numbers aptitude questions

81. 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

Answer: Option B

Explanation:

 

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.


82. Which one of the following is a prime number ?
A. 119 B. 187
C. 247 D. 551
E. None of these

Answer: Option E

Explanation:

 

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.


83. The sum all even natural numbers between 1 and 31 is:
A. 16 B. 128
C. 240 D. 512

Answer: Option C

Explanation:

 

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)   = 240.
2 2

84. 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

Answer: Option C

Explanation:

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


85. 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

Answer: Option A

Explanation:

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


86. Which one of the following numbers is completely divisible by 99?
A. 3572404 B. 135792
C. 913464 D. 114345
E. None of these

Answer: Option D

Explanation:

 

99 = 11 x 9, where 11 and 9 are co-prime.

By hit and trial, we find that 114345 is divisibleby 11 as well as 9. So, it is divisible by 99.


87. 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

Answer: Option B

Explanation:

 

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.


88. (51+ 52 + 53 + … + 100) = ?
A. 2525 B. 2975
C. 3225 D. 3775

Answer: Option D

Explanation:

 

This is an A.P. in which a = 51, l = 100 and n = 50.

 

Sum = n (a + l) = 50 x (51 + 100)   = (25 x 151)   = 3775.
2 2

89. 1904 x 1904 = ?
A. 3654316 B. 3632646
C. 3625216 D. 3623436
E. None of these

Answer: Option C

Explanation:

 

1904 x 1904 = (1904)2
= (1900 + 4)2
= (1900)2 + (4)2 + (2 x 1900 x 4)
= 3610000 + 16 + 15200.
= 3625216.

90. What is the unit digit in(795 – 358)?
A. 0 B. 4
C. 6 D. 7

Answer: Option B

Explanation:

 

Unit digit in 795 = Unit digit in [(74)23 x 73]
= Unit digit in [(Unit digit in(2401))23 x (343)]
= Unit digit in (123 x 343)
= Unit digit in (343)
= 3

Unit digit in 358 = Unit digit in [(34)14 x 32]
= Unit digit in [Unit digit in (81)14 x 32]
= Unit digit in [(1)14 x 32]
= Unit digit in (1 x 9)
= Unit digit in (9)
= 9

Unit digit in (795 – 358) = Unit digit in (343 – 9) = Unit digit in (334) = 4.

So, Option B is the answer.

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