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Results

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#1. Which one of the following is not a prime number?

Answer: Option D Explanation:
91 is divisible by 7. So, it is not a prime number.

#2. (112 x 5^4) = ?

Answer: Option B

Explanation:

(112 x 54) = 112 x 10 4 = 112 x 104 = 1120000 = 70000
2 24 16

#3. It is being given that (2^32 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?

Answer: Option D

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 ?

Answer: Option A

Explanation:

 23) 1056 (45
      92
      ---
      136
      115
      ---
       21
      ---
     
 Required number = (23 - 21)    
                 = 2.

#5. 1397 x 1397 = ?

Answer: Option A

Explanation:

1397 x 1397 = (1397)2
= (1400 – 3)2
= (1400)2  (3)2 – (2 x 1400 x 3)
= 1960000 9 – 8400
= 1960009 – 8400
= 1951609.

#6. How many of the following numbers are divisible by 132 ? 264, 396, 462, 792, 968, 2178, 5184, 6336

Answer: Option A

Explanation:

132 = 4 x 3 x 11

So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also.

264  11,3,4 (/)

396  11,3,4 (/)

462  11,3 (X)

792  11,3,4 (/)

968  11,4 (X)

2178  11,3 (X)

5184  3,4 (X)

6336  11,3,4 (/)

Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336.

Required number of number = 4.

#7. (935421 x 625) = ?

Answer: Option B

Explanation:

935421 x 625 = 935421 x 54 = 935421 x 10 4
2
= 935421 x 104 = 9354210000
24 16

= 584638125

#8. The largest 4 digit number exactly divisible by 88 is:

The largest 4 digit number exactly divisible by 88 is:

Answer: Option A

Explanation:

Largest 4-digit number = 9999

 88) 9999 (113
     88
     ----
     119
      88
     ----
      319
      264
      ---
       55
      ---
       
 Required number = (9999 - 55)
                 = 9944.

#9. Which of the following is a prime number ?

Answer: Option D

Explanation:

Clearly, 97 is a prime number.

#10. What is the unit digit in {(6374)^1793 x (625)^317 x (341^491)}?

Answer: Option A

Explanation:

Unit digit in (6374)1793 = Unit digit in (4)1793

= Unit digit in [(42)896 x 4]

= Unit digit in (6 x 4) = 4

Unit digit in (625)317 = Unit digit in (5)317 = 5

Unit digit in (341)491 = Unit digit in (1)491 = 1

Required digit = Unit digit in (4 x 5 x 1) = 0.

#11. 5358 x 51 = ?

Answer: Option A

Explanation:

5358 x 51 = 5358 x (50 1)
= 5358 x 50 5358 x 1
= 267900 5358
= 273258.

#12. The sum of first five prime numbers is:

Answer: Option D

Explanation:

Required sum = (2 3 5 7 11) = 28.

Note: 1 is not a prime number.

Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.

#13. The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?

Answer: Option B

Explanation:

Let the smaller number be x. Then larger number = (x  1365).

 x  1365 = 6x  15

 5x = 1350

 x = 270

Smaller number = 270.

#14. (12)^3 x 6^4 ÷ 432 = ?

Answer: Option A

Explanation:

Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62

#15. 72519 x 9999 = ?

Answer: Option A

Explanation:

72519 x 9999 = 72519 x (10000 – 1)
= 72519 x 10000 – 72519 x 1
= 725190000 – 72519
= 725117481.

#16. If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be:

Answer: Option C

Explanation:

Sum of digits = (5 1 7  x  3 2 4) = (22  x), which must be divisible by 3.

  x = 2.

#17. The smallest 3 digit prime number is

Answer: Option A

Explanation:

The smallest 3-digit number is 100, which is divisible by 2.

 100 is not a prime number.

101 < 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.

101 is a prime number.

Hence 101 is the smallest 3-digit prime number.

#18. Which one of the following numbers is exactly divisible by 11?

Answer: Option D

Explanation:

(4 5 2) – (1 6 3) = 1, not divisible by 11.

(2 6 4) – (4 5 2) = 1, not divisible by 11.

(4 6 1) – (2 5 3) = 1, not divisible by 11.

(4 6 1) – (2 5 4) = 0, So, 415624 is divisible by 11.

#19. (?) - 19657 - 33994 = 9999

Answer: Option A

Explanation:

 19657         Let x - 53651  = 9999
 33994         Then, x = 9999   53651 = 63650
 -----
 53651
 -----

#20. The sum of first 45 natural numbers is:

Answer: Option A

Explanation:

Let Sn =(1 2 3 … 45). This is an A.P. in which a =1, d =1, n = 45.

Sn = n [2a  (n – 1)d] = 45 x [2 x 1 (45 – 1) x 1] = 45 x 46 = (45 x 23)
2 2 2

= 45 x (20 3)

= 45 x 20 45 x 3

= 900 135

= 1035.

Shorcut Method:

Sn = n(n  1) = 45(45 1) = 1035.
2 2
finish