Aptitude - Numbers

Exercise : Numbers - General Questions
1.
Which one of the following is not a prime number?
31
61
71
91
Answer: Option
Explanation:
91 is divisible by 7. So, it is not a prime number.

2.
(112 x 54) = ?
67000
70000
76500
77200
Answer: Option
Explanation:
(112 x 54) = 112 x 10 4 = 112 x 104 = 1120000 = 70000
2 24 16

3.
It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
(216 + 1)
(216 - 1)
(7 x 223)
(296 + 1)
Answer: Option
Explanation:

Let 232 = x. Then, (232 + 1) = (x + 1).

Let (x + 1) be completely divisible by the natural number N. Then,

(296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.


4.
What least number must be added to 1056, so that the sum is completely divisible by 23 ?
2
3
18
21
None of these
Answer: Option
Explanation:
 23) 1056 (45
      92
      ---
      136
      115
      ---
       21
      ---
     
 Required number = (23 - 21)    
                 = 2.   

5.
1397 x 1397 = ?
1951609
1981709
18362619
2031719
None of these
Answer: Option
Explanation:
1397 x 1397 = (1397)2
= (1400 - 3)2
= (1400)2 + (3)2 - (2 x 1400 x 3)
= 1960000 + 9 - 8400
= 1960009 - 8400
= 1951609.