One kilogram

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gmat25: Master | Next Rank: 500 Posts; Posts: 189; Joined: Wed Jul 06, 2011 6:57 amFollowed by: 1 member; Thanked: 17 times

by gmat25 » Sat Jul 23, 2011 1:40 pm

One kilogram of a certain coffee blend consists of x kilogram of type I coffee and y kilogram of type II coffee. 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

OA B

Last edited by gmat25 on Sun Jul 24, 2011 12:32 am, edited 1 time in total.

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Source: Beat The GMAT — Data Sufficiency | Sat Jul 23, 2011 1:40 pm

goalevan: Master | Next Rank: 500 Posts; Posts: 111; Joined: Tue Dec 30, 2008 1:25 pm; Location: USA; Thanked: 28 times; GMAT Score:770

by goalevan » Sat Jul 23, 2011 3:34 pm

It's given that x + y = 1 because the type I and type II coffee weigh 1 kilogram together. It's also given that the cost per kilogram C = 6.5x + 8.5y

So C = 6.5x + 8.5(1 - x) = 6.5x - 8.5x + 8.5 = -2x + 8.5

x < 0.8?

Statement 1) y > 0.15, and x + y = 1, so 1 - x > 0.15, and x < 0.85.

x could be less than or greater than 0.8, so statement 1 alone is insufficient.

Statement 2) C >= 7.3, so -2x + 8.5 >= 7.3, and x <= 0.6.

x is less than or equal to 0.6, so x must be less than 0.8. Statement 2 alone is sufficient.

IMO B

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gmat25: Master | Next Rank: 500 Posts; Posts: 189; Joined: Wed Jul 06, 2011 6:57 amFollowed by: 1 member; Thanked: 17 times

by gmat25 » Sun Jul 24, 2011 12:31 am

goalevan wrote:It's given that x + y = 1 because the type I and type II coffee weigh 1 kilogram together. It's also given that the cost per kilogram C = 6.5x + 8.5y

So C = 6.5x + 8.5(1 - x) = 6.5x - 8.5x + 8.5 = -2x + 8.5

x < 0.8?

Statement 1) y > 0.15, and x + y = 1, so 1 - x > 0.15, and x < 0.85.

x could be less than or greater than 0.8, so statement 1 alone is insufficient.

Statement 2) C >= 7.3, so -2x + 8.5 >= 7.3, and x <= 0.6.

x is less than or equal to 0.6, so x must be less than 0.8. Statement 2 alone is sufficient.

IMO B

nice explanation, thanks a lot!!!!

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