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Aptitude - Numbers

Exercise : Numbers - General Questions
111.
If (64)2 - (36)2 = 20 x x, then x = ?
70
120
180
140
None of these
Answer: Option
Explanation:

20 x x = (64 + 36)(64 - 36) = 100 x 28

     x = 100 x 28 = 140
20

112.
Which one of the following can't be the square of natural number ?
32761
81225
42437
20164
None of these
Answer: Option
Explanation:

The square of a natural number never ends in 7.

42437 is not the square of a natural number.

113.
(22 + 42 + 62 + ... + 202) = ?
770
1155
1540
385 x 385
Answer: Option
Explanation:

(22 + 42 + 62 + ... + 202) = (1 x 2)2 + (2 x 2)2 + (2 x 3)2 + ... + (2 x 10)2

= (22 x 12) + (22 x 22) + (22 x 32) + ... + (22 x 102)

= 22 x [12 + 22 + 32 + ... + 102]

Ref: (12 + 22 + 32 + ... + n2) = 1 n(n + 1)(2n + 1)    
6

= 4 x 1 x 10 x 11 x 21
6

= (4 x 5 x 77)

= 1540.

114.
854 x 854 x 854 - 276 x 276 x 276 = ?
854 x 854 + 854 x 276 + 276 x 276
1130
578
565
1156
None of these
Answer: Option
Explanation:
Given Exp. = (a3 - b3) = (a - b) = (854 - 276) = 578
(a2 + ab + b2)
115.
35 + 15 x 1.5 = ?
85
51.5
57.5
5.25
None of these
Answer: Option
Explanation:
Given Exp. = 35 + 15 x 3   = 35 + 45   = 35 + 22.5   = 57.5
2 2
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