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Inequalities - When to combine and when not to

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pmmalkan+gmat
 Post subject: Inequalities - When to combine and when not to
 Post Posted: Thu Dec 02, 2010 11:03 am 
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Students


Posts: 21
If 8x > 4 + 6x, what is the value of the integer x?

(1) 6 – 5x > -13

(2) 3 – 2x < -x + 4 < 7.2 – 2x

Normally, I would have solved this in the easiest and the most obvious way possible. That is:
1. Solve the If statement and get x > 2
2. Solve (1) and get x < 3.8 so I get x = integer 3 (SUFF.)
3. Solve (2) and also get the same result x = integer 3 (SUFF.)

However, I had seen Ron's Thursday lecture on combining inequalities just the day before and it kinda stuck in my head so I went ahead and combined the if statement inequality with stmt. (1) and I get a different result ->
I get x = integers 3 and 4.

Am I doing anything wrong conceptually? When should I combine and should I not?
I know in this problem it would be foolish to combine. But is it wrong as well? Any specific rule to combine?

Thanks very much,
Priya
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tim
 Post subject: Re: Inequalities - When to combine and when not to
 Post Posted: Tue Dec 07, 2010 10:10 am 
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ManhattanGMAT Staff


Posts: 2242
Location: Southwest Airlines, seat 21C
You haven't given any information about what you did to combine the statements, so it's possible you made an algebra mistake. In general, however, it's not wise to collapse two pieces of information into one piece if that's what you did, because you lose important information. If you can get useful information out of the two pieces of information separately, you should do so..

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Tim Sanders
Manhattan GMAT Instructor
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yousuf_azim
 Post subject: Re: Inequalities - When to combine and when not to
 Post Posted: Tue Sep 06, 2011 9:28 am 
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Students


Posts: 45
Dears.

What is the ANS?

BR
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JohnHarris
 Post subject: Re: Inequalities - When to combine and when not to
 Post Posted: Thu Sep 08, 2011 12:26 am 
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Posts: 38
pmmalkan wrote:
However, I had seen Ron's Thursday lecture on combining inequalities ... get x = integers 3 and 4.


First, let's finish reducing the equations to get:
If x > 2, what is the value of the integer x?

(1) x < 3.8

(2) -1 < x < 3.2

combining either (1) or (2) with the given X> 2, we get
2 < x < 3 + d
where d is either 0.8 [for (1)] or 0.2 [for (2)]. So, as you indicated, the answer is 3 and both are sufficient individually.

If I'm understanding you correctly, you are referring to
a > b
c > d
implies
a + c > b + d
as is referred to in
guide3-inequalities-when-shud-we-really-add-two-inequalities-t9449.html
for example

To do the add properly we first have to have the inequalities pointing in the same direction so we have to re-write the if and (1) as
x > 2
3.8 > x
Adding now gives
x + 3.8 > x + 2
which just tells you 3.8 is greater than 2. If this not what you were referring to, you will have to give more details as mentioned by tim
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jnelson0612
 Post subject: Re: Inequalities - When to combine and when not to
 Post Posted: Mon Oct 17, 2011 12:25 am 
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ManhattanGMAT Staff


Posts: 1857
yousuf_azim wrote:
Dears.

What is the ANS?

BR


John, nice!

Yousuf, the answer is D.

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Jamie Nelson
ManhattanGMAT Instructor
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