Q: Statements: A > B, B ≥ C = D < E Conclusions: I. C < A II. D ≤ B

If both conclusion I and II follow.

Q: Statements: A ≥ B = C, D > C = E Conclusions: I. E > A II. A < D

If either conclusion I or II follows

Q: Statements: L > U ≥ K, Z Z II. K < R

Split them as L > U ...(i) Combining (i) and (ii), We get L > U > Z or L > Z Hence I follows. Combining (ii) and (iv) we get K ≤ U < R or K < R Hence II follows.

Q: Statements: V ≥ K > M = N, M > S, T< K Conclusions: I. T < N II. V = S

V ≥ K > M = N > S K > T I. T < N is not true, II. V = S is true.

Q: Statements: F ≤ X < A, R < X ≤ F Conclusions: I. F ≤ E II. R < F

Split them as F ≤ X ...(i) X < A ...(ii) R < X ...(ii) and X ≤ E ...(iv) Combining (i) and (iv) we get F ≤ X ≤ F or F ≤ E. Hence I follow. From (i) and (iii) R and F can't be compared. Hence II does not follow.

Q: Which of the following sets of operation with the usual notations replacing the starts in the order given makes the statements valid? √ 100 * √ 16 * √ 225 * √ 1

√100 + √16 = √225 -√1 10 + 4 = 15 - 1 ⇒ 14 = 14

Q: Select the correct combination of mathematical signs to replace '*' signs and to balance the given equation. 24 * 34 * 2 * 5 * 12

From option (c), 24 = 34 ÷ 2 - 5 + 12 ⇒ 24 = 17 - 5 + 12 ⇒ 24 = 29 - 5 → 24 = 24

Q: If A means '-' , B means '+', C means 'x', and D means '÷' then 32 D 4 B 7 C 2 A 6

32 D 4 B 7 C 2 A 6 = 32 ÷ 4 + 7 x 2 - 6 = 8 + 7 x 2 - 6 = 8 + 14 - 6 = 22 - 6 = 16

Question 1

Statements: A > B, B ≥ C = D < E Conclusions: I. C < A II. D ≤ B

Accepted Answer

If both conclusion I and II follow.

Question 2

Statements: H > J = K, K ≥ L, L > T, T < V Conclusions: I. K > T II. L ≤ H

Accepted Answer

If only conclusion I follows

Question 3

Statements: A ≥ B = C, D > C = E Conclusions: I. E > A II. A < D

Accepted Answer

If either conclusion I or II follows

Question 4

Statements: A ≥ B = C, B < D ≤ E Conclusions: I. D > A II. E > C

Accepted Answer

A ≥ B = C < D ≤ E I. D > A is not true, II. E > C is true.

Question 5

Statements: L > U ≥ K, Z < U < R Conclusions: I. L > Z II. K < R

Accepted Answer

Split them as L > U ...(i) Combining (i) and (ii), We get L > U > Z or L > Z Hence I follows. Combining (ii) and (iv) we get K ≤ U < R or K < R Hence II follows.

Question 6

Statements: Y < J = P ≥ R > I Conclusions: I. J > I II. Y < R

Accepted Answer

Y < J = P ≥ R > I I. J > I is true, II. Y < R is not true.

Question 7

Statements: V ≥ K > M = N, M > S, T< K Conclusions: I. T < N II. V = S

Accepted Answer

V ≥ K > M = N > S K > T I. T < N is not true, II. V = S is true.

Question 8

Statements: F ≤ X < A, R < X ≤ F Conclusions: I. F ≤ E II. R < F

Accepted Answer

Split them as F ≤ X ...(i) X < A ...(ii) R < X ...(ii) and X ≤ E ...(iv) Combining (i) and (iv) we get F ≤ X ≤ F or F ≤ E. Hence I follow. From (i) and (iii) R and F can't be compared. Hence II does not follow.

Question 9

Which of the following sets of operation with the usual notations replacing the starts in the order given makes the statements valid? √ 100 * √ 16 * √ 225 * √ 1

Accepted Answer

√100 + √16 = √225 -√1 10 + 4 = 15 - 1 ⇒ 14 = 14

Question 10

Select the correct combination of mathematical signs to replace '*' signs and to balance the given equation. 24 * 34 * 2 * 5 * 12

Accepted Answer

From option (c), 24 = 34 ÷ 2 - 5 + 12 ⇒ 24 = 17 - 5 + 12 ⇒ 24 = 29 - 5 → 24 = 24

Question 11

If A means '-' , B means '+', C means 'x', and D means '÷' then 32 D 4 B 7 C 2 A 6

Accepted Answer

32 D 4 B 7 C 2 A 6 = 32 ÷ 4 + 7 x 2 - 6 = 8 + 7 x 2 - 6 = 8 + 14 - 6 = 22 - 6 = 16

Question 12

If K denotes 'X', B denotes '÷', 'T' denotes '-' and 'M' denotes '+', then 40 B 8 T 6 M 3 K 4 =?

