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Number Systems
December 19, 2003
What is the remainder when 1044 * 1047 * 1050 * 1053 is divided by 33?
| (A) | 3 |
| (B) | 27 |
| (C) | 30 |
| (D) | 21 |
| (E) | 18 |
Correct Answer Choice (C)
Solution:
You can solve this problem if you know one basic rule about remainders.
Let us say a number x, divides the product of A and B.
The remainder that you will get will be the product of the remainders when x divides A and when x divides B.
Using this information,
The remainder when 33 divides 1044 is 21.
The remainder when 33 divides 1047 is 24
The remainder when 33 divides 1050 is 27 and
The remainder when 33 divides 1053 is 30.
The net remainder is 21*24*27*30.
However, as the value of 21*24*27*30 is more than 33, the final remainder will be the remainder when 33 divides 21*24*27*30.
When 33 divides 21*24, the remainder is 9.
Similarly when 33 divides 27*30, the remainder is 18.
The final remainder is the remainder when 9*18 is divided by 33 = 30.
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