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# AMCAT Mathematics Questions on Divisibility

## AMCAT Mathematics Questions on Divisibility

1. The number of prime factors of (3 x 5)12 (2 x 7)10 (10)25 is:

A): 47
B): 60
C): 72
D): None of these

2. What least value must be assigned to * so that the number 63576*2 is divisible by 8?

A): 1
B): 2
C): 3
D): 4

3. Which of the following numbers is exactly divisible by 24 ?

A): 35718
B): 63810
C): 537804
D): 3125736

4. The number nearest to 15207, which is divisible by 467, is:

A): 14342
B): 15211
C): 14944
D): 15411

5. The smallest number, which is a perfect square and contains 7936 as a factor is:

A): 251664
B): 231564
C): 246016
D): 346016

6. In a division problem, the divisor is twenty times the quotient and five times the remainder. If remainder is 16, the number will be:

A): 3360
B): 336
C): 1616
D): 20516

7. If a number is exactly divisible by 85, then what will be the remainder when the same number is
divided by 17?

A): 3
B): 1
C): 4
D): 0

8. The least perfect square number which is exactly divisible by 3, 4, 7, 10 and 12 is:

A): 8100
B): 17600
C): 44100
D): None of these

9. (xn+yn) is divisible by (x-y):

A): for all values of n
B): only for even values of n
C): only for odd values of n
D): for no values of n

10. The greatest number that will divide 63, 138 and 228 so as to leave the same remainder in each case:

A): 15
B): 20
C): 35
D): 40

11. Find the largest number, smaller than the smallest four-digit number, which when divided by 4,5,6and 7 leaves a remainder 2 in each case:

A): 422
B): 842
C): 12723
D): None of these

12. What is the highest power of 5 that divides 90 x 80 x 70 x 60 x 50 x 40 x 30 x 20 x 10?
A): 10
B): 12
C): 14
D): None of these

13. If a and b are natural numbers and a-b is divisible by 3, then a3-b3 is divisible by:

A): 3 but not by 9
B): 9
C): 6
D): 27

14. What is the greatest positive power of 5 that divides 30! exactly?

A): 5
B): 6
C): 7
D): 8

15. In how many ways can a number 6084 be written as a product of two different factors ?
A): 27
B): 26
C): 13
D): 14

16. What is the smallest four-digit number which when divided by 6, leaves a remainder of 5 and when divided by 5 leaves a remainder of 3?

A): 1043
B): 1073
C): 1103
D): None of these

17. P is an integer. P>883. If P-7 is a multiple of 11, then the largest number that will always divide (P+4) (P+15) is:

A): 11
B): 121
C): 242
D): None of these

18. Let C be a positive integer such that C + 7 is divisible by 5. The smallest positive integer n (>2) such that C + n2 is divisible by 5 is:

A): 4
B): 5
C): 3
D): Does not exist

19. Four bells begin to toll together and then each one at intervals of 6 s, 7 s, 8 s and 9 s respectively.
The number of times they will toll together in the next 2 hr is:

A): 14 times
B): 15 times
C): 13 times
D): 11 times

20. On dividing a number by 999,the quotient is 366 and the remainder is 103.The number is:

A): 364724
B): 365387
C): 365737
D): 366757

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