Overview Exercise "Loneliness is the most terrible poverty."
- Mother Teresa
41.
On dividing a number by 357, we get 39 as remainder. On dividing the same number 17, what will be the remainder ?
Answer: B
Explanation:
Let x be the number and y be the quotient. Then,
x = 357 x y + 39
= (17 x 21 x y ) + (17 x 2) + 5
= 17 x (21y + 2) + 5)
42.
If the product 4864 x 9 P 2 is divisible by 12, then the value of P is:
Answer: B
Explanation:
Clearly, 4864 is divisible by 4.
So, 9P2 must be divisible by 3. So, (9 + P + 2) must be divisible by 3.
43.
Which one of the following is the common factor of (4743 + 4343 ) and (4747 + 4347 ) ?
A. (47 - 43) B. (47 + 43) C. (4743 + 4343 ) D. None of these
Answer: E
Explanation:
When n is odd, (x n a n x + a ).
43 + 4343 ) and (4747 + 4343 ) is divisible by (47 + 43).
44.
-84 x 29 + 365 = ?
Answer: B
Explanation:
Given Exp.
= -84 x (30 - 1) + 365
= -(84 x 30) + 84 + 365
= -2520 + 449
= -2071
45.
A number when divided by 296 leaves 75 as remainder. When the same number is divided by 37, the remainder will be:
Answer: E
Explanation:
Let x = 296q + 75
= (37 x 8q + 37 x 2) + 1
= 37 (8q + 2) + 1
Thus, when the number is divided by 37, the remainder is 1.
46.
In dividing a number by 585, a student employed the method of short division. He divided the number successively by 5, 9 and 13 (factors 585) and got the remainders 4, 8, 12 respectively. If he had divided the number by 585, the remainder would have been
Answer: E
Explanation:
5 | x z = 13 x 1 + 12 = 25
--------------
9 | y - 4 y = 9 x z + 8 = 9 x 25 + 8 = 233
--------------
13| z - 8 x = 5 x y + 4 = 5 x 233 + 4 = 1169
--------------
| 1 -12
585) 1169 (1
585
---
584
---
Therefore, on dividing the number by 585, remainder = 584.
47.
In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 46, what is the dividend ?
Answer: B
Explanation:
Divisor = (5 x 46) = 230
230
= 23
10
Dividend = (Divisor x Quotient) + Remainder
= (230 x 23) + 46
= 5290 + 46
= 5336.
48.
4500 x ? = 3375
Answer: A
Explanation:
4500 x x = 3375 x =
3375 75 =
3
4500 100 4
49.
What smallest number should be added to 4456 so that the sum is completely divisible by 6 ?
Answer: D
Explanation:
6) 4456 (742
42
---
25
24 Therefore, Required number = (6 - 4) = 2.
---
16
12
---
4
50.
What least number must be subtracted from 13601, so that the remainder is divisible by 87 ?
Answer: A
Explanation:
87) 13601 (156
87
----
490
435
----
551
522
---
29
---
Therefore, the required number = 29.
Required remainder = 5.
=