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The integer x has a tens digit of 6 and a units digit of 7.

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by regor60 » Tue Oct 04, 2016 6:27 am
alanforde800Maximus wrote:The integer x has a tens digit of 6 and a units digit of 7. The units digit of integer y is 8.
The product of x and y has a tens digit of 8. Which of the following is a possible tens digit of integer y?

A. 3
B. 4
C. 5
D. 6
E. 7

Please assist with above problem.
Since the question doesn't tell you what the other digits of X are, they must not matter, so X=67 for this purpose.

Since the question wants to know tens digit of Y, call Y = 10*A + 8.

The product of X and Y is therefore 670*A + 536. In order for this product to have a tens digit of 8, the sum of the tens digit of 670*A and 3 must have 8 in the ones place.

So, A*7, whose ones digit is the tens digit of 670* A, must be a multiple of 5, because 5+3=8. Answer [spoiler]"C"[/spoiler]
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