Aptitude - Numbers

Exercise :: Numbers - General Questions

41. 

On dividing a number by 357, we get 39 as remainder. On dividing the same number 17, what will be the remainder ?

A. 0
B. 3
C. 5
D. 11

Answer: Option C

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)

Required remainder = 5.


42. 

If the product 4864 x 9 P 2 is divisible by 12, then the value of P is:

A. 2
B. 5
C. 6
D. 8
E. None of these

Answer: Option E

Explanation:

Clearly, 4864 is divisible by 4.

So, 9P2 must be divisible by 3. So, (9 + P + 2) must be divisible by 3.

P = 1.


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: Option B

Explanation:

When n is odd, (xn + an) is always divisible by (x + a).

Each one of (4743 + 4343) and (4747 + 4347) is divisible by (47 + 43).


44. 

-84 x 29 + 365 = ?

A. 2436
B. 2801
C. -2801
D. -2071
E. None of these

Answer: Option D

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:

A. 1
B. 2
C. 8
D. 11

Answer: Option A

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

A. 24
B. 144
C. 292
D. 584

Answer: Option D

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 ?

A. 4236
B. 4306
C. 4336
D. 5336
E. None of these

Answer: Option D

Explanation:

Divisor = (5 x 46) = 230

10 x Quotient = 230     = 230 = 23
10

Dividend = (Divisor x Quotient) + Remainder

    = (230 x 23) + 46

    = 5290 + 46

    = 5336.


48. 

4500 x ? = 3375

A.
2
5
B.
3
4
C.
1
4
D.
3
5
E. None of these

Answer: Option B

Explanation:

4500 x x = 3375      x = 337575 = 3
4500100 4

49. 

What smallest number should be added to 4456 so that the sum is completely divisible by 6 ?

A. 4
B. 3
C. 2
D. 1
E. None of these

Answer: Option C

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 ?

A. 23
B. 31
C. 29
D. 37
E. 49

Answer: Option C

Explanation:

 87) 13601 (156
     87
     ----
      490
      435
      ----
       551
       522
       ---
        29
       ---
       
 Therefore, the required number = 29.