Quantitative Aptitude

General Questions

Quantitative Aptitude Exercise Mode

General Questions

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Question 51
The difference of the squares of two consecutive even integers is divisible by which of the following integers ?

A
3
B
4
C
6
D
7
Correct Answer: Option B

Let the two consecutive even integers be 2n and (2n + 2). Then,

(2n + 2)2 = (2n + 2 + 2n)(2n + 2 - 2n)

             = 2(4n + 2)

             = 4(2n + 1), which is divisible by 4.

Question 52
The difference between the place value and the face value of 6 in the numeral 856973 is

A
973
B
6973
C
5994
D
None of these
Correct Answer: Option C

(Place value of 6) - (Face value of 6) = (6000 - 6) = 5994

Question 53
The sum of how many terms of the series 6 + 12 + 18 + 24 + ... is 1800 ?

A
16
B
24
C
20
D
18
E
22
Correct Answer: Option B

This is an A.P. in which a = 6, d = 6 and Sn = 1800

Then, n [2a + (n - 1)d] = 1800
2

  n [2 x 6 + (n - 1) x 6] = 1800
2

3n (n + 1) = 1800

n(n + 1) = 600

n2 + n - 600 = 0

n2 + 25n - 24n - 600 = 0

n(n + 25) - 24(n + 25) = 0

(n + 25)(n - 24) = 0

n = 24

Number of terms = 24.

Question 54
Which one of the following is a prime number ?

A
119
B
187
C
247
D
551
E
None of these
Correct Answer: Option E

551 > 22

All prime numbers less than 24 are : 2, 3, 5, 7, 11, 13, 17, 19, 23.

119 is divisible by 7; 187 is divisible by 11; 247 is divisible by 13 and 551 is divisible by 19.

So, none of the given numbers is prime.

Question 55
If a and b are odd numbers, then which of the following is even ?

A
a + b
B
a + b + 1
C
ab
D
ab + 2
E
None of these
Correct Answer: Option A

The sum of two odd number is even. So, a + b is even.

Question 56
The sum all even natural numbers between 1 and 31 is:

A
16
B
128
C
240
D
512
Correct Answer: Option C

Required sum = (2 + 4 + 6 + ... + 30)

This is an A.P. in which a = 2, d = (4 - 2) = 2 and l = 30.

Let the number of terms be n. Then,
tn = 30 a + (n - 1)d = 30
2 + (n - 1) x 2 = 30
n - 1 = 14
n = 15

Sn = n (a + l) = 15 x (2 + 30)
2 2

= (15 x 16) = 240.

Question 57
476 ** 0 is divisible by both 3 and 11. The non-zero digits in the hundred's and ten's places are respectively:

A
7 and 4
B
7 and 5
C
8 and 5
D
None of these
Correct Answer: Option C

Let the given number be 476 xy 0.

Then (4 + 7 + 6 + x + y + 0) = (17 + x + y) must be divisible by 3.

And, (0 + x + 7) - (y + 6 + 4) = (x - y -3) must be either 0 or 11.

x - y - 3 = 0     y = x - 3

(17 + x + y) = (17 + x + x - 3) = (2x + 14)

 x= 2 or x = 8.

 x = 8 and y = 5.

Question 58
A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 9 are wrong and the other digits are correct, then the correct answer would be:

A
553681
B
555181
C
555681
D
556581
Correct Answer: Option C

987 = 3 x 7 x 47

So, the required number must be divisible by each one of 3, 7, 47

553681 --> (Sum of digits = 28, not divisible by 3)

555181 --> (Sum of digits = 25, not divisible by 3)

555681 --> is divisible by 3, 7, 47.

Question 59
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
Correct Answer: Option C

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.

Question 60
If the product 4864 x 9P2 is divisible by 12, then the value of P is:

A
2
B
5
C
6
D
8
E
None of these
Correct Answer: Option E

Clearly, 4864 is divisible by 4.

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

P = 1.

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