If a, b, c, d, e, f, g, and h represent any . . .

Vincen wrote:If a, b, c, d, e, f, g, and h represent any of the digits from 1 to 9, inclusive and the 5-digit number abcd9 is divisible by the 3-digit number ef7, then the quotient could be

A. gh3
B. gh4
C. gh5
D. gh6
E. gh7

The OA is E .

How can I know which is the correct option without knowing the entire number?

Notice that among the answer choices, only the units digit varies. So effectively, the question is asking us what a possible units digit is when we divide a 5-digit number ending in 9 by a 3-digit number ending in 7.

Let's say XXXX9/XX7 = q, where q is the quotient. Put another way XXXX9 = XX7 * q. So when we multiply one number ending in 7 by q, we'll get a product ending in 9. Now we can go to the answer choices and multiply each possible units digit of the quotient by 7 and see which will give us a units of 9. Only E works. If we have XX7 * gh7, we know the result will end in 9, as 7*7 = 49.