Exercise: Numbers

Questions for: Numbers

666 ÷ 6 ÷ 3 = ?
A:
37
B:
333
C:
111
D:
84
Answer: A
Given Exp. = 666 x 1 x 1 = 37.
6 3
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35 + 15 x 1.5 = ?
A:
85
B:
51.5
C:
57.5
D:
5.25
Answer: C
Given Exp. = 35 + 15 x 3   = 35 + 45   = 35 + 22.5   = 57.5
2 2
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854 x 854 x 854 - 276 x 276 x 276 = ?
854 x 854 + 854 x 276 + 276 x 276
A:
1130
B:
578
C:
565
D:
1156
Answer: B
Given Exp. = (a3 - b3) = (a - b) = (854 - 276) = 578
(a2 + ab + b2)
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(22 + 42 + 62 + ... + 202) = ?
A:
770
B:
1155
C:
1540
D:
385 x 385
Answer: C

(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.

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Which one of the following can't be the square of natural number ?
A:
32761
B:
81225
C:
42437
D:
20164
Answer: C

The square of a natural number never ends in 7.

42437 is not the square of a natural number.

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