# numbers aptitude questions

71.

397 x 397 + 104 x 104 + 2 x 397 x 104 = ?
A.     250001    B.     251001
C.     260101    D.     261001

Explanation:

Given Exp.     = (397)2 + (104)2 + 2 x 397 x 104
= (397 + 104)2
= (501)2 = (500 + 1)2
= (5002) + (1)2 + (2 x 500 x 1)
= 250000 + 1 + 1000
= 251001

72.

(35423 + 7164 + 41720) – (317 x 89) = ?
A.     28213    B.     84307
C.     50694    D.     56094
E.     None of these

Explanation:

35423         317 x 89 = 317 x (90 -1 )
+  7164                  = (317 x 90 – 317)
+ 41720                  = (28530 – 317)
—–                  = 28213
84307
– 28213
—–
56094
—–

73.

(xn – an) is completely divisible by (x – a), when
A.     n is any natural number     B.     n is an even natural number
C.     n is and odd natural number     D.     n is prime

Explanation:

For every natural number n, (xn – an) is completely divisible by (x – a).

74.

Which one of the following numbers is completely divisible by 45?
A.     181560    B.     331145
C.     202860    D.     2033555
E.     None of these

Explanation:

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.

75.

Which of the following numbers will completely divide (325 + 326 + 327 + 328) ?
A.     11    B.     16
C.     25    D.     30

Explanation:

(325 + 326 + 327 + 328) = 325 x (1 + 3 + 32 + 33) = 325 x 40

= 324 x 3 x 4 x 10

= (324 x 4 x 30), which is divisible by30.

76.

A number when divide by 6 leaves a remainder 3. When the square of the number is divided by 6, the remainder is:
A.     0     B.     1
C.     2    D.     3

Explanation:

Let x = 6q + 3.

Then, x2 = (6q + 3)2

= 36q2 + 36q + 9

= 6(6q2 + 6q + 1) + 3

Thus, when x2 is divided by 6, then remainder = 3.

77.

The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers ?
A.
12
35
B.
1
35
C.
35
8
D.
7
32

Explanation:

Let the numbers be a and b. Then, a + b = 12 and ab = 35.

a + b     =     12                      1     +     1         =     12
ab     35     b     a     35

Sum of reciprocals of given numbers =     12
35

V
78.

What will be remainder when 17200 is divided by 18 ?
A.     17    B.     16
C.     1    D.     2

Explanation:

When n is even. (xn – an) is completely divisibly by (x + a)

(17200 – 1200) is completely divisible by (17 + 1), i.e., 18.

(17200 – 1) is completely divisible by 18.

On dividing 17200 by 18, we get 1 as remainder.

79.

If 1400 x x = 1050. Then, x = ?
A.
1
4
B.
3
5
C.
2
3
D.
3
4
E.     None of these

Explanation:

1400 x x = 1050      x =     1050     =     3
1400     4

80.

(12 + 22 + 32 + … + 102) = ?
A.     330    B.     345
C.     365    D.     385