Aptitude - Numbers

Exercise : 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:
7 and 4
7 and 5
8 and 5
None of these
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:
3
2
1
5
None of these
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) = ?
385
2485
2870
3255
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 * = ?
2
3
6
7
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) ?
8
14
46
50
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.