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In-equalities - GMAT Prep question

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by gmattesttaker2 » Mon Jul 29, 2013 7:13 pm
Hello,

This is from GMAT Prep:

Is Y<2X?

1) Y/4<X/2

2) (Y-2X)/3<0

I was clear with Statement 1 i.e.

y/4 < x/2

So y < 2x

My approach to Statement 2 was as follows:

(y-2x)/3 < 0

So, y - 2x < 0

However, I was stuck at this point. I was thinking if it is correct to add 2x on both sides of the in-equality since we don't know whether x is positive or negative ( or zero ?) Can you please assist?

Thanks,
Sri
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by Brent@GMATPrepNow » Mon Jul 29, 2013 8:10 pm
gmattesttaker2 wrote: Is Y < 2X?

1) Y/4 < X/2

2) (Y-2X)/3 < 0
You were almost done, Sri.
Here's the full solution . .

Target question: Is Y < 2X?

Statement 1: Y/4 < X/2
Multiply both sides by 4 to get Y < 2X
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: (Y-2X)/3 < 0
Multiply both sides by 3 to get Y - 2X < 0
Add 2X to both sides to get Y < 2X
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

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Brent
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by vishugogo » Tue Jul 30, 2013 4:57 am
(y-2x)/3 < 0

So, y - 2x < 0

However, I was stuck at this point. I was thinking if it is correct to add 2x on both sides of the in-equality since we don't know whether x is positive or negative ( or zero ?) Can you please assist?

The inequality sign only changes when you multiply or divide by a number whose sign is -ve.
Last edited by vishugogo on Tue Jul 30, 2013 10:33 am, edited 1 time in total.
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by [email protected] » Tue Jul 30, 2013 9:38 am
Hi vishugogo,

Inequalities "work" the same way that equal signs do:

If you do math to one side of the inequality, then you have to do it to the other side...

eg y - 2x < 0

y - 2x - 5 < 0 - 5

or

y - 2x + 2x < 0 + 2x

The inequality will "change direction" only if you multiply OR divide by a negative:

eg -5x > 10

-5x/-5 < 10/-5

x < -2

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