1. Find the missing number:

A. 2250 B. 8100 C. 11036 D. 1216

Answer - Option B
Explanation -
4 × 3 = 12 and [latex]{(12)}^{2}[/latex] = 144
11 × 9 = 99 and [latex]{(99)}^{2}[/latex] = 9801
15 × 6 = 90 and [latex]{(90)}^{2}[/latex] = 8100
2. Find the missing number:

A. 75 B. 60 C. 30 D. 90

Answer - Option B
Explanation -
12 × 4 = 48
[latex]\sqrt{125}[/latex] = 5
16 × 4 = 64
[latex]\sqrt{81} [/latex] = 9
Similarly,
15 × 4 = 60
[latex]\sqrt{49} [/latex] = 7
3. Find the missing number:

A. 9 B. 12 C. 8 D. 13

Answer - Option B
Explanation -
(27 + 18) – (12 + 13)
45 – 25 = 20
(16 + 12) – (6 + 9)
28 – 15 = 13
(10 + 11) – (5 + 4)
21 – 9 = 12
4. Find the missing number:

A. 3 B. 4 C. 5 D. 6

Answer - Option C
Explanation -
27 = 9 × (2 + 1)
35 = 7 × (3 + 2)
36 = 4 × (4 + 5)
5. Select the missing number from the given responses.

A. 12 B. 10 C. 8 D. 6

Answer - Option D
Explanation -
First figure
12 – 6 = 6;
15 – 9 = 6
Second figure
12 – 4 = 8;
16 – 8 = 8
Third figure
11 – 5 = 6;
14 – 8 = 6
6. In the following question find the missing number.

A. 5 B. 6 C. 7 D. 10

Answer - Option C
Explanation -
In column 1, 4 × 5 – 3 = 17
In column 2, 6 × 7 – 4 = 38
i.e, In column 3, 8 × 9 – ? = 65
? = 7
7. In the following question find the missing number:

A. 12 B. 15 C. 18 D. 20

Answer - Option D
Explanation -
In column 1, (2 + 3) × 5 = 25
In column 2, (1 + 4) × 10 = 50
i.e, In column 3, (3 + 2) × ? = 100
? = 20.
8. In the following question find the missing number:

A. 1 B. 3 C. 5 D. 6

Answer - Option B
Explanation -
In column 1, 17 × 6 ÷ 3 = 34
In column 2, 23 × 8 ÷ 2 = 92
i.e, In column 3, 25 × 18 ÷ ? = 150
? = 3.
Directions (9 - 10):
Some equations are solved on the basis of certain system. Find out the correct answer for the unsolved equation on that basis.
9.

A. 2 B. 3 C. 4 D. 0

Answer - Option B
Explanation -

i.e, ? = 3
10.

A. 554 B. 693 C. 184 D. 717

Answer - Option D
Explanation -
In column 1,
(3 + 1) (4 ÷ 2) (7 – 1) = 426.
In column 2,
(5 + 1) (8 ÷ 2) (4 – 1) = 643.
Similarly, in column 3,
(6 + 1) (2 ÷ 2) (8 – 1) = 717.
11. If 92 + 53 = 72 and 31 + 33 = 20, then 52 + 91 = ?

A. 38 B. 143 C. 39 D. 75

Answer - Option A
Explanation -
Expression 92 + 53 = 72
9 – 2 = 7 and 5 – 3 = 2
Expression 31 + 33 = 20
3 – 1 = 2 and 3 – 3 = 0.
i.e, 52 + 91 = (5 – 2) = 3 and (9 – 1) = 8 → 38.
12. If 37 + 17 = 20 and 68 + 42 = 26, then 96 + 63 = ?

A. 74 B. 159 C. 33 D. 62

Answer - Option C
Explanation -
Expression 37 + 17 = 20
3 – 1 = 2 and 7 – 7 = 0.
Expression 68 + 42 = 26
6 – 4 = 2 and 8 – 2 = 6.
i.e, 96 + 63 = (9 – 6) = 3 and (6 – 3) = 3 → 33
13. If 53 + 21 = 73 and 45 + 32 = 106, then 29 + 63 = ?

A. 150 B. 49 C. 202 D. 179

Answer - Option C
Explanation -
Expression 53 + 21 = 73 → [latex]{(5 + 3)}^{2} + {(2 + 1)}^{2} = {8}^{2} + {3}^{2}[/latex] = 73.
Expression 45 + 32 = 106
→ [latex]{(4 + 5)}^{2} + {(3 + 2)}^{2} = {9}^{2} + {5}^{2}[/latex] = 106.
i.e, 29 + 63
→ [latex]{(2 + 9)}^{2} + {(6 + 3)}^{2} = {11}^{2} + {9}^{2}[/latex] = 202.
14. 5 × 2 × 7 = 752, 4 × 7 × 3 = 347,1 × 4 × 9 = ?

