Aptitude - Numbers

Exercise :: Numbers - General Questions

91. 

Which one of the following is a prime number ?

A. 161
B. 221
C. 373
D. 437
E. None of these

Answer: Option C

Explanation:

437 > 22

All prime numbers less than 22 are : 2, 3, 5, 7, 11, 13, 17, 19.

161 is divisible by 7, and 221 is divisible by 13.

373 is not divisible by any of the above prime numbers.

373 is prime.


92. 

The smallest 6 digit number exactly divisible by 111 is:

A. 111111
B. 110011
C. 100011
D. 110101
E. None of these

Answer: Option C

Explanation:

The smallest 6-digit number 100000.

 111) 100000 (900
      999
      -----
        100
        ---

 Required number = 100000 + (111 - 100)
                 = 100011.       

93. 

The largest 5 digit number exactly divisible by 91 is:

A. 99921
B. 99918
C. 99981
D. 99971
E. None of these

Answer: Option B

Explanation:

Largest 5-digit number = 99999

 91) 99999 (1098
     91
     ---
     899
     819
     ----
      809
      728
      ---
       81
      ---
 
 Required number = (99999 - 81)
                 = 99918.      

94. 

768 x 768 x 768 + 232 x 232 x 232 = ?
768 x 768 - 768 x 232 + 232 x 232

A. 1000
B. 536
C. 500
D. 268
E. None of these

Answer: Option A

Explanation:

Given Exp. = (a3 + b3) = (a + b) = (768 + 232) = 1000
(a2 - ab + b2)

95. 

The smallest 5 digit number exactly divisible by 41 is:

A. 1004
B. 10004
C. 10045
D. 10025
E. None of these

Answer: Option B

Explanation:

The smallest 5-digit number = 10000.

 41) 10000 (243
     82
     ---
     180
     164
     ----
      160
      123
      ---
       37
      --- 

 Required number = 10000 + (41 - 37)
                 = 10004.      

96. 

How many terms are there in the G.P. 3, 6, 12, 24, ... , 384 ?

A. 8
B. 9
C. 10
D. 11
E. 7

Answer: Option A

Explanation:

Here a = 3 and r = 6 = 2. Let the number of terms be n.
3

Then, tn = 384     arn-1 = 384

3 x 2n - 1 = 384

2n-1 = 128 = 27

n - 1 = 7

n = 8

Number of terms = 8.


97. 

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.


98. 

9548 + 7314 = 8362 + (?)

A. 8230
B. 8410
C. 8500
D. 8600
E. None of these

Answer: Option C

Explanation:

  9548          16862 = 8362 + x 
+ 7314          x  = 16862 - 8362 
 -----             = 8500 
 16862
 ----- 

99. 

In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 35 as quotient. What is the correct quotient ?

A. 0
B. 12
C. 13
D. 20

Answer: Option D

Explanation:

Number = (12 x 35)

Correct Quotient = 420 21 = 20


100. 

2 + 22 + 23 + ... + 29 = ?

A. 2044
B. 1022
C. 1056
D. None of these

Answer: Option B

Explanation:

This is a G.P. in which a = 2, r = 22 = 2 and n = 9.
2

Sn = a(rn - 1) = 2 x (29 - 1) = 2 x (512 - 1)   = 2 x 511   = 1022.
(r - 1) (2 - 1)