Aptitude - Numbers

Exercise :: Numbers - General Questions

111. 

If (64)2 - (36)2 = 20 x x, then x = ?

A. 70
B. 120
C. 180
D. 140
E. None of these

Answer: Option D

Explanation:

20 x x = (64 + 36)(64 - 36) = 100 x 28

     x = 100 x 28 = 140
20


112. 

Which one of the following can't be the square of natural number ?

A. 32761
B. 81225
C. 42437
D. 20164
E. None of these

Answer: Option C

Explanation:

The square of a natural number never ends in 7.

42437 is not the square of a natural number.


113. 

(22 + 42 + 62 + ... + 202) = ?

A. 770
B. 1155
C. 1540
D. 385 x 385

Answer: Option C

Explanation:

(22 + 42 + 62 + ... + 202) = (1 x 2)2 + (2 x 2)2 + (2 x 3)2 + ... + (2 x 10)2

= (22 x 12) + (22 x 22) + (22 x 32) + ... + (22 x 102)

= 22 x [12 + 22 + 32 + ... + 102]

Ref: (12 + 22 + 32 + ... + n2) = 1 n(n + 1)(2n + 1)    
6

= 4 x 1 x 10 x 11 x 21
6

= (4 x 5 x 77)

= 1540.


114. 

854 x 854 x 854 - 276 x 276 x 276 = ?
854 x 854 + 854 x 276 + 276 x 276

A. 1130
B. 578
C. 565
D. 1156
E. None of these

Answer: Option B

Explanation:

Given Exp. = (a3 - b3) = (a - b) = (854 - 276) = 578
(a2 + ab + b2)

115. 

35 + 15 x 1.5 = ?

A. 85
B. 51.5
C. 57.5
D. 5.25
E. None of these

Answer: Option C

Explanation:

Given Exp. = 35 + 15 x 3   = 35 + 45   = 35 + 22.5   = 57.5
2 2

116. 

The sum of first 45 natural numbers is:

A. 1035
B. 1280
C. 2070
D. 2140

Answer: Option A

Explanation:

Let Sn = (1 + 2 + 3 + ... + 45)

This is an A.P. in which a = 1, d = 1, n = 45 and l = 45

Sn = n (a + l) = 45 x (1 + 45)   = (45 x 23)   = 1035
2 2

Required sum = 1035.


117. 

666 6 3 = ?

A. 37
B. 333
C. 111
D. 84
E. None of these

Answer: Option A

Explanation:

Given Exp. = 666 x 1 x 1 = 37
6 3

118. 

The sum of all two digit numbers divisible by 5 is:

A. 1035
B. 1245
C. 1230
D. 945
E. None of these

Answer: Option D

Explanation:

Required numbers are 10, 15, 20, 25, ..., 95

This is an A.P. in which a = 10, d = 5 and l = 95.

tn = 95       a + (n - 1)d = 95

10 + (n - 1) x 5 = 95

(n - 1) x 5 = 85

(n - 1) = 17

n = 18

Requuired Sum = n (a + l) = 18 x (10 + 95)   = (9 x 105)   = 945.
2 2


119. 

The difference between the place values of two sevens in the numeral 69758472 is

A. 0
B. 6993
C. 699930
D. None of these

Answer: Option C

Explanation:

Required difference = (700000 - 70) = 699930

120. 

On dividing a number by 68, we get 269 as quotient and 0 as remainder. On dividing the same number by 67, what will the remainder ?

A. 0
B. 1
C. 2
D. 3

Answer: Option B

Explanation:

Number = 269 x 68 + 0 = 18292

 67) 18292 (273
     134
     ----
      489
      469
      ----
       202
       201
       ---
         1
       ---
       
Therefore, Required remainder = 1