A. 914 B. 441 C. 419 D. 941

Answer - Option A
Explanation -

15. If 83 ÷ 42 = 5, 63 ÷ 21 = 6, then 56 ÷ 23 = ?

A. 11 B. 6 C. 9 D. 17

Answer - Option B
Explanation -
83 ÷ 42 = 5 ⇒ (8 – 4) + (3 – 2) = 4 + 1 = 5.
63 ÷ 21 = 6 ⇒ (6 – 2) + (3 – 1) = 4 + 2 = 6.
Similarly, 56 ÷ 23 ⇒ (5 – 2) + (6 – 3) = 3 + 3 = 6.

1. If 52 ÷ 24 = 1, and 83 ÷ 45 = 2, then 41 ÷ 33 = ?

A. 1 B. 0 C. -1 D. 2

Answer - Option C
Explanation -
52 ÷ 24 = 1 ⇒ (5 – 2) + (2 – 4) = 3 – 2 = 1
83 ÷ 45 = 2 ⇒ (8 – 4) + (3 – 5) = 4 – 2 = 2
Similarly, 41 ÷ 33 ⇒ (4 – 3) + (1 – 3) = 1 – 2 = – 1
2. In the following question, select the number which can be placed at the sign of question mark (?) from the given alternatives.

A. 43 B. 49 C. 59 D. 71

Answer - Option D
3. If 3 @ 3 * 3 = 3 and 48 @ 4 * 3 = 36, then 91 @ 13 * 2 = ?

A. 4 B. 8 C. 10 D. 14

Answer - Option D
4. In the following question, select the number which can be placed at the sign of question mark (?) from the given alternatives.

A. 11 B. 16 C. 21 D. 31

Answer - Option A
5. If [latex]{(3)}^{2} @ 1 * 7 = 98 and {(4)}^{2} @ 2 * 16 =178,then {(5)}^{2}[/latex] @ 3 * 9 = ?

A. 218 B. 262 C. 253 D. 259

Answer - Option B
6. In the following question, select the number which can be placed at the sign of question mark (?) from the given alternatives.

A. 35 B. 42 C. 45 D. 95

Answer - Option A
7. In the following question, select the number which can be placed at the sign of question mark (?) from the given alternatives.

A. 14 B. 15 C. 17 D. 19

Answer - Option B
8. If 6 @ 4 @ 7 = 101 and 2 @ 5 @ 11 = 150, then what is the value of A in A @ 8 @ 9 =289

A. 5 B. 8 C. 12 D. 17

Answer - Option C
9. In the following question, select the number which can be placed at the sign of question mark (?) from the given alternatives.

A. 112 B. 144 C. 156 D. 186

Answer - Option C
10. In the following question, select the number which can be placed at the sign of question mark (?) from the given alternatives.

A. 216 B. 1024 C. 1296 D. 2024

Answer - Option C
11. In the following question, select the number which can be placed at the sign of question mark (?) from the given alternatives.

A. 2 B. 4 C. 6 D. 8

Answer - Option B
12. If 9 * 2 * 5 = 23 and 1 * 4 * 8 = 29, then 1 * 6 * 3 = ?

A. 19 B. 21 C. 31 D. 39

Answer - Option A
13. In the following question, select the number which can be placed at the sign of question mark (?) from the given alternatives.

A. 48 B. 52 C. 55 D. 58

Answer - Option D
14. In the following question, select the number which can be placed at the sign of question mark (?) from the given alternatives

A. 11 B. 31 C. 32 D. 37

Answer - Option B

1. Find the missing number.

A. 3 B. 33 C. 22 D. 9

Answer - Option C
Explanation -
We have
7 × 5 + (6 + 4) = 45
12 × 7 + (5 + 4) = 93
Similarly, 22 × 3 + (11 + x) = 99
x = 22.
2. Find the missing number.

A. 111 B. 113 C. 36 D. 288

Answer - Option B
Explanation -
We have
[latex]{1}^{2} + {2}^{2} + {3}^{2} + {4}^{2} = 30[/latex]
[latex]{1}^{2} + {2}^{2} + {3}^{2} + {4}^{2} = 46[/latex]
[latex]{2}^{2} + {8}^{2} + {6}^{2} + {3}^{2} = 113[/latex]
3. Find the missing number.

