Aptitude - Numbers
Exercise : Numbers - General Questions
- Numbers - Formulas
- Numbers - General Questions
26.
The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is:
Answer: Option
Explanation:
Let the required fraction be x. Then | 1 | - x = | 9 |
x | 20 |
1 - x^{2} | = | 9 | |
x | 20 |
20 - 20x^{2} = 9x
20x^{2} + 9x - 20 = 0
20x^{2} + 25x - 16x - 20 = 0
5x(4x + 5) - 4(4x + 5) = 0
(4x + 5)(5x - 4) = 0
x = | 4 |
5 |
27.
On dividing a number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder ?
Answer: Option
Explanation:
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.
28.
If n is a natural number, then (6n^{2} + 6n) is always divisible by:
Answer: Option
Explanation:
(6n^{2} + 6n) = 6n(n + 1), which is always divisible by 6 and 12 both, since n(n + 1) is always even.
29.
107 x 107 + 93 x 93 = ?
Answer: Option
Explanation:
107 x 107 + 93 x 93 | = (107)^{2} + (93)^{2} |
= (100 + 7)^{2} + (100 - 7)^{2} | |
= 2 x [(100)^{2} + 7^{2}] [Ref: (a + b)^{2} + (a - b)^{2} = 2(a^{2} + b^{2})] | |
= 20098 |
30.
What will be remainder when (67^{67} + 67) is divided by 68 ?
Answer: Option
Explanation:
(x^{n} + 1) will be divisible by (x + 1) only when n is odd.
(67^{67} + 1) will be divisible by (67 + 1)
(67^{67} + 1) + 66, when divided by 68 will give 66 as remainder.
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers