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# If r + s > 2t, is r > t ? (1) t > s (2) r > s

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Intern
Joined: 17 May 2008
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If r + s > 2t, is r > t ? (1) t > s (2) r > s [#permalink]

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31 May 2008, 09:49
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If r + s > 2t, is r > t ?

(1) t > s

(2) r > s
_________________

Impossible is nothing...

Director
Joined: 10 Sep 2007
Posts: 943
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Kudos [?]: 303 [0], given: 0

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31 May 2008, 10:06
Statement 1:
Tells us t > s => t = s + x => s = t - x (where x is some +ve number).
=> r + s = r + t - x > 2t => r > t + x. As x is +ve so r is greater than t. So answer can only be A or D.

Statement 2:
Tells us r > s => r = s + y => s = r - y (where y is some +ve number).
=> r + s = r + r - y > 2t => 2r > 2t + y => r > t + y/2. As y is +ve so r is greater than t. So answer is D.
VP
Joined: 10 Jun 2007
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31 May 2008, 10:44
2
KUDOS
mrwaxy wrote:
If r + s > 2t, is r > t ?

(1) t > s

(2) r > s

D.

(1)
r + s > 2t
t > s
get: r + s + t > 2t + s
=> r + t > 2t
=> r > t
SUFFICIENT

(2)
r + s > 2t
r > s
get 2r + s > 2t + s
=> 2r > 2t
=> r > t
SUFFICIENT
Director
Joined: 14 Oct 2007
Posts: 754
Location: Oxford
Schools: Oxford'10
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31 May 2008, 15:28
bkk145, you're on fire today

bkk145 wrote:
mrwaxy wrote:
If r + s > 2t, is r > t ?

(1) t > s

(2) r > s

D.

(1)
r + s > 2t
t > s
get: r + s + t > 2t + s
=> r + t > 2t
=> r > t
SUFFICIENT

(2)
r + s > 2t
r > s
get 2r + s > 2t + s
=> 2r > 2t
=> r > t
SUFFICIENT
VP
Joined: 18 May 2008
Posts: 1265
Followers: 17

Kudos [?]: 449 [0], given: 0

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31 May 2008, 21:56
+1 from me 2

bkk145 wrote:
mrwaxy wrote:
If r + s > 2t, is r > t ?

(1) t > s

(2) r > s

D.

(1)
r + s > 2t
t > s
get: r + s + t > 2t + s
=> r + t > 2t
=> r > t
SUFFICIENT

(2)
r + s > 2t
r > s
get 2r + s > 2t + s
=> 2r > 2t
=> r > t
SUFFICIENT
Re: DS If r+s....   [#permalink] 31 May 2008, 21:56
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