The GMAT quant practice question is about finding the remainder when the product of 4 numbers is divided by a divisor. Knowledge of a rule of remainders that the remainder of product is the same as the product of remainders is needed to solve this question.

Question 8: What is the remainder when 1044 * 1047 * 1050 * 1053 is divided by 33?

- 3
- 27
- 30
- 21
- 18

@ INR

You can solve this problem if you know this rule about remainders.

Let a number x divide the product of A and B.

The remainder will be the product of the remainders when x divides A and when x divides B.

Using this rule,

The remainder when 33 divides 1044 is 21.

The remainder when 33 divides 1047 is 24.

The remainder when 33 divides 1050 is 27.

The remainder when 33 divides 1053 is 30.

∴ the remainder when 33 divides 1044 * 1047 * 1050 * 1053 is 21 * 24 * 27 * 30.

Note: The remainder when a number is divided by a divisor 'd' will take values from 0 to (d - 1). It will not be equal to or more than 'd'.

The value of 21 * 24 * 27 * 30 is more than 33.

When the value of the remainder is more than the divisor, the final remainder will be the remainder of dividing the product by the divisor.

i.e., the final remainder is the remainder when 33 divides 21 * 24 * 27 * 30.

When 33 divides 21 * 24 * 27 * 30, the remainder is 30.

Try it free!

Register in 2 easy steps and

Start learning in 5 minutes!

Next Integrated (Online + Offline) Batch

Starts Thu, Dec 3, 2020

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

Copyrights © 2016 - 20 All Rights Reserved by Wizako.com - An Ascent Education Initiative.

Privacy Policy | Terms & Conditions

GMAT^{®} is a registered trademark of the Graduate Management Admission Council (GMAC). This website is not endorsed or approved by GMAC.

GRE^{®} is a registered trademarks of Educational Testing Service (ETS). This website is not endorsed or approved by ETS.

SAT^{®} is a registered trademark of the College Board, which was not involved in the production of, and does not endorse this product.

Wizako - GMAT, GRE, SAT Prep

An Ascent Education Initiative

48/1 Ramagiri Nagar

Velachery Taramani Link Road.,

Velachery, Chennai 600 042. India

**Phone:** (91) 44 4500 8484

**Mobile:** (91) 95000 48484

**WhatsApp:** WhatsApp Now

**Email:** learn@wizako.com

Leave A Message