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Official GRE Guide 3rd ed: Section 5 Quantitative Reasoning, Question 9
Tue Aug 8, 2017
what is the best approach to answer this question?
Wed Aug 9, 2017
Start by setting up your scratch paper: ABCD and your possibility matrix™.
Record What You Know:
7w - 4
2w + 5
w > 1
try out a simple value, like w = 2.
w = 2, A: 10, B: 9
Right now, A is bigger, so cross out B and C.
Now for your second value, think what value for w that would lead to a different outcome. Perhaps try w = 4.
w = 4, A: 24, B: 13
Well, we've reached the same result, except what happened? The difference between A and B got bigger! A got dramatically larger than B.
This tells you your work is going in the wrong direction.
Consider the other kinds of numbers you might want to try, negatives, zero, fractions, etc.
Negatives and zero don't work because of the conditions given (w > 1), but what about fractions? Clearly 1/2 is excluded, but what about 1.5
Try it out.
w = 1.5, A: 6.5, B: 8
Now we've got it! B is greater, so the answer is D.