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Squares
Source: Beat The GMAT — Data Sufficiency |
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Brian@VeritasPrep
- GMAT Instructor
- Posts: 1031
- Location: Malibu, CA
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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
Looking for GMAT practice questions? Try out the Veritas Prep Question Bank. Learn More.
GMAT Instructor
Chief Academic Officer
Veritas Prep
Looking for GMAT practice questions? Try out the Veritas Prep Question Bank. Learn More.
thanks Brain!! 
