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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
2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276
- A.5
- C.7
- B.6
- D.None of these
- Answer & Explanation
- Report
Answer : [B]
Explanation :
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. |
2.
The difference between the squares of two consecutive odd integers is always divisible by:
- A.3
- C.7
- B.6
- D.8
- Answer & Explanation
- Report
Answer : [D]
Explanation :
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 | |||||
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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
- Answer & Explanation
- Report
Answer : [A]
Explanation :
Explanation :
| (1000 + N) > (1000N). Clearly, N = 1. |
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
- Answer & Explanation
- Report
Answer : [B]
Explanation :
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. | |||
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5.
What largest number of five digits is divisible by 99?
- A.99909
- C.99990
- B.99981
- D.99999
- Answer & Explanation
- Report
Answer : [C]
Explanation :
Explanation :
| Largest number of 5 digits = 99999. On dividing 99999 by 99, we get 9 as remainder. | |||
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