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.
If 1 > g > 1/2 and -1 < h < -1/2, then which of
This topic has expert replies
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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.
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
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.
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Given: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
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
Answer: E
Cheers,
Brent
GMAT/MBA Expert
- Jeff@TargetTestPrep
- GMAT Instructor
- Posts: 1462
- Joined: Thu Apr 09, 2015 9:34 am
- Location: New York, NY
- Thanked: 39 times
- Followed by:22 members
If we multiply the second inequality by -1, we have: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
1 > -h > 1/2
Adding the two inequalities together, we have:
2 > g - h > 1
Answer:E
Jeffrey Miller
Head of GMAT Instruction
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews