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Inequality problem

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Source: — Data Sufficiency |
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by bharathh » Tue Sep 08, 2009 11:30 am
IMO C

There are 2 ways to do this.

1. Draw a graph for the eqn y=-x+1 and color in the required area. On doing so you'll see that statements 1 and 2 are not sufficient on their own. OTHH combining statements 1 and 2 regardless of the values of x and y, the eqn holds true.


2. Sub in values .. this can be tricky as which values will you choose? Regardless it's possible to show that either statement is insufficient by choosing large -ve and positive values for the x or y depending on what is given in the statement.
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Re: Inequality problem

by Ian Stewart » Tue Sep 08, 2009 1:22 pm
Abhi81 wrote:Is x + y < 1 ?

(1) x < 8/9
(2) y < 1/8
If x < 8/9 and y < 1/8, the most you can say about x+y is that it must be less than 8/9 + 1/8 = 73/72. So x+y can still be (very slightly) greater than 1.

We can see this with numbers (it's a bit easier to use decimals here); since 8/9 = 0.8888.... and 1/8 = 0.125, we might have, for example, that x = 0.88 and y = 0.121, in which case x + y is equal to 1.01, so the answer to the question can be no. E.
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by Abhi81 » Tue Sep 08, 2009 2:02 pm
Got it. Thanks a ton.
OA is E.

Can you shed some light on the below problem. Inequalities seem to be a pain area for me.

is x^4 + y^4 > z^4?

(1) x^2 + y^2 > z^2
(2) x + y > z

According to me (1) should be sufficient since if we square (1), we get x^4 + y^4 + 2.x^2.y^2 > z^4
which implies that z^4 > x^4 + y^4 since 2.x^2.y^2 will always be positive.

Please let me know if there is an easy way to tackle inequality problems.
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by Ian Stewart » Tue Sep 08, 2009 2:34 pm
Abhi81 wrote:Got it. Thanks a ton.
OA is E.

Can you shed some light on the below problem. Inequalities seem to be a pain area for me.

is x^4 + y^4 > z^4?

(1) x^2 + y^2 > z^2
(2) x + y > z

According to me (1) should be sufficient since if we square (1), we get x^4 + y^4 + 2.x^2.y^2 > z^4
which implies that z^4 > x^4 + y^4 since 2.x^2.y^2 will always be positive.

Please let me know if there is an easy way to tackle inequality problems.
I've posted a solution to that problem here (and there are two other solutions there as well):

www.beatthegmat.com/gmatprep-is-x-4-y-4-z-4-t23339.html
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
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