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DS - Solving Inequality

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DS - Solving Inequality

by karthikpandian19 » Thu Jul 05, 2012 7:29 pm
If a - b < 20, is a - b > a + b?

b = 30
a = 25

Somehow i solved the problem, but my question is :

1. Cross multiplying of variables with inequalities is not allowed as we dont no about the signs - I agree with this.

2. Adding or Subtracting of variables of either side of the inequality is allowed or not allowed ???
Becoz for this problem, i simplified the prompt from "a - b > a + b" to

-b > b
0 > 2b
0 > b
b < 0 Is it allowed proceed in this way ?????
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by eagleeye » Thu Jul 05, 2012 7:34 pm
karthikpandian19 wrote:If a - b < 20, is a - b > a + b?

b = 30
a = 25

Somehow i solved the problem, but my question is :

1. Cross multiplying of variables with inequalities is not allowed as we dont no about the signs - I agree with this.

2. Adding or Subtracting of variables of either side of the inequality is allowed or not allowed ???
Becoz for this problem, i simplified the prompt from "a - b > a + b" to

-b > b
0 > 2b
0 > b
b < 0 Is it allowed proceed in this way ?????
Karthik, you should almost always rephrase the questions into an easier form wherever possible. So the answer to your question is a big YES! You CAN proceed this way and you should!
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by Brent@GMATPrepNow » Fri Jul 06, 2012 6:04 am
karthikpandian19 wrote: 2. Adding or Subtracting of variables of either side of the inequality is allowed or not allowed ???
Becoz for this problem, i simplified the prompt from "a - b > a + b" to

-b > b
0 > 2b
0 > b
b < 0 Is it allowed proceed in this way ?????
Yes, adding or subtracting variables to/from both sides of the inequality is perfectly acceptable (and desirable in this case).

You have now rephrased the target question as "Is b < 0?" Perfect!
Now that you have rephrased the target question, the question is much easier.

Statement 1: b = 30
This statement is sufficient because we can be certain that b is not less than zero.

Statement 2: a = 25
Well, we're also told that a-b < 20
Let's plug a = 25 into that inequality to get 25 - b < 20
Subtract 25 from both sides to get -b < -5
Multiply both sides by -1 (and reverse inequality) to get b > 5
If b > 5, then we can be certain that b is not less than zero.
So, statement 2 is sufficient.

So, the answer is D

Cheers,
Brent

For more information about rephrasing the target question, you can watch this free video: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Brent Hanneson - Creator of GMATPrepNow.com
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