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Post subject: If r + s > 2t, is r > t ? (1) t > s (2) r > s  Posted: Sun Jul 29, 2007 9:20 pm |
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If r + s > 2t, is r > t ?
(1) t > s
(2) r > s
Looking at the solution, it appears the inequalities are just added to each other and solved. Do inequalities work the same way as regular equations? For instance, if you have:
X - Y = 5
X + Y = 7
You get: 2X = 12
Can you do the same thing with inequalities?
For instance, in the equation above:
r + s > 2t
t > s
You get: r + s + t > 2t +s
Therefore: r>t
Can someone please confirm this for me?
My initial reaction was not to add inequalities as the solution did. Rather, I wanted to plug in numbers and identify under what circumstances each equation would work - if at all (for instance, I checked values of negative s, and negative t....compared the values.....for the second equation "r>s" - since there was no relation to t provided, I assumed that it was insufficient....which was obviously incorrect)
Any thoughts?
Thank You
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Borcho
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Post subject: My solution Posted: Sun Jul 29, 2007 10:38 pm |
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If r + s > 2t, is r > t ?
(1) t > s
(2) r > s
1) t>s <=> t-s>0
r+s > 2t =>
r > t+(t-s) where t-s>0 =>
r>t SUFFICIENT
2) r>s =>
r+r>r+s
2r>r+s>2t
r>t
Sufficient
Answer D.
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Harish Dorai
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Post subject: Posted: Mon Jul 30, 2007 9:51 am |
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We should not add/subtract/multiply/divide variables to the inequalities without knowing whether the integers presented are non-zero or non-negative. I feel the answer is still (D).
Given r + s > 2t
Statement (1) says t > s which means s < t
So the given inequality r + s > 2t can be re-written as
r + (<t) > 2t ==> This implies r has to be greater than t to satisfy the inequality r + s > 2t.
SUFFICIENT.
Statement (2) says that r > s which can be re-written as s < r
So the given inequality can be re-written as r + (<r) > 2t ==> this also implies that r has to be greater than t.
SUFFICIENT.
So the answer is (D).
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StaceyKoprince
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Post subject: Posted: Tue Jul 31, 2007 1:07 am |
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| ManhattanGMAT Staff |
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Posts: 6077
Location: San Francisco
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You can, indeed, add inequalities AS LONG AS the signs are identical and pointing in the same direction. And, in fact, when we can do this, it is often the easiest way to handle the math.
Trying numbers is a great fall-back method, and on some problems it should be the main method, but the one drawback is that we might not try all the right numbers or find the circumstances we need to prove or disprove something. So just have to be careful there.
Separately, for inequalities, you do not want to multiply or divide by variables if you do not know whether those variables are positive or negative.
_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT
Last edited by StaceyKoprince on Thu Sep 04, 2008 9:32 am, edited 1 time in total.
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Guest
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Post subject: If r + s > 2t, is r > t ? (1) t > s (2) r > s Posted: Thu Jul 31, 2008 5:31 am |
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Stacey,
In the above post you have mentioned that we can add or substract ineqalities, I have read other of your posts and you have mentioned that we can add but not substract them. So I was just making sure that this adding is allowed and substracting not allowed and that this was just by mistake
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StaceyKoprince
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Post subject: Posted: Thu Sep 04, 2008 9:32 am |
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| ManhattanGMAT Staff |
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Posts: 6077
Location: San Francisco
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Oops - yes, it should've just said "add" not "add or subtract." Sorry about that! I've edited the post.
_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT
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