Question 1
(1015)2 = ?
 A 1040125 B 1030225 C 1050125 D 1025125
Arithmetic Aptitude    Simplification and Approximation
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Question 1 Explanation:

10152 = (1000+15)2

= 10002 + 152 +2 x 1000 x 15

=1000000 + 225 + 30000

=1030225

 Question 2
103 x 103 + 97 x 97 = ?
 A 21348 B 20018 C 19648 D 21428
Arithmetic Aptitude    Simplification and Approximation
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Question 2 Explanation:
103 x 103 + 97 x 97
= (100+3)2 + (100-3)2
= 2 (1002 + 32 )
[ (X +Y)2 + ( X – Y)2 = 2 ( X2 + Y2 ) ]
= 2 (10000 + 9 )
= 2 x 10009
= 20018
 Question 3
9848 x 125 = ?
 A 1232000 B 1242000 C 1231000 D 1233000
Arithmetic Aptitude    Simplification and Approximation
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Question 3 Explanation:
9848 x 125 = 9848 x 53
= 9848 x (10 / 2) 3
= 9848 x (103 / 23)
= 9848 x (10008/8)
= 1231000
 Question 4
512 x 512 + 488 x 488 = ?
 A 512438 B 502568 C 500288 D 514318
Arithmetic Aptitude 2    Simplification and Approximation
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Question 4 Explanation:
X2 + Y2 = 1/2[(X + Y)2 + (X – Y)2]
5122 + 4882 = ½ [(512+488)2 + (512-488)2]
= 1/2[10002+242]
= 1/2(1000000+576)
= 500288
 Question 5
What should be the value of x in equation (x / √216) = (√96 / x)
 A 12 B 13 C 9 D 11
Arithmetic Aptitude 2    Simplification and Approximation
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Question 5 Explanation:
Let (x / √216) = (√96 / x)

Then x2 = √(216 x 96)
= √(36 x 2 x 3 x 16 x 2 x 3)
= √(62 x 42 x 22 x 32)
= 6 x 4 x 2 x 3
= 144
Or x = 12
 Question 6
7 + 72 + 73...........76 =?
 A 140136 B 142156 C 133256 D 137256
Arithmetic Aptitude 4    Simplification and Approximation
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Question 6 Explanation:
Given series is a G. P. with a = 7, r = 7 and n = 6

∴ Sn = a(rn-1) / (r-1)

∴ Sn = 7(76-1) / 6

Sn = = 137256
 Question 7
What could be the maximum value of Y in the following equation given that neither of X, Y, Z is zero? 5X8 + 3Y4 + 2Z1 = 1103
 A 0 B 7 C 8 D 9
Numbers    Simplification and Approximation
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Question 7 Explanation:
1 1    <- CARRY

5 X 8
+ 3 Y 4
+ 2 Z 1
--------
11 0 3
--------
Clearly, X + Y + Z + 1 = 10 => X + Y + Z = 9 Now, since neither of X, Y, Z can be zero, the value of Y will be maximum when X = Z = 1. => Max Y = 7
 Question 8
What is the unit's digit in the product (267)153 x (66666)72 ?
 A 7 B 6 C 1 D 2
Numbers    Simplification and Approximation
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Question 8 Explanation:
The unit's digit in (267)153 x (66666)72 is same as unit's digit in (7)153 x (6)72. Now, unit's digit in 74 is 1. => Unit's digit in 7z is 1, where 'z' is a multiple of 4. 152 is the nearest number to 153, which is a multiple of 4. => Unit's digit in 7152 is 1 => Unit's digit in 7153 is 1 x 7 = 7   Also, unit's digit when 6 is raised to any power remains 6, i.e., for all 'n', 6n will have 6 in the unit's place. Therefore, unit's digit in (267)153 x (66666)72 = unit's digit in (7)153 x (6)72 = unit's digit in 7 x 6 = 2 Hence, D (2) is the correct answer.
 Question 9
√7321 x 35.999 = ?
 A 3060 B 3204 C 3410 D 2930
Simplification and Approximation
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Question 9 Explanation:
85*9*100/25=765*4=3060
 Question 10
5432.91 ÷ 2324.65 × 210.05 =?
 A 471 B 431 C 491 D 501
Simplification and Approximation
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Question 10 Explanation:
Approx: 2.3*210 = 483
 Question 11
25.675% of 1321 + 64.328% of 4001=?
 A 3121 B 3038 C 2912 D 2821
Simplification and Approximation
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Question 11 Explanation:
1321/4+0.64*4001 =330+2560 = 2890
 Question 12
(5√7 + 2√7) (6√7 + 3√7)= ?
 A 521 B 381 C 441 D 481
Simplification and Approximation
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Question 12 Explanation:
7*7*9 = 441
 Question 13
(38/85) x (255/114) ÷ (19/5) + (14/19) = ?
 A 2.3 B 1 C 4.7 D 3.8
Simplification and Approximation
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Question 13 Explanation:
0.4*2.2/4+.68 = .88/4+.68 = .22+.68 = .9
 Question 14
(14.2)²+ (16.4)² − (17.9)² = ? + 32.99
 A 100 B 125 C 130 D 117
Simplification and Approximation
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Question 14 Explanation:
198+265 – 320 =x + 33 463-357 =x x > 106 (approx)
 Question 15
 A 84/305 B 62/205 C 84/254 D 72/305
Simplification and Approximation
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Question 15 Explanation:
 Question 16
 A 141/12 B 131/12 C 121/12 D 111/12
Simplification and Approximation
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Question 16 Explanation:
 Question 17
If a * b = 2a - 4b + 2ab, then 3*4 + 4*3 = ?
 A 26 B 34 C 24 D 28
Simplification and Approximation
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Question 17 Explanation:
3*4 = 6-16+24 =14 4*3 = 20 =>14+20 = 34
 Question 18
b - [b -(a+b) - {b - (b - a+b)} + 2a] = ?
 A 2a B a+b C b-2a D 0
Simplification and Approximation
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Question 18 Explanation:
BODMAS rule b - [b -(a+b) - {b - (2b - a)} + 2a] b-[b-a-b-{-b+a}+2a] b-[b-a-b-a+b+2a] b-b=0
 Question 19
5 + 5 / 5 = ?
 A 6 B 2 C 1 D 10
Simplification and Approximation
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Question 19 Explanation:
5+1 = 6
 Question 20
25 / 5 × 5 = ?
 A 1 B 25 C 5 D 125
Simplification and Approximation
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Question 20 Explanation:
5*5 =25
 Question 21
8 / 4 / 2 = ?
 A 1 B 4 C 8 D 2
Simplification and Approximation
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Question 21 Explanation:
(8/4)/2 = 2/2 =1
 Question 22
[(723+1992)2−(723−1992)2]/(723×1992) = ?
 A 4 B 723 C 1992 D 2715
Simplification and Approximation
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Question 22 Explanation:
4*723*1992/(723*1992) = 4
 Question 23
If p - q = 6 and p2 + q2 = 116, what is the value of pq?
 A 20 B 60 C 40 D 10
Simplification and Approximation
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Question 23 Explanation:
p2 + q2 -2pq = 36 => pq = 40
There are 23 questions to complete.

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