Practice GMAT Data Sufficiency Question
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Is (2y+z)(3x)(5y)(7z) < (90y)(14z)?
- y and z are positive integers; x = 1
- x and z are positive integers; y = 1
Correct Answer: A
- Simplify the equation:
Is (2y+z)(3x)(5y)(7z) < (90y)(14z)?
Simplified: is (2y+z)(3x)(5y)(7z) < ((2*5*3*3)y)((7*2)z)?
Simplified: is (2y+z)(3x)(5y)(7z) < (2y)(5y)(32y)(7z)(2z)?
Simplified: is (2y+z)(3x)(5y)(7z) < (2y+z)(5y)(32y)(7z)?
Cancel out 2y+z, 5y, and 7z
Simplified: is 3x < 32y?
-
Evaluate Statement (1) alone.
- Statement (1) says that x = 1. So, plug that information in and work from there.
Simplified Question: is 31 < 32y 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, 3x will always be less than 32y.
Statement (1) is SUFFICIENT.
-
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 3x < 32(1)?
Or: is 3x < 32?
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.
- Since Statement (1) alone is SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, answer A is correct.
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