Aptitude - Numbers

Exercise :: Numbers - General Questions

101. 

The sum of even numbers between 1 and 31 is:

A. 6
B. 28
C. 240
D. 512

Answer: Option C

Explanation:

Let Sn = (2 + 4 + 6 + ... + 30). This is an A.P. in which a = 2, d = 2 and l = 30

Let the number of terms be n. Then,

a + (n - 1)d = 30

     2 + (n - 1) x 2 = 30

    n = 15.

Sn = n (a + l) = 15 x (2 + 30) = (15 x 16) = 240.
2 2


102. 

If the number 91876 * 2 is completely divisible by 8, then the smallest whole number in place of * will be:

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

Answer: Option C

Explanation:

Then number 6x2 must be divisible by 8.

   x = 3, as 632 is divisible 8.


103. 

2056 x 987 = ?

A. 1936372
B. 2029272
C. 1896172
D. 1926172
E. None of these

Answer: Option B

Explanation:

2056 x 987 = 2056 x (1000 - 13)
= 2056 x 1000 - 2056 x 13
= 2056000 - 26728
= 2029272.

104. 

On multiplying a number by 7, the product is a number each of whose digits is 3. The smallest such number is:

A. 47619
B. 47719
C. 48619
D. 47649

Answer: Option A

Explanation:

By hit and trial, we find that

47619 x 7 = 333333.


105. 

If 60% of 3 of a number is 36, then the number is:
5

A. 80
B. 100
C. 75
D. 90

Answer: Option B

Explanation:

Let the number be x. Then

60% of 3 of x = 36
5

60 x 3 x x = 36
100 5

x = 36 x 25 = 100
9

Required number = 100


106. 

If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x + y = ?

A. 2 or 6
B. 4
C. 4 or 8
D. 8
E. None of these

Answer: Option A

Explanation:

80 = 2 x 5 x 8

Since 653xy is divisible by 2 and 5 both, so y = 0.

Now, 653x is divisible by 8, so 13x should be divisible by 8.

This happens when x = 6.

x + y = (6 + 0) = 6.


107. 

The difference of the squares of two consecutive odd integers is divisible by which of the following integers ?

A. 3
B. 6
C. 7
D. 8

Answer: Option D

Explanation:

Let the two consecutive odd integers be (2n + 1) and (2n + 3). Then,

(2n + 3)2 - (2n + 1)2 = (2n + 3 + 2n + 1) (2n + 3 - 2n - 1)

     = (4n + 4) x 2

     = 8(n + 1), which is divisible by 8.


108. 

What is the unit digit in (4137)754?

A. 1
B. 3
C. 7
D. 9

Answer: Option D

Explanation:

Unit digit in (4137)754 = Unit digit in {[(4137)4]188 x (4137)2}

=Unit digit in { 292915317923361 x 17114769 }

= (1 x 9) = 9


109. 

587 x 999 = ?

A. 586413
B. 587523
C. 614823
D. 615173

Answer: Option A

Explanation:

587 x 999 = 587 x (1000 - 1)
= 587 x 1000 - 587 x 1
= 587000 - 587
= 586413.

110. 

A number was divided successively in order by 4, 5 and 6. The remainders were respectively 2, 3 and 4. The number is:

A. 214
B. 476
C. 954
D. 1908

Answer: Option A

Explanation:

 4 | x            z = 6 x 1 + 4  = 10
 -----------
 5 | y -2         y = 5 x z + 3  = 5 x 10 + 3  = 53
 -----------
 6 | z - 3        x = 4 x y + 2  = 4 x 53 + 2  = 214
 -----------
   | 1 - 4
   
Hence, required number = 214.