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Aptitude - Numbers

Exercise : Numbers - General Questions
126.
If the number 653 xy is divisible by 90, then (x + y) = ?
2
3
4
6
Answer: Option
Explanation:

90 = 10 x 9

Clearly, 653xy is divisible by 10, so y = 0

Now, 653x0 is divisible by 9.

So, (6 + 5 + 3 + x + 0) = (14 + x) is divisible by 9. So, x = 4.

Hence, (x + y) = (4 + 0) = 4.

127.
3897 x 999 = ?
3883203
3893103
3639403
3791203
None of these
Answer: Option
Explanation:
3897 x 999 = 3897 x (1000 - 1)
= 3897 x 1000 - 3897 x 1
= 3897000 - 3897
= 3893103.
128.
What is the unit digit in 7105 ?
1
5
7
9
Answer: Option
Explanation:

Unit digit in 7105 = Unit digit in [ (74)26 x 7 ]

But, unit digit in (74)26 = 1

Unit digit in 7105 = (1 x 7) = 7

129.
Which of the following numbers will completely divide (461 + 462 + 463 + 464) ?
3
10
11
13
Answer: Option
Explanation:

(461 + 462 + 463 + 464) = 461 x (1 + 4 + 42 + 43) = 461 x 85

     = 460 x (4 x 85)

     = (460 x 340), which is divisible by 10.

130.
106 x 106 - 94 x 94 = ?
2400
2000
1904
1906
None of these
Answer: Option
Explanation:
106 x 106 - 94 x 94 = (106)2 - (94)2
= (106 + 94)(106 - 94)    [Ref: (a2 - b2) = (a + b)(a - b)]
= (200 x 12)
= 2400.
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