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]
7^x + 9^y
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Source: Beat The GMAT — Data Sufficiency |
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cramya
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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
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
Last edited by cramya on Thu Feb 19, 2009 7:10 pm, edited 1 time in total.
