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?
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.
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.
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