Bunuel 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
Kudos for a correct solution.
800score Official Solution:(To understand units and tens, in 75 7 is tens and 5 is units.) This question is testing your knowledge of the fact that when you multiply multi-digit integers, the units digit of the result is the same as the units digit on the product of the units digits of the original integers. For example, the units digit of the result of 1,237 × 653 is 1, because the units digit on the result of 7 × 3 is 1.
So if abcd9 is divisible by ef7, we know that:
(abcd9) / (ef7) = some integer.
Rearranging this equation, we have:
ef7 × (some integer) = abcd9.
Let’s think about possibilities for the units digit of this unknown integer, given the rule above:
7 × 1 = 7
7 × 2 = 14
7 × 3 = 21
…
7 × 7 = 49.
We can see that if the unknown integer has a units digit of 7, then abcd9 may be divisible by ef7.
gh7 is the only answer with a units digit of 7.
The correct answer is choice (E). _________________