Accepted Answer

∵ 40 B 8 T 6 M 3 K 4 = ? ⇒ 40 ÷ 8 - 6 + 3 x 4 = ? ⇒ 5 - 6 + 12 = ? ⇒ 17 - 6 = ? ∴ ? = 11

Question 13

16 (27) 43, 29 (?) 56, 36 (12) 48

Accepted Answer

Here, Right number - Left number = Middle number As, 43 - 16 = 27, 48 - 36 = 12 similarly, 56 - 29 = 27 ∴ ? = 27

Question 14

7 4 8 2 = 24

Accepted Answer

Let us check all the options one-by-one. From option (a), 7 - 4 x 8 x 2 = 24 (using VBODMAS rule) ⇒ 7 - 64 = 24 ⇒ -57 = 24 ∴ LHS ≠ RHS ≠ RHS So, option (a) is incorrect. From option (b), 7 - 4 x 8 ÷ 2 = 24 (using VBODMAS rule) ⇒ 7 - 4 x 8 ÷ 2 = 24 (using VBODMAS rule) ⇒ 7 - 4 x 4 = 24 ⇒ 7 - 16 = 24 ⇒ -9 = 24 ⇒ LHS ≠ RHS So, option (b) is incorrect . From option (c), 7 x 4 - 8 ÷ 2 = 24 (using VBODMAS rule) ⇒ 7 x 4 - 4 = 24 ⇒ 28 - 4 = 24 ⇒ 24 = 24 ⇒ LHS = RHS So, option (c) is correct and hence, there is no need to check option (d).

Question 15

If 264 * 2 = 6, 870 * 3 = 11, then what should 735 *5 be?

Accepted Answer

Divide and add all numbers. As, 264/2 = 132 ⇒ 1 + 3 + 2 = 6 ⇒ 870/3 = 290 ⇒ 2 + 9 + 0 = 11 Similarly, 735/5 = 147 ⇒ 1 + 4 + 7 = 12

Question 16

23 15 12 X 24 49 If 'X' is the resultant of the first row, what is the resultant of the second row?

Accepted Answer

Rules (i) (2-digit odd number) + (2-digit odd number) (ii) 2-digit even number → 2-digit perfect square odd number then, (odd number) - (Even number) (iii) (3-digit number) ÷ (2-digit number) (iv) (Prime number) + (Even number) (v) (Even number) x (Even number) Solution: 1st Row 23 15 12 ⇒ 23 + 15 = 38 [rule (i)] ⇒ 38 x 12 = 456 [rule (v)] 2nd Row X 24 49 ⇒ 456 24 49 ⇒ 456 ÷ 24 = 19 [rule (iii)] ⇒ 19 + 49 = 68 [rule (i)] ∴ Resultant of second row = 68

Question 17

37 12 21 38 81 14 What is the difference between the resultants of the two rows?

Accepted Answer

Rules (i) (2-digit odd number) + (2-digit odd number) (ii) 2-digit even number → 2-digit perfect square odd number then, (odd number) - (Even number) (iii) (3-digit number) ÷ (2-digit number) (iv) (Prime number) + (Even number) (v) (Even number) x (Even number) Solution: 1st Row 37 12 21 ⇒ 37 + 12 = 49 [rule (iv)] ⇒ 49 + 21 = 70 [rule (i)] 2nd Row 38 81 14 ⇒ 81 - 38 = 43 [rule (ii)] ⇒ 43 + 14 = 57 [rule (iv)] ∴ Required difference = 70 - 57 = 13

Question 18

16 8 32 132 11 X 2 If X is the resultant of the first row, what is the resultant of the second row?

Accepted Answer

Rules (i) (2-digit odd number) + (2-digit odd number) (ii) 2-digit even number → 2-digit perfect square odd number then, (odd number) - (Even number) (iii) (3-digit number) ÷ (2-digit number) (iv) (Prime number) + (Even number) (v) (Even number) x (Even number) Solution: 1st Row 16 8 32 ⇒ 16 x B = 128 [rule (v)] ⇒ 128 ÷ 32 = 4 [rule (iii)] X 2nd Row 132 11 X2 ⇒ 132 11 16 ⇒ 132 ÷ 11 = 12 [rule (iii)] ⇒ 12 x 16 = 192 [rule (v)] ∴ Resultant of second row = 192

Question 19

345 23 X 45 17 81 It 'X' is the resultant of the second row, what is the resultant of the first row?

Accepted Answer

Rules (i) (2-digit odd number) + (2-digit odd number) (ii) 2-digit even number → 2-digit perfect square odd number then, (odd number) - (Even number) (iii) (3-digit number) ÷ (2-digit number) (iv) (Prime number) + (Even number) (v) (Even number) x (Even number) Solution: 2nd Row 45 17 81 ⇒ 45 + 17 = 62 [rule (i)] ⇒ 81 - 62 = 19 [rule (ii)] 1st Row 345 23 X ⇒ 345 23 19 ⇒ 345 ÷ 23 = 15 [rule (iii)] ⇒ 345 ÷ 15 + 19 [rule (i)] ∴ Resultant of first row = 34

Question 20

12 28 84 37 22 18 What is the sum of the resultant of the two rows?

Accepted Answer

Rules (i) (2-digit odd number) + (2-digit odd number) (ii) 2-digit even number → 2-digit perfect square odd number then, (odd number) - (Even number) (iii) (3-digit number) ÷ (2-digit number) (iv) (Prime number) + (Even number) (v) (Even number) x (Even number) Solution: 1st Row 12 28 84 ⇒ 12 x 28 = 336 [rule (v)] ⇒ 336 ÷ 84 = 4 [rule (iii)] 2nd Row 37 22 18 ⇒ 37 + 22 = 59 [rule (iv)] ⇒ 59 + 18 = 77 [rule (iv)] ∴ Required sum = 4 + 77 = 81

Mathematical Operations Questions