Units' digit

by **Capthan** Tue Jul 22, 2008 8:24 am

If x and y are positive integers such that the product of x and y is prime, what is the units’ digit of 7x + 9y?

(1) 24 < y < 32
(2) x = 1

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient

by **Amit** Tue Jul 22, 2008 2:28 pm

Is the answer A?

by **Sumit** Tue Jul 22, 2008 6:33 pm

i think the answer should be E as there are two primes b/n 24 and 32 i.e. 29 and 31. So y could be either of these and therefore it would not be possible to determine the units digit

by **Capthan** Wed Jul 23, 2008 5:42 am

Yes, the answer is A,
Can you explain, why you think it is A.

by **rfernandez** Sat Jul 26, 2008 5:21 am

Capthan, what is the source of this question? Is it from one of the Math Strategy Guides? It does not ring a bell.

If you do not post the source, we will need to delete the question from the forum. If it is not from one of the Math Strategy Guides, it should not be posted on this forum. And if it's from one of the banned sources identified in the sticky, then it should not be posted anywhere on our forums. Thanks.

by **Capthan** Sun Jul 27, 2008 6:27 am

Rey
It is a question from MGMAT 250 extremely challenging quantitative problems. please help me on this one.
Thnanks

by **Sush** Tue Jul 29, 2008 2:14 am

7x+9y unit digit?
x,y +ve integers
xy is prime

so one has to be 1 and one has to be a prime number

1. 24<y<32
Therefore x = 1, and y = 29 or 31
Therefore combinations are
7 + 9*29
Unit digit 8

7 + 9*31
Unit digit 6

Cannot tell

2. x = 1
Then y could be any prime number 2,3,5,7,11 etc
Each time then the units digit would be different.

So with both we cannot tell what the units' digit is

Answer - E

by **rfernandez** Fri Aug 08, 2008 4:52 am

Capthan, what's the name of this challenge problem? Are you sure the answer is A?

My solution matches Sumit's and Sush's... and I got E as well.

by **Capthan** Fri Aug 08, 2008 6:37 am

http://www.manhattangmat.com/EventShow. ... entID=2602

Rey,
You can find this question by clicking to above link.

by **Guest** Fri Aug 08, 2008 10:36 pm

The question is not 7X +9Y, instead it is 7^x +9^y
Using A, y is either 29 or 31, 9^29 gives the units digit as 9. Similarly, 9^31 gives the units digit as 9
As the product of xy=prime, this necessisates that x=1. Hence the units digit of 7^x +9^y is 6 (7+9)

by **rfernandez** Sat Aug 09, 2008 1:18 am

What a difference a little symbol makes! Good solution, Guest!

Capthan - the devil is in the details. A good thing to remember for the GMAT!