Aptitude - Numbers
Exercise : Numbers - General Questions
- Numbers - Formulas
- Numbers - General Questions
1.
Which one of the following is not a prime number?
Answer: Option
Explanation:
91 is divisible by 7. So, it is not a prime number.
2.
(112 x 5^{4}) = ?
Answer: Option
Explanation:
(112 x 5^{4}) = 112 x | 10 | 4 | = | 112 x 10^{4} | = | 1120000 | = 70000 | ||
2 | 2^{4} | 16 |
3.
It is being given that (2^{32} + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
Answer: Option
Explanation:
Let 2^{32} = x. Then, (2^{32} + 1) = (x + 1).
Let (x + 1) be completely divisible by the natural number N. Then,
(2^{96} + 1) = [(2^{32})^{3} + 1] = (x^{3} + 1) = (x + 1)(x^{2} - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.
4.
What least number must be added to 1056, so that the sum is completely divisible by 23 ?
Answer: Option
Explanation:
23) 1056 (45 92 --- 136 115 --- 21 --- Required number = (23 - 21) = 2.
5.
1397 x 1397 = ?
Answer: Option
Explanation:
1397 x 1397 | = (1397)^{2} |
= (1400 - 3)^{2} | |
= (1400)^{2} + (3)^{2} - (2 x 1400 x 3) | |
= 1960000 + 9 - 8400 | |
= 1960009 - 8400 | |
= 1951609. |
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