1.
How many of the following numbers are divisible by 3 but not by 9?
2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276
• A.
5
• C.
7
• B.
6
• D.
None of these
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Explanation :
 Taking the sum of the digits, we have : S1 = 9, S2 = 12, S3 = 18, S4 = 9, S5 = 21, S6 = 12, S7 = 18, S8 = 21, S9 = 15, S10 = 24. Clearly, S2, S5, S6, S8, S9, S10 are all divisible by 3 but not by 9. So, the number of required numbers = 6.
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2.
The difference between the squares of two consecutive odd integers is always divisible by:
• A.
3
• C.
7
• B.
6
• D.
8
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Explanation :

Let the two consecutive odd integers be (2x + 1) and �(2x + 3)

Then, (2x + 3)2 - (2x + 1)2 = (2x + 3 + 2x + 1) (2x + 3 - 2x - 1) = (4 + 4) x 2

 = 8 (x + 1), which is always divisible by 8

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3.
A positive integer, which when added to 1000, gives a sum which is greater than when it is multiplied by 1000. This positive integer is:
• A.
1
• C.
5
• B.
3
• D.
7
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Explanation :
 (1000 + N) > (1000N). Clearly, N = 1.
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4.
The smallest value of n, for which� 2n + 1 is not a prime number, is:
• A.
3
• C.
5
• B.
4
• D.
None of these
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Explanation :

(2 x 1 + 1) = 3, (2 x 2 + 1) = 5, (2 x 3 + 1) = 7. (2 x 4 + 1) = 9. which is not prime.

 n = 4.

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5.
What largest number of five digits is divisible by 99?
• A.
99909
• C.
99990
• B.
99981
• D.
99999