alphabetical order. The alphabetical positions of the letters are:

A = 1 C = 3 H = 8 L = 12 O = 15 P = 16 R = 18 V = 22

For the word APPROACH, writing the positional values of the letters sequentially gives: A(1) P(16) P(16) R(18) O(15) A(1) C(3) H(8) which forms 116161815138.

Similarly, for the word APPROVAL: A(1) P(16) P(16) R(18) O(15) V(22) A(1) L(12) which forms 11616181522112.

Applying the same logic to the word POOL: P = 16 O = 15 O = 15 L = 12

Combining these numerical values sequentially yields 16151512.

Explanation

By replacing the asterisk signs with the mathematical operators from option B, the given equation becomes:

14 × 5 + 41 − 76 = 35

Following the standard order of operations, first calculate the multiplication: 14 × 5 = 70

Now substitute this value back and perform the addition: 70 + 41 = 111

Finally, perform the subtraction: 111 − 76 = 35

Both sides of the equation are equal, which balances the expression.

Explanation

Substituting the mathematical signs of the correct option into the given expression yields:

78 ÷ 3 + 12 × 5 − 59 + 17 = 44

Using the BODMAS rule, the operations are performed in the sequence of Division, Multiplication, Addition, and Subtraction:

First, execute the division: 78 ÷ 3 = 26

Second, execute the multiplication: 12 × 5 = 60

Now substitute these values back into the equation: 26 + 60 − 59 + 17 = 44

Perform the addition and subtraction from left to right: 86 − 59 + 17 = 44 27 + 17 = 44 44 = 44

Both sides of the equation are equal, balancing it successfully.

Explanation

The given sequence is an alternating series composed of two distinct arithmetic progressions.

The first progression consists of the terms at the odd positions: 78, 64, 50 The common difference here is -14, as 78 - 14 = 64, and 64 - 14 = 50.

The second progression consists of the terms at the even positions: 112, ?, 140 This series increases by a constant difference of +14. Calculating the missing fourth term: 112 + 14 = 126

To verify, the next term in this progression is: 126 + 14 = 140

Explanation

The code for each word is calculated by multiplying the alphabetical positions of its letters and then subtracting the total number of letters in that word.

The alphabetical positions of the letters are C = 3, A = 1, T = 20, R = 18, E = 5, N = 14, and O = 15.

For ARE: 1 × 18 × 5 = 90 90 - 3 = 87

For NOT: 14 × 15 × 20 = 4200 4200 - 3 = 4197

For CAT: 3 × 1 × 20 = 60 60 - 3 = 57

Explanation

Substituting the mathematical signs from option D (+, =, ×, ×) in place of the asterisks in the equation gives:

13 + 5 = 3 × 3 × 2

Calculating both sides of the equation:

Left-hand side: 13 + 5 = 18

Right-hand side: 3 × 3 × 2 = 9 × 2 = 18

Since both sides are equal to 18, the equation is balanced.

Explanation

From the given conditions, P scored higher than only U and R, and R scored higher than U. This determines the positions of the lowest three scorers: Rank 5: P Rank 6: R Rank 7: U

The remaining four positions (Rank 1 to Rank 4) must be shared among Q, S, T, and V. We are told that Q scored higher than S but lesser than T, which means T scored higher than Q, who scored higher than S (T > Q > S). Since T did not score the highest, the only remaining person, V, must have scored the highest. This determines the order of the top four positions: Rank 1: V Rank 2: T Rank 3: Q Rank 4: S

Combining all positions from highest to lowest, the order is: V > T > Q > S > P > R > U

The persons who scored between Q (Rank 3) and R (Rank 6) are S (Rank 4) and P (Rank 5). This means there are exactly 2 persons who scored between Q and R.