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Is x² ≤ 10y² ?

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Source: — Data Sufficiency |
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by eagleeye » Mon Jul 16, 2012 5:02 am
kartikshah wrote:Is x² ≤ 10y² ?
1. 0 < x < 2
2. 1 < y < 2


Correct Answer: C

Please explain.
Thanks!
Source: Princeton Review Practice Test 10
Clearly either statement is not sufficient as it only talks about 1 variable. Lets look at them together.

Maximum value of x^2 < 4
Minimum value of y^2 > 1. Hence min. value of 10*y^2 > 10.

Hence, x^2 < 10y^2.

C is correct.
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by tisrar02 » Tue Jul 17, 2012 7:19 pm
Here's my logic:

1) X is given, no Y. Can not solve for Y so we don't assume. Not Sufficient.. Move on

2) Now we have Y but here's the tricky part. FORGET STATEMENT 1. We don't have a value for X, move on.

1) and 2).. We are given values for both X and Y. Plug into the answer choice.
x= 1.9 y= 1.1===> 1.9^2<10(1.1)^2--> Use Extreme Values to figure it out at this point and you will notice all the answer choices lead to one answer.

I used these numbers because I wanted to try to prove that the left side was larger than the right side but it is evident that this statement with the given constraints will only yield one answer and that is the Right side will always be larger than the left side!

Correct Answer: C


Thanks
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