A. 14400 B. 15600 C. 23040 D. 17400

Answer - Option A
Explanation -
1 × 2 × 3 × 4 = 24
24 × 24 = 576
2 × 3 × 5 × 4 = 120
120 × 120 = 14400
4. Find the missing number.

A. 8 B. 3 C. 6 D. 36

Answer - Option c
Explanation -
Column 1
2 × 7 × 9 = 126
Column 2
7 × 3 × 8 = 168
Column 3
9 × 4 × = 216
Hence, 6 should replace the ‘question mark’.
5. Find the missing number.

A. 20 B. 30 C. 15 D. 35

Answer - Option B
Explanation -
The sum of the numbers in a row is equal to 120.
i.e. 18 + 27 + 75 = 45 + 75 = 120
41 + 60 + 19 = 79 + 41 = 120
Similarly, 45 + 45 + 30 = 120
Hence, 30 should replace the question mark
6. Find the missing number.

A. 117 B. 120 C. 107 D. 110

Answer - Option A
Explanation -
Difference of the numbers in the bottom row is 10 times the difference of the number in the upper row.
i.e, ? – 57 = 10(69 – 63) = 10 × 6
? = 57 + 60 = 117
7. Find the missing number shown by the question mark (?) in the center of the third figure.

A. 8 B. 10 C. 12 D. 14

Answer - Option A
Explanation -
In each figure, sum of the numbers at the right hand side vertices of the square is subtracted from the sum of the numbers at the left hand side vertices of the square to get the number in the center.
Therefore, the required number is
(20 + 12) – (10 + 14) = 8
8. Which of the following number can replace the question mark in the figure given below?

A. 3 B. 9 C. 1 D. 2

Answer - Option D
Explanation -
[latex]({(5)}^{2} + {(4)}^{2}) - ({(3)}^{2} + {(2)}^{2}) = [/latex]
= (25 + 16) – (9 + 4) = 41 – 13 = 28
Similarly, [latex]({(8)}^{2} + {(4)}^{2}) - ({(8)}^{2} + {(x)}^{2}) = [/latex] = 12 (Let x = ?)
(64 + 16) – (64 + [latex]{(x)}^{2}[/latex]) = 12
[latex]{(x)}^{2}[/latex] = 4
x = 2
9. Find the missing number.

A. 3 B. 9 C. 1 D. 2

Answer - Option B
Explanation -
Corresponding sector have square and cubes of a number.
[latex]{(5)}^{2}[/latex] = 25, [latex]{(5)}^{2}[/latex] = 125 and [latex]{(3)}^{2}[/latex] = 9, [latex]{(3)}^{2}[/latex] = 27 [latex]{(4)}^{2}[/latex]= 16,[latex]{(4)}^{3}[/latex] = 64 and [latex]{(7)}^{2}[/latex] = 49, [latex]{(7)}^{3}[/latex] = 343.
10. Find the missing letters

A. F, G B. F, F C. G, H D. H, F

Answer - Option A

11. Find the missing number:

A. 82 B. 83 C. 86 D. 26

Answer - Option A
Explanation -
Take the sum of the products of the upper and lower numbers respectively to get the central number.
5 × 3 = 15 and 6 × 8 = 48
15 + 48 = 63
2 × 7 = 14 and 3 × 9 = 27
14 + 27 = 41
Therefore,
6 × 7 = 42 and 8 × 5 = 40
42 + 40 = 82
12. Find the missing number:

A. 27 B. 21 C. 28 D. 17

Answer - Option B
Explanation -
7 × 4 = 28; 19 + 9 = 28
8 × 5 = 40; 28 + 12 = 14
9 × 3 = 27; 27 – 6 = 21
13. Find the missing number:

A. 35 B. 36 C. 37 D. 38

Answer - Option C
Explanation -
12 + 13 = 25
27 + 24 = 51
i.e, ? = 64 – 27 = 37
14. Find the missing number:

A. 36 B. 33 C. 45 D. 60

Answer - Option B
Explanation -
25 + 45 + 35 + 30 = 135
[latex]\frac{135}{5}[/latex] = 27
60 + 20 + 40 + 30 = 150
[latex]\frac{150}{5}[/latex] = 30
25 + 40 + 35 + 65 = 165
[latex]\frac{165}{5}[/latex] = 33
15. Find the missing number:

A. 40 B. 41 C. 31 D. 51

Answer - Option B
Explanation -
24 + 22 = 46
27 + 42 = 69
i.e, ? = 79 – 38 = 41