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OverviewExercise"To err is human; to forgive, divine."
- Alexander Pope
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| 21. |
Which of the following number is divisible by 24 ?
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Answer: Option D
Explanation:
24 = 3 x8, where 3 and 8 co-prime.
Clearly, 35718 is not divisible by 8, as 718 is not divisible by 8.
Similarly, 63810 is not divisible by 8 and 537804 is not divisible by 8.
Cibsuder oart (d).
Sum of digits = (3 + 1 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 3.
Also, 736 is divisible by 8.
 3125736 is divisible by (3 x 8), i.e., 24.
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| 22. |
| 753 x 753 + 247 x 247 - 753 x 247 |
= ? |
| 753 x 753 x 753 + 247 x 247 x 247 |
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Answer: Option A
Explanation:
| Given Exp. = |
(a2 + b2 - ab) |
= |
1 |
= |
1 |
= |
1 |
| (a3 + b3) |
(a + b) |
(753 + 247) |
1000 |
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| 23. |
(?) + 3699 + 1985 - 2047 = 31111
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Answer: Option D
Explanation:
x + 3699 + 1985 - 2047 = 31111
 x + 3699 + 1985 = 31111 + 2047
x + 5684 = 33158
x = 33158 - 5684 = 27474.
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| 24. |
If the number 481 * 673 is completely divisible by 9, then the smallest whole number in place of * will be:
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Answer: Option B
Explanation:
Sum of digits = (4 + 8 + 1 + x + 6 + 7 + 3) = (29 + x), which must be divisible by 9.
x = 7.
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| 25. |
The difference between the local value and the face value of 7 in the numeral 32675149 is
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Answer: Option A
Explanation:
(Local value of 7) - (Face value of 7) = (70000 - 7) = 69993
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| 26. |
The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is: |
Answer: Option B
Explanation:
| Let the required fraction be x. Then |
1 |
- x = |
9 |
| x |
20 |
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1 - x2 |
= |
9 |
| x |
20 |
20 - 20x2 = 9x
20x2 + 9x - 20 = 0
20x2 + 25x - 16x - 20 = 0
5x(4x + 5) - 4(4x + 5) = 0
(4x + 5)(5x - 4) = 0
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| 27. |
On dividing a number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder ? |
Answer: Option D
Explanation:
No answer description available for this question. Let us discuss.
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| 28. |
If n is a natural number, then (6n2 + 6n) is always divisible by:
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| A. |
6 only | B. |
6 and 12 both | | C. |
12 only | D. |
by 18 only |
Answer: Option A
Explanation:
(6n2 + 6n) = 6n(n + 1), which is always divisible by 6 and 12 both, since n(n + 1) is always even.
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| 29. |
107 x 107 + 93 x 93 = ?
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Answer: Option C
Explanation:
| 107 x 107 + 93 x 93 |
= (107)2 + (93)2 |
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= (100 + 7)2 + (100 - 7)2 |
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= 2 x [(100)2 + 72] [Ref: (a + b)2 + (a - b)2 = 2(a2 + b2)] |
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= 20098 |
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| 30. |
What will be remainder when (6767 + 67) is divided by 68 ?
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Answer: Option D
Explanation:
(xn + 1) will be divisible by (x + 1) only when n is odd.
(6767 + 1) will be divisible by (67 + 1)
(6767 + 1) + 66, when divided by 68 will give 66 as remainder.
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