Aptitude - Numbers
Exercise : Numbers - General Questions
- Numbers - Formulas
- Numbers - General Questions
51.
476 ** 0 is divisible by both 3 and 11. The non-zero digits in the hundred's and ten's places are respectively:
Answer: Option
Explanation:
Let the given number be 476 xy 0.
Then (4 + 7 + 6 + x + y + 0) = (17 + x + y) must be divisible by 3.
And, (0 + x + 7) - (y + 6 + 4) = (x - y -3) must be either 0 or 11.
x - y - 3 = 0 y = x - 3
(17 + x + y) = (17 + x + x - 3) = (2x + 14)
x= 2 or x = 8.
x = 8 and y = 5.
52.
If the number 97215 * 6 is completely divisible by 11, then the smallest whole number in place of * will be:
Answer: Option
Explanation:
Given number = 97215x6
(6 + 5 + 2 + 9) - (x + 1 + 7) = (14 - x), which must be divisible by 11.
x = 3
53.
(112 + 122 + 132 + ... + 202) = ?
Answer: Option
Explanation:
(112 + 122 + 132 + ... + 202) = (12 + 22 + 32 + ... + 202) - (12 + 22 + 32 + ... + 102)
![]() |
Ref: (12 + 22 + 32 + ... + n2) = | 1 | n(n + 1)(2n + 1) | ![]() |
|
6 |
= | ![]() |
20 x 21 x 41 | - | 10 x 11 x 21 | ![]() |
6 | 6 |
= (2870 - 385)
= 2485.
54.
If the number 5 * 2 is divisible by 6, then * = ?
Answer: Option
Explanation:
6 = 3 x 2. Clearly, 5 * 2 is divisible by 2. Replace * by x.
Then, (5 + x + 2) must be divisible by 3. So, x = 2.
55.
Which of the following numbers will completely divide (4915 - 1) ?
Answer: Option
Explanation:
(xn - 1) will be divisibly by (x + 1) only when n is even.
(4915 - 1) = {(72)15 - 1} = (730 - 1), which is divisible by (7 +1), i.e., 8.
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