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

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Joined: 02 Sep 2009
Posts: 52285
If 1 > g > 1/2 and -1 < h < -1/2, then which of the following expresse  [#permalink]

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02 Jan 2017, 04:28
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Difficulty:

45% (medium)

Question Stats:

60% (01:49) correct 40% (02:07) wrong based on 125 sessions

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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

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Posts: 1003
Re: If 1 > g > 1/2 and -1 < h < -1/2, then which of the following expresse  [#permalink]

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02 Jan 2017, 10:29
Bunuel 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

Min value of g-h is when g=0.51 h=-0.51
thus g-h=1.02
Max value of g-h is when g=0.99 and h=-0.99
g-h =0.99-(-0.99)==2*0.99==1.98

thus option E satisfies both case

Hence E
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Joined: 13 Oct 2016
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Re: If 1 > g > 1/2 and -1 < h < -1/2, then which of the following expresse  [#permalink]

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02 Jan 2017, 10:43
2
Bunuel 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

1/2<g<1 and -1<h<-1/2

(g-h)(min) < g-h < (g-h)(max)

(g-h) (max) = g(max) - h(min) = 1 - (-1) = 2

(g-h) (min) = g(min) - h(max) = 1/2 - (-1/2) = 1

1<g-h<2

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Joined: 11 Sep 2015
Posts: 3334
Re: If 1 > g > 1/2 and -1 < h < -1/2, then which of the following expresse  [#permalink]

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06 Feb 2018, 10:39
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Top Contributor
Bunuel 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 ... /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

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Re: If 1 > g > 1/2 and -1 < h < -1/2, then which of the following expresse  [#permalink]

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12 Feb 2018, 16:09
Bunuel 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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Re: If 1 > g > 1/2 and -1 < h < -1/2, then which of the following expresse &nbs [#permalink] 12 Feb 2018, 16:09
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