numbers aptitude questions

91.

Which one of the following is a prime number ?
A.     161    B.     221
C.     373    D.     437
E.     None of these
Answer & Explanation

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 & Explanation

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 & Explanation

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 & Explanation

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 & Explanation

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 & Explanation

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 & Explanation

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

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 & Explanation

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 & Explanation

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)

 

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