Number Properties - Remainders & Divisors

Concept: Remainder of product of numbers

The GMAT quant practice question is about finding the remainder of the division of the product of 4 numbers by a divisor.

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

  1. 3
  2. 27
  3. 30
  4. 21
  5. 18

Video Explanation

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Explanatory Answer

Useful result pertaining to remainders

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 cannot 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, 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.

Choice C is the correct answer.

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