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Chemical X costs $4 per ounce, and Chemical Y costs $8 per ounce. If 3

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Chemical X costs $4 per ounce, and Chemical Y costs $8 per ounce. If 3  [#permalink]

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New post 29 Dec 2017, 09:25
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Chemical X costs $4 per ounce, and Chemical Y costs $8 per ounce. If 30 ounces of a mixture consists of x ounces of Chemical X and y ounces of Chemical Y, does the cost of Chemical X in the mixture exceed that of Chemical Y ?

1. The cost of the 30 ounce mixture is less than $160.
2. y < 15

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Chemical X costs $4 per ounce, and Chemical Y costs $8 per ounce. If 3  [#permalink]

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New post 29 Dec 2017, 09:58
Chemical X costs $4 per ounce,
Chemical Y costs $8 per ounce.

Given x + y = 30

so cost of the mixture : 4x + 8y = 4x + 8(