Exercise: Numbers

Questions for: Numbers

What will be remainder when (6767 + 67) is divided by 68 ?
A:
1
B:
63
C:
66
D:
67
Answer: C

(xn + 1) will be divisible by (x + 1) only when n is odd.

(6767 + 1) will be divisible by (67 + 1)

(6767 + 1) + 66, when divided by 68 will give 66 as remainder.

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107 x 107 + 93 x 93 = ?
A:
19578
B:
19418
C:
20098
D:
21908
Answer: C
107 x 107 + 93 x 93 = (107)2 + (93)2
= (100 + 7)2 + (100 - 7)2
= 2 x [(100)2 + 72]       [Ref: (a + b)2 + (a - b)2 = 2(a2 + b2)]
= 20098
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If n is a natural number, then (6n2 + 6n) is always divisible by:
A:
6 only
B:
6 and 12 both
C:
12 only
D:
by 18 only
Answer: B

(6n2 + 6n) = 6n(n + 1), which is always divisible by 6 and 12 both, since n(n + 1) is always even.

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On dividing a number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder ?
A:
4
B:
5
C:
6
D:
7
Answer: B

Formula: (Divisor*Quotient) + Remainder = Dividend.

Soln:

(56*Q)+29 = D -------(1)

D%8 = R -------------(2)

From equation(2),

((56*Q)+29)%8 = R.

=> Assume Q = 1.

=> (56+29)%8 = R.

=> 85%8 = R

=> 5 = R.

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The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is:
A:
3
5
B:
3
10
C:
4
5
D:
4
3
Answer: C

Let the required fraction be x. Then 1 - x = 9
x 20

    1 - x2 = 9
x 20

     20 - 20x2 = 9x

     20x2 + 9x - 20 = 0

     20x2 + 25x - 16x - 20 = 0

     5x(4x + 5) - 4(4x + 5) = 0

     (4x + 5)(5x - 4) = 0

x = 4
5

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