Question:
3251 + 587 + 369 – ? = 3007

[A].

1250

[B].

1300

[C].

1375

[D].

1200

Answer: Option D

Explanation:

3251 Let 4207 – x = 3007
+ 587 Then, x = 4207 – 3007 = 1200
+ 369
—-
4207
—-

Question: How many of the following numbers are divisible by 132 ?
264, 396, 462, 792, 968, 2178, 5184, 6336
[A].

4

[B].

5

[C].

6

[D].

7

Answer: Option A

Explanation:

132 = 4 x 3 x 11

So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also.

264 11,3,4 (/)

396 11,3,4 (/)

462 11,3 (X)

792 11,3,4 (/)

968 11,4 (X)

2178 11,3 (X)

5184 3,4 (X)

6336 11,3,4 (/)

Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336.

Required number of number = 4.

Question:
Which of the following numbers is divisible by each one of 3, 7, 9 and 11 ?

[A].

639

[B].

2079

[C].

3791

[D].

37911

Answer: Option B

Explanation:

639 is not divisible by 7

2079 is divisible by each of 3, 7, 9, 11.

Question: How many of the following numbers are divisible by 3 but not by 9 ?
2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276
[A].

5

[B].

6

[C].

7

[D].

None of these

Answer: Option B

Explanation:

Marking (/) those which are are divisible by 3 by not by 9 and the others by (X), by taking the sum of digits, we get:s

2133 9 (X)

2343 12 (/)

3474 18 (X)

4131 9 (X)

5286 21 (/)

5340 12 (/)

6336 18 (X)

7347 21 (/)

8115 15 (/)

9276 24 (/)

Required number of numbers = 6.

Question:
If the number 653 xy is divisible by 90, then (x + y) = ?

[A].

2

[B].

3

[C].

4

[D].

6

Answer: Option C

Explanation:

90 = 10 x 9

Clearly, 653xy is divisible by 10, so y = 0

Now, 653×0 is divisible by 9.

So, (6 + 5 + 3 + x + 0) = (14 + x) is divisible by 9. So, x = 4.

Hence, (x + y) = (4 + 0) = 4.

Question:
If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will be divisible by 11 ?

[A].

4x + 6y

[B].

x + y + 4

[C].

9x + 4y

[D].

4x – 9y

Answer: Option D

Explanation:

By hit and trial, we put x = 5 and y = 1 so that (3x + 7y) = (3 x 5 + 7 x 1) = 22, which is divisible by 11.

(4x + 6y) = ( 4 x 5 + 6 x 1) = 26, which is not divisible by 11;

(x + y + 4 ) = (5 + 1 + 4) = 10, which is not divisible by 11;

(9x + 4y) = (9 x 5 + 4 x 1) = 49, which is not divisible by 11;

(4x – 9y) = (4 x 5 – 9 x 1) = 11, which is divisible by 11.

Question: A 3-digit number 4a3 is added to another 3-digit number 984 to give a 4-digit number 13b7, which is divisible by 11. Then, (a + b) = ?

[A].

10

[B].

11

[C].

12

[D].

15

Answer: Option A

Explanation:

4 a 3 |
9 8 4 } ==> a + 8 = b ==> b – a = 8
13 b 7 |

Also, 13 b7 is divisible by 11      (7 + 3) – (b + 1) = (9 – b)

  (9 – b) = 0

  b = 9

(b = 9 and a = 1)     (a + b) = 10.

Question:
Which of the following numbers will completely divide (325 + 326 + 327 + 328) ?

[A].

11

[B].

16

[C].

25

[D].

30

Answer: Option D

Explanation:

(325 + 326 + 327 + 328) = 325 x (1 + 3 + 32 + 33) = 325 x 40

     = 324 x 3 x 4 x 10

     = (324 x 4 x 30), which is divisible by30.

Question:
Which of the following numbers will completely divide (461 + 462 + 463 + 464) ?

[A].

3

[B].

10

[C].

11

[D].

13

Answer: Option B

Explanation:

(461 + 462 + 463 + 464) = 461 x (1 + 4 + 42 + 43) = 461 x 85

     = 460 x (4 x 85)

     = (460 x 340), which is divisible by 10.

Question: It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
[A].

(216 + 1)

[B].

(216 – 1)

[C].

(7 x 223)

[D].

(296 + 1)

Answer: Option D

Explanation:

Let 232 = x. Then, (232 + 1) = (x + 1).

Let (x + 1) be completely divisible by the natural number N. Then,

(296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 – x + 1), which is completely divisible by N, since (x + 1) is divisible by N.