This GMAT sample question is about finding the divisor given remainders of dividing a number and twice the number by the same divisor. Number Theory and Number Properties are often-tested topics in the GMAT quant section.

Question 3: A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?

- 13
- 59
- 35
- 37
- 12

@ INR

Let the original number be 'a'.

Let the divisor be 'd'.

Let the quotient of dividing 'a' by 'd' be 'x'.

Therefore, we can write the division as \\frac{a}{d}\\) = x and the remainder is 24.

i.e., a = dx + 24

Twice the original number is divided by 'd' means 2a is divided by d.

We know from Step 1 that a = dx + 24.

Therefore, 2a = 2(dx + 48) or 2a = 2dx + 48

When (2dx + 48) is divided by 'd' the remainder is 11.

2dx is divisible by 'd' and will therefore, not leave a remainder.

The remainder of 11 would be the remainder of dividing 48 by d.

The question essentially becomes **"What number will leave a remainder of 11 when it divides 48?"**

When 37 divides 48, the remainder is 11.

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1. Number Systems | Types of Numbers | Chart

2. Number Properties | Rational & Irrational Numbers

3. GMAT Number Properties | Indices & Rule of Exponents

4. Number Systems | Surds & Conjugates

5. Number Properties | Tests of divisibility

6. Number Properties | How to check whether a number is prime?

7. Number Properties | How to prime factorize a number?

8. GMAT Number Theory | Prime factorization | Properties of squares & cubes

9. Number Properties | What is HCF? | How to find HCF?

10. Number Properties | What is LCM? | How to find LCM?

11. 3 important properties of LCM & HCF | LCM & HCF of fractions

12. Number Properties | When to use LCM and HCF?

13. Number Theory | How to find number of factors?

14. Number Theory | Number of ways to express as a product of 2 factors

15. Number Theory | Sum of all factors of a number

16. Number Theory | Product of all factors of a number

17. Number Theory | Remainders of sum & product

18. Number Theory | Remainder of dividing x^{n} by 'd'

19. Polynomials | Remainder when a monomial divides it

20. Number Theory | Highest power of a prime that divides factorial of 'n'

21. Number Theory | Highest power of a composite number that divides factorial of 'n'

22. Number Theory | Number of trailing zeroes in a number

23. Number Theory | Unit digit of higher powers of numbers

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