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## If 1 > g > 1/2 and -1 < h < -1/2, then which of

tagged by: AAPL

This topic has 3 expert replies and 0 member replies

### Top Member

AAPL Moderator
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#### If 1 > g > 1/2 and -1 < h < -1/2, then which of

Wed Dec 06, 2017 9:59 am
If 1 > g > 1/2 and -1 < h < -1/2, then which of the following expresses all possible values of g - h?

A. 0 < g - h < 1
B. 0 < g - h < 2
C. 1/2 < g - h < 2
D. 1 < g - h < 3/2
E. 1 < g - h < 2

The OA is E.

In this PS question I have to do the subtraction of g-h, then

(1 > g > 1/2) - (1 < h < -1/2) = 2 ? g-h ? 1.

My question is, how should be the results of the inequalities symbol? It should be >? or < ? I don't have clear this part.

Experts, can you help me with it, please? Thanks.

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
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Wed Dec 06, 2017 10:20 am
Hi AAPL,

We're told that If 1 > G > 1/2 and -1 < H < -1/2. We're asked for the range of all possible values of (G - H). To start, notice that G will be positive and H will be negative, so we'll be subtracting a negative from a positive (which will make the result BIGGER than whatever value G is). You might find it useful to TEST VALUES here...

As G approaches 1 and H approaches -1, (G - H) approaches +2.
As G approaches 1/2 and H approaches -1/2, (G - H) approaches +1.
Thus, we have the range.

GMAT assassins aren't born, they're made,
Rich

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### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
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Wed Dec 06, 2017 5:03 pm
AAPL wrote:
If 1 > g > 1/2 and -1 < h < -1/2, then which of the following expresses all possible values of g - h?

A. 0 < g - h < 1
B. 0 < g - h < 2
C. 1/2 < g - h < 2
D. 1 < g - h < 3/2
E. 1 < g - h < 2
Given:
1 > g > 1/2
-1 < h < -1/2

IMPORTANT
If we have two different inequalities in which the inequality signs are facing the same direction, then we can ADD the inequalities to get a new, valid inequality.
However, we can't SUBTRACT them (for more on this, watch: https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/video/982)

That said, we can still use the above ADDITION strategy once we do one thing first
Take -1 < h < -1/2 and multiply all 3 parts by -1
Since we're multiplying by a NEGATIVE value, we must REVERSE the inequality signs to get: 1 > -h > 1/2

We now have:
1 > g > 1/2
1 > -h > 1/2

Since the inequality signs are facing the same direction, we can ADD the inequalities to get: 1 + 1 > g + (-h) > 1/2 + 1/2
Simplify to get: 2 > g - h > 1
We can also write this as 1 < g - h < 2

Cheers,
Brent

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### GMAT/MBA Expert

Jeff@TargetTestPrep GMAT Instructor
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Mon Feb 12, 2018 4:19 pm
AAPL wrote:
If 1 > g > 1/2 and -1 < h < -1/2, then which of the following expresses all possible values of g - h?

A. 0 < g - h < 1
B. 0 < g - h < 2
C. 1/2 < g - h < 2
D. 1 < g - h < 3/2
E. 1 < g - h < 2
If we multiply the second inequality by -1, we have:

1 > -h > 1/2

Adding the two inequalities together, we have:

2 > g - h > 1

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