Coffee Blend

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tonebeeze: Master | Next Rank: 500 Posts; Posts: 158; Joined: Mon Nov 02, 2009 5:49 pmFollowed by: 3 members; Thanked: 2 times

by tonebeeze » Tue May 10, 2011 5:39 pm

x + y =

Last edited by tonebeeze on Wed May 11, 2011 11:39 am, edited 1 time in total.

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Source: Beat The GMAT — Data Sufficiency | Tue May 10, 2011 5:39 pm

sourabh33: Master | Next Rank: 500 Posts; Posts: 135; Joined: Tue Mar 22, 2011 12:01 pmFollowed by: 3 members; Thanked: 21 times; GMAT Score:720

by sourabh33 » Tue May 10, 2011 6:15 pm

B

Given

X + Y =1

C = 6.5X + 8.5Y
C = 6.5X + 8.5 (1-X)
X = (8.5 - C)/2.5

Statement 1

y>0.15

if y = 0.18 then x = 0.82 hence x>0.8
if y = 0.45 then x = 0.55 hence x<0.8
Therefor statement 1 is insufficient

Statement 2

C â‰¥ 7.30
putting c = 7.3 in X = (8.5 - C)/2.5 --> 1.2/2.5 hence x<0.8
this will hold true for all values of c>7.3

hence sufficient

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smackmartine: Legendary Member; Posts: 516; Joined: Fri Jul 31, 2009 3:22 pmFollowed by: 13 members; Thanked: 112 times

by smackmartine » Tue May 10, 2011 6:16 pm

Given X+Y= 1 &

C= 6.5 X + 8.5 Y

Asked Is X < 0.8?

Lets rewrite equation C= 6.5 X + 8.5 Y in terms of C & X

C= 6.5 X + 8.5 (1-X) ---> now in order to get the value of X all we need is Value of C, which is only given by Statement 2

Considering statement 2,
Lets take extreme value of C i.e 7.3
so
7.3= 6.5 X + 8.5 (1-X)
Solving for X, 2 X = 1.2 => x=0.6 (So,Yes X < 0.8)

Lets try to take a higher value of X to prove the statement 2, Insufficient.
Now Lets take value of X=0.8
C = 6.5 *0.8 + 8.5 (1-0.8) =6.9 (which contradicts statement 2)
So X has to be less than 0.8
So , B

tonebeeze 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 â‰¥ 7.30

OA = B

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tonebeeze: Master | Next Rank: 500 Posts; Posts: 158; Joined: Mon Nov 02, 2009 5:49 pmFollowed by: 3 members; Thanked: 2 times

by tonebeeze » Wed May 11, 2011 10:56 am

In simplifying the problem, can you review this step:

"C = 6.5X + 8.5 (1-X) --->X = (8.5 - C)/2.5 "

thanks

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smackmartine: Legendary Member; Posts: 516; Joined: Fri Jul 31, 2009 3:22 pmFollowed by: 13 members; Thanked: 112 times

by smackmartine » Wed May 11, 2011 9:50 pm

You are correct.

tonebeeze wrote:In simplifying the problem, can you review this step:

"C = 6.5X + 8.5 (1-X) --->X = (8.5 - C)/2.5 "

thanks

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