ExamAdept

1397 x 1397 = ?

A:

1951609

B:

1981709

C:

18362619

D:

2031719

Answer: A

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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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

Answer: A

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

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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: D

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.

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(112 x 5⁴) = ?

A:

67000

B:

70000

C:

76500

D:

77200

Answer: B

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

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Which one of the following is not a prime number?

A:

31

B:

61

C:

71

D:

91

Answer: D

91 is divisible by 7. So, it is not a prime number.

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Questions for: Numbers