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Quantitative Aptitude Practice Test: Divisibility Rules of Prime Numbers
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Prime numbers are only divisible by one and by the number itself. When prime numbers are divided by numerals other than one or its exact positive divisor, its product has a remainder or exists as a fraction.

Quantitative Aptitude Practice Test: Divisibility Rules of Prime Numbers
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20 Questions

1. Which of the following number is divisible by 7, 11 and 13?
2. Which of the following is not necessarily true for a number m(m+1)(2m+1), m being a natural number?
3. Which of the following number is divisible by 19?
4. A chewing gum produced 58335 packs of gum. The company produced the same number of packs of each flavor of gum. How many different flavors of gum could the company have produced?
5. If p and q are integers divisible by 5, which of the following is not necessarily true?
6. Which of the following number divides 7386071?
7. Which of the following is divisible by 29?
8. If 23XY70 is a number with all distinct digits and divisible by 11, find XY.
9. Find the value of X, if 1245X42 is divisible by 11.
10. If the sum of numbers (x49)2 and x3 is divisible by 7, then which of the following may be a least value of x?
11. Find the greatest 5-digit number which is exactly divisible by 47.
12. If a positive integer n is divisible by 7, the remainder is 3, which of the following number yields remainder 1 when divided by 7?
13. Which of the following numbers divide 111111111?
14. Find the least number that must by subtracted from 2000 to get a number exactly divisible by 31.
15. m is a positive integer such that m2 + 12 is divisible by m. Find all the possible values of m.
16. Which of the following is/are true?
I. For a number to be divisible by 19, multiply last digit by 2 and add it to the rest of the number and the answer should be a multiple of 19.
II. For a number to be divisible by 29, multiply last digit by 3 and subtract it to the rest of the number and the answer should be a multiple of 29.
17. Find the number of positive integer p in the range 50≥x≥10, such that the product (p-1)(p-2)(9-3)……3*2*1 is not divisible by p.
18. What is the value of n when 34041 and 32506 are divided by a 3-digit number n, leave the same remainder?
19. If a number is divisible by both 7 and 13, then in which of the number case the number is divisible?
20. What least number should be added to 3000 to obtain a number exactly divisible by 17?

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