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by neelgandham » Thu Dec 01, 2011 8:09 am
One kilogram of a certain coffee blend consists of X kilogram of type I and Y kilogram of type II. The cost of the blend is C dollars per kilogram, where C=6.5X + 8.5Y. Is X < 0.8?

(1) Y > 0.15 (2) C ≥ 7.30
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by GMATGuruNY » Thu Dec 01, 2011 8:41 am
neelgandham wrote:One kilogram of a certain coffee blend consists of X kilogram of type I and Y kilogram of type II. The cost of the blend is C dollars per kilogram, where C=6.5X + 8.5Y. Is X < 0.8?

(1) Y > 0.15 (2) C ≥ 7.30
Since X+Y = 1, Y = 1-X.
Thus:
C = 6.5X + 8.5(1-X) = 8.5 - 2X.

Statement 1: Y > .15
Thus:
1 - X > .15
X < .85
Since it's possible that X < .8 or that X > .8, INSUFFICIENT.

Statement 2: C ≥ 7.3
8.5 - 2X ≥ 7.3
1.2 ≥ 2X
X ≤ .6.
SUFFICIENT.

The correct answer is B.
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by urshohini » Thu Dec 08, 2011 5:25 am
Since X+Y = 1, Y = 1-X.
Mitch,
Can you pl tell me why are we considering X+y=1? It can be come other amount as well.
Pl explain under what circumstances should we consider this?
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by GMATGuruNY » Thu Dec 08, 2011 5:34 am
urshohini wrote:
Since X+Y = 1, Y = 1-X.
Mitch,
Can you pl tell me why are we considering X+y=1? It can be come other amount as well.
Pl explain under what circumstances should we consider this?
ONE KILOGRAM of a certain coffee blend CONSISTS OF X kilogram of type I and Y kilogram of type II.
Thus, X+Y=1.

The cost of the blend is C dollars PER KILOGRAM, where C=6.5X + 8.5Y.
Since C = the cost of ONE KILOGRAM, and X+Y form ONE KILOGRAM, we can substitute Y=1-X into the formula for C.
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by urshohini » Tue Dec 13, 2011 5:57 am
Ohh yes, my bad for not reading the question properly!! :(
Thanks Mitch for your response!
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