7^x + 9^y

[frizo]

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

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

[ebehboud]

if the product of xy=prime then either x or y has to be 1 and the other one must be prime. Otherwise the product will not be prime.

1) 24<y<32: y = 29 or 31, x = 1
7^1 + 9^29 : Unit digit = 7 +9=16, Unit digit = 6
7^1 + 9^31 : Unit digit = 7 +9=16, Unit digit = 6
Unit digit of 9 to the power of any positive odd integer is 9.

Sufficient

2) x=1, we have no information on the value of y.
Not Sufficient

IMO: answer = A[/spoiler]

[cramya]

I would go with A

Stmt I

7^x + 9^y

24 < y < 32

y can be 29,31 based on x and y are positive integers such that the product of x and y is prime. If we take any other number that is non prime the product of that a prime or no prime would not be a prime.

Unit's digit of 9^ exponent cycles as follow 9,1,9

9^29 or 9 ^ 31 would end with 1.

x has to be 1. Therefore we can find the units digit of 7^x+9^y

SUFF

Stmt II

x=1

y can be 2 or 3 or 5 .........
Unit's digit of 7^ exponent cycles as follow 7,9,3,1,7,9...

If y=2 the units digit is different compared to y=3.

INSUFF

[x2suresh]

agree with A..