Number System

1.	Which one of the following is not a prime number?
	A. 31 B. 61 C. 71 D. 91 Answer & Explanation Answer: Option D Explanation: 91 is divisible by 7. So, it is not a prime number.

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

4. 

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?
	A. (216 + 1) B. (216 - 1) C. (7 x 223) D. (296 + 1) Answer & Explanation 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 ?
	A. 2 B. 3 C. 18 D. 21 E. None of these Answer & Explanation Answer: Option A Explanation:  23) 1056 (45       92       ---       136       115       ---        21       ---       Required number = (23 - 21)                     = 2.

5.	1397 x 1397 = ?
	A. 1951609 B. 1981709 C. 18362619 D. 2031719 E. None of these Answer & Explanation 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.

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

A. 4 B. 5 C. 6 D. 7 Answer & Explanation 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) = ?
	A. 575648125 B. 584638125 C. 584649125 D. 585628125 Answer & Explanation Answer: Option B Explanation: 935421 x 625 = 935421 x 54 = 935421 x 10 4 2 = 935421 x 104 = 9354210000 24 16 = 584638125

.	The largest 4 digit number exactly divisible by 88 is:
	A. 9944 B. 9768 C. 9988 D. 8888 E. None of these Answer & Explanation 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 ?
	A. 33 B. 81 C. 93 D. 97 Answer & Explanation Answer: Option D Explanation: Clearly, 97 is a prime number.

10.	What is the unit digit in {(6374)1793 x (625)317 x (341491)}?
	A. 0  B. 2 C. 3 D. 5 Answer & Explanation 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.

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