Quantitative Aptitude

General Questions

Quantitative Aptitude Exercise Mode

General Questions

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Question 31
A number when divided successively by 4 and 5 leaves remainders 1 and 4 respectively. When it is successively divided by 5 and 4, then the respective remainders will be:

A
1, 2
B
2, 3
C
3, 2
D
4, 1
Correct Answer: Option B 
 4 | x       y = (5 x 1 + 4) = 9
 --------
 5 | y -1    x  = (4 x y + 1)
             = (4 x 9 + 1) = 37
 --------
   | 1 -4

Now, 37 
when divided successively by 5 and 4, 
we get

 5 | 37
 ---------
 4 | 7 - 2
 ---------
   | 1 - 3
 
Respective remainders are 2 and 3.
Question 32
Which one of the following can't be the square of natural number ?

A
30976
B
75625
C
28561
D
143642
E
None of these
Correct Answer: Option D

The square of a natural number never ends in 2.

 143642 is not the square of natural number.

Question 33
{(476 + 424)2 - 4 x 476 x 424} = ?

A
2906
B
3116
C
2704
D
2904
E
None of these
Correct Answer: Option C

Given Exp.

= [(a + b)2 - 4ab], where a = 476 and b = 424
= [(476 + 424)2 - 4 x 476 x 424]
= [(900)2 - 807296]
= 810000 - 807296
= 2704.
Question 34
8796 x 223 + 8796 x 77 = ?

A
2736900
B
2638800
C
2658560
D
2716740
E
None of these
Correct Answer: Option B

[Ref: By Distributive Law ]

8796 x 223 + 8796 x 77 = 8796 x (223 + 77)   
= (8796 x 300)
= 2638800
Question 35
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
Correct Answer: Option A 
On dividing, we get

 75) 8485 (113
     75
     ---
      98
      75
      ----
       235
       225
       ---
        10
       ---
 
Required number = (8485 - 10) 
// Because 10 < (75 - 10)
                 = 8475.
Question 36
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
Correct Answer: Option B 
On dividing we get, 

 88) 9217 (104
     88
     ----
      417
      352
      ----
       65
      ----
  
Therefore, 
Required number = 9217 + (88 - 65) 
// Because (88 - 65) < 65.

                       = 9217 + 23
                       = 9240.
Question 37
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
Correct Answer: Option B

639 is not divisible by 7

2079 is divisible by each of 3, 7, 9, 11.

Question 38
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
Correct Answer: Option B

Let n = 4q + 3. Then 2n = 8q + 6 = 4(2q + 1 ) + 2.

Thus, when 2n is divided by 4, the remainder is 2.

Question 39
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
Correct Answer: Option C

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.

Question 40
Which one of the following numbers is completely divisible by 45?

A
181560
B
331145
C
202860
D
2033555
E
None of these
Correct Answer: Option C

45 = 5 x 9, where 5 and 9 are co-primes.

Unit digit must be 0 or 5 and sum of digits must be divisible by 9.

Among given numbers, such number is 202860.

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