Positive integer n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5. If n is greater

BTGmoderatorDC wrote: ↑

Tue Sep 13, 2022 3:52 am

Positive integer n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5. If n is greater than 30, what is the remainder that n leaves after division by 30?

A. 3
B. 12
C. 18
D. 22
E. 28


OA E

Source: Manhattan Prep

Notice that 4 is 2 less than 6 and 3 is also 2 less than 5; thus, a number that has both requirements (i.e., a remainder of 4 after division by 6 and a remainder of 3 after division by 5) is 2 less than the LCM of 6 and 5. Since the LCM of 6 and 5 is 30, that number will be 28. Although we are given that n is greater than 30, we can modify the number by adding 30 to it. That is, n = 28 + 30 = 58, and the remainder when 58 is divided by 30 is 28 (note that 58/6 = 9 R 4 and 58/5 = 11 R 3, satisfying the requirements).

Answer: E