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OverviewExercise"No one is as deaf as the man who will not listen."
- (Proverb)
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| 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 ?
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Answer: Option C
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
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| 62. |
(51 + 52 + 53 + ... + 100) = ?
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Answer: Option C
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.
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| 63. |
(800 ÷ 64) x (1296 ÷36) = ?
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Answer: Option E
Explanation:
| Given Exp. = |
800 |
x |
1296 |
= 450 |
| 64 |
36 |
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| 64. |
Which natural number is nearest to 8485, which is completely divisible by 75 ? |
Answer: Option C
Explanation:
On dividing, we get
75) 8485 (113
75
---
98
75
----
235
225
---
10
---
Required number = (8485 - 10)
= 8475.
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| 65. |
If the number 42573 * is exactly divisible by 72, then the minimum value of * is:
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Answer: Option E
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.
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| 66. |
Which of the following numbers is divisible by each one of 3, 7, 9 and 11 ?
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Answer: Option E
Explanation:
639 is not divisible by 7
2079 is divisible by each of 3, 7, 9, 11.
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| 67. |
Which natural number is nearest to 9217, which is completely divisible by 88 ?
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Answer: Option B
Explanation:
On dividing we get,
88) 9217 (104
88
----
417
352
----
65
----
Therefore, Required number = 9217 + (88 -65)
= 9217 + 23
= 9240.
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| 68. |
(4300731) - ? = 2535618
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| A. |
1865113 | B. |
1775123 | | C. |
1765113 | D. |
1675123 | | E. |
None of these |
Answer: Option B
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 ?
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Answer: Option A
Explanation:
Let n = 4q + 3. Then 2n = 8q + 6 = 4(2q + 1 ) + 2.
Thus, when 2n is divided by 4, the remainder is 2.
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| 70. |
| (489 + 375)2 - (489 - 375)2 |
= ? |
| (489 x 375) |
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Answer: Option B
Explanation:
| Given Exp. = |
(a + b)2 - (a - b)2 |
= |
4ab |
= 4 |
| ab |
ab |
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