Practice GMAT Data Sufficiency Question
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Is (2^{y+z})(3^{x})(5^{y})(7^{z}) < (90^{y})(14^{z})?
 y and z are positive integers; x = 1
 x and z are positive integers; y = 1
Correct Answer: A
 Simplify the equation:
Is (2^{y+z})(3^{x})(5^{y})(7^{z}) < (90^{y})(14^{z})?
Simplified: is (2^{y+z})(3^{x})(5^{y})(7^{z}) < ((2*5*3*3)^{y})((7*2)^{z})?
Simplified: is (2^{y+z})(3^{x})(5^{y})(7^{z}) < (2^{y})(5^{y})(3^{2y})(7^{z})(2^{z})?
Simplified: is (2^{y+z})(3^{x})(5^{y})(7^{z}) < (2^{y+z})(5^{y})(3^{2y})(7^{z})?
Cancel out 2^{y+z}, 5^{y}, and 7^{z}
Simplified: is 3^{x} < 3^{2y}? 
Evaluate Statement (1) alone.
 Statement (1) says that x = 1. So, plug that information in and work from there.
Simplified Question: is 3^{1} < 3^{2y} where y is a positive integer?
Further Simplified: is 1 < 2y where y is a positive integer?  At this point, some students can see that Statement (1) is SUFFICIENT. However, a more thorough analysis is provided just to be clear.
 Since x and y are given as positive integers, the smallest possible value for y is 1. In this case 1 < 2(1). Since the inequality held true when y=1, it will hold true for any legal value of y since y will only get larger and x will not change.
 Thus, 3^{x} will always be less than 3^{2y}.
Statement (1) is SUFFICIENT.
 Statement (1) says that x = 1. So, plug that information in and work from there.

Evaluate Statement (2) alone.
 Statement (2) says y = 1 and x and z are positive integers. So, plug that information and work from there.
Is 3^{x} < 3^{2(1)}?
Or: is 3^{x} < 3^{2}?
Or: is x < 2?  Since the only restriction on x is that it is a positive integer, x could be 1 (in which case the inequality would be true and the answer to the question would be "Yes") or, x could be 2 (in which case the inequality would not be true and the answer to the question would be "No").
 Since different answers to the question "is x < 2?" are possible, there is no definitive answer to the question. Statement (2) is NOT SUFFICIENT.
 Statement (2) says y = 1 and x and z are positive integers. So, plug that information and work from there.
 Since Statement (1) alone is SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, answer A is correct.
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