61.
When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ?
A. 339 B. 349
C. 369 D. Data inadequate
Answer & Explanation
Answer: Option B
Explanation:
x = 13p + 11 and x = 17q + 9
13p + 11 = 17q + 9
17q – 13p = 2
q = 2 + 13p
17
The least value of p for which q = 2 + 13p is a whole number is p = 26
17
x = (13 x 26 + 11)
= (338 + 11)
= 349
62.
(51 + 52 + 53 + … + 100) = ?
A. 2525 B. 2975
C. 3225 D. 3775
Answer & Explanation
Answer: Option D
Explanation:
Sn = (1 + 2 + 3 + … + 50 + 51 + 52 + … + 100) – (1 + 2 + 3 + … + 50)
= 100 x (1 + 100) – 50 x (1 + 50)
2 2
= (50 x 101) – (25 x 51)
= (5050 – 1275)
= 3775.
63.
(800 ÷ 64) x (1296 ÷36) = ?
A. 420 B. 460
C. 500 D. 540
E. None of these
Answer & Explanation
Answer: Option E
Explanation:
Given Exp. = 800 x 1296 = 450
64 36
64.
Which natural number is nearest to 8485, which is completely divisible by 75 ?
A. 8475 B. 8500
C. 8550 D. 8525
E. None of these
65.
If the number 42573 * is exactly divisible by 72, then the minimum value of * is:
A. 4 B. 5
C. 6 D. 7
E. 8
Answer & Explanation
Answer: Option C
Explanation:
72 = 9 x8, where 9 and 8 are co-prime.
The minimum value of x for which 73x for which 73x is divisible by 8 is, x = 6.
Sum of digits in 425736 = (4 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 9.
Required value of * is 6.
66.
Which of the following numbers is divisible by each one of 3, 7, 9 and 11 ?
A. 639 B. 2079
C. 3791 D. 37911
E. None of these
67.
Which natural number is nearest to 9217, which is completely divisible by 88 ?
A. 9152 B. 9240
C. 9064 D. 9184
E. None of these
Answer & Explanation
Answer: Option B
Explanation:
On dividing we get,
88) 9217 (104
88
—-
417
352
—-
65
—-
Therefore, Required number = 9217 + (88 – 65) // Because (88 – 65) < 65.
= 9217 + 23
= 9240.
68.
(4300731) – ? = 2535618
A. 1865113 B. 1775123
C. 1765113 D. 1675123
E. None of these
Answer & Explanation
Answer: Option C
Explanation:
Let 4300731 – x = 2535618
Then x, = 4300731 – 2535618 = 1765113
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69.
n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4 ?
A. 3 B. 2
C. 1 D. 0
Answer & Explanation
Answer: Option B
Explanation:
Let n = 4q + 3. Then 2n = 8q + 6 = 4(2q + 1 ) + 2.
Thus, when 2n is divided by 4, the remainder is 2.
70.
(489 + 375)2 – (489 – 375)2 = ?
(489 x 375)
A. 144 B. 864
C. 2 D. 4
E. None of these
Answer & Explanation
Answer: Option D
Explanation:
Given Exp. = (a + b)2 – (a – b)2 = 4ab = 4
ab ab