Aptitude - Numbers

Exercise :: Numbers - General Questions

31. 

On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5 ?

A. 0
B. 1
C. 2
D. 4

Answer: Option D

Explanation:

Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder.

    x = 5k + 3

    x2 = (5k + 3)2

   = (25k2 + 30k + 9)

   = 5(5k2 + 6k + 1) + 4

On dividing x2 by 5, we get 4 as remainder.


32. 

How many 3-digit numbers are completely divisible 6 ?

A. 149
B. 150
C. 151
D. 166

Answer: Option B

Explanation:

3-digit number divisible by 6 are: 102, 108, 114,... , 996

This is an A.P. in which a = 102, d = 6 and l = 996

Let the number of terms be n. Then tn = 996.

a + (n - 1)d = 996

102 + (n - 1) x 6 = 996

6 x (n - 1) = 894

(n - 1) = 149

n = 150

Number of terms = 150.


33. 

How many natural numbers are there between 23 and 100 which are exactly divisible by 6 ?

A. 8
B. 11
C. 12
D. 13
E. None of these

Answer: Option D

Explanation:

Required numbers are 24, 30, 36, 42, ..., 96

This is an A.P. in which a = 24, d = 6 and l = 96

Let the number of terms in it be n.

Then tn = 96    a + (n - 1)d = 96

24 + (n - 1) x 6 = 96

(n - 1) x 6 = 72

(n - 1) = 12

n = 13

Required number of numbers = 13.


34. 

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.


35. 

(963 + 476)2 + (963 - 476)2 = ?
(963 x 963 + 476 x 476)

A. 1449
B. 497
C. 2
D. 4
E. None of these

Answer: Option C

Explanation:

Given Exp. = (a + b)2 + (a - b)2 = 2(a2 + b2) = 2
(a2 + b2) (a2 + b2)

36. 

How many 3 digit numbers are divisible by 6 in all ?

A. 149
B. 150
C. 151
D. 166

Answer: Option B

Explanation:

Required numbers are 102, 108, 114, ... , 996

This is an A.P. in which a = 102, d = 6 and l = 996

Let the number of terms be n. Then,

a + (n - 1)d = 996

   102 + (n - 1) x 6 = 996

   6 x (n - 1) = 894

   (n - 1) = 149

   n = 150.


37. 

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.


38. 

8597 - ? = 7429 - 4358

A. 5426
B. 5706
C. 5526
D. 5476
E. None of these

Answer: Option C

Explanation:

 7429          Let 8597 - x = 3071
-4358          Then,      x = 8597 - 3071
 ----                       = 5526
 3071
 ----

39. 

The smallest prime number is:

A. 1
B. 2
C. 3
D. 4

Answer: Option B

Explanation:

The smallest prime number is 2.

40. 

(12345679 x 72) = ?

A. 88888888
B. 888888888
C. 898989898
D. 9999999998

Answer: Option B

Explanation:

12345679 x 72 = 12345679 x (70 +2)
= 12345679 x 70 + 12345679 x 2
= 864197530 + 24691358
= 888888888