hard Math question !!

<p>Let a, b, c, d, e, f, g, and h be positive integers
from 1 through 9, but we are not telling you what
they are. a b c d 9 is exactly divisible by e f 7.
The quotient could be
A. g h 3
B. g h 4
C. g h 5
D. g h 6
E. g h 7</p>

<p>answer is E .. i need explanation</p>

<p>It’s really easier than it looks.</p>

<p>The quotient of [a b c d 9] / [e f 7] is an integer.</p>

<p>What integer (the quotient – denoted below as xxxD) multiplied by [e f 7] has 9 as its units digit – i.e. [e f 7] x [xxxD] = [a b c d 9]</p>

<p>Just consider the units digit of the product of [xxxD] and [e f 7] where xxx is anything. It needs to be 9:</p>

<p>xxx0 x ef7 has 0 as the units digit
xxx1 x ef7 has 7 as the units digit
xxx2 x ef7 has 4 as the units digit
xxx3 x ef7 has 1 as the units digit
xxx4 x ef7 has 8 as the units digit
xxx5 x ef7 has 5 as the units digit
xxx6 x ef7 has 2 as the units digit
xxx7 x ef7 has 9 as the units digit
xxx8 x ef7 has 6 as the units digit
xxx9 x ef7 has 3 as the units digit</p>

<p>So only the product of xxx7 x ef7 has 9 as the units digit</p>

<p>Thanks … got it now</p>