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)