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Arithmetic Aptitude :: Numbers
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Which one of the following is not a prime number?
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Answer : Option D
Explanation :
91 is divisible by 7. So, it is not a prime number.
Answer : Option B
Explanation :
112 x54 =112 x (102)4 = (112X10424)= (112000016) =70000
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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?
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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.
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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
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136
115
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21
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Required number = (23 - 21)
= 2.
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
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.
Answer : Option B
Explanation :
935421 *625=935421*54 =935421*(102)4
=935421×10424
= 584638125
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The largest 4 digit number exactly divisible by 88 is:
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Answer : Option A
Explanation :
Largest 4-digit number = 9999
88) 9999 (113
88
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119
88
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319
264
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55
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Required number = (9999 - 55)
= 9944.
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Which of the following is a prime number ?
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Answer : Option D
Explanation :
Clearly, 97 is a prime number.
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What is the unit digit in {(6374)1793 x (625)317 x (341491)}?
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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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