Squares
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Source: Beat The GMAT — Data Sufficiency |
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Brian@VeritasPrep
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Great question! And nice work, gmatblood.
Here, I think it's pretty important to recognize when you see this setup:
-Dealing with squares of variables
-the real constraint is that "the variables are positive"
You recognize that for any values >1, squaring them makes them increase. But for positive values less than 1 (0 < x < 1), squaring them makes them decrease. It's a small band of numbers, but they react really differently so you want to be aware of that.
So with statement 1, it's pretty easy to get "No", as y could be 1,000,000 and x could be 1, and no way is x greater than y^2 there. But how could you start with y bigger than x^2 and end up with x bigger than y^2? Make them fractions: x = 1/2 and y = 2/3, so the statement is satisfied (y is bigger than x^2, which would be 1/4) but x is bigger than y^2 (which would be 4/9).
Statement 2, however, tells you that y is going to be greater than 1, since we know x at a minimum is a shade over 0 (maybe .000000001, with y then at 1.000000001). And since y will start bigger than x, and when we square it it will only increase, we know that y^2 will be bigger than x, so this time the answer is always "No". And the answer is B.
Here, I think it's pretty important to recognize when you see this setup:
-Dealing with squares of variables
-the real constraint is that "the variables are positive"
You recognize that for any values >1, squaring them makes them increase. But for positive values less than 1 (0 < x < 1), squaring them makes them decrease. It's a small band of numbers, but they react really differently so you want to be aware of that.
So with statement 1, it's pretty easy to get "No", as y could be 1,000,000 and x could be 1, and no way is x greater than y^2 there. But how could you start with y bigger than x^2 and end up with x bigger than y^2? Make them fractions: x = 1/2 and y = 2/3, so the statement is satisfied (y is bigger than x^2, which would be 1/4) but x is bigger than y^2 (which would be 4/9).
Statement 2, however, tells you that y is going to be greater than 1, since we know x at a minimum is a shade over 0 (maybe .000000001, with y then at 1.000000001). And since y will start bigger than x, and when we square it it will only increase, we know that y^2 will be bigger than x, so this time the answer is always "No". And the answer is B.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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GMAT Instructor
Chief Academic Officer
Veritas Prep
Looking for GMAT practice questions? Try out the Veritas Prep Question Bank. Learn More.
thanks Brain!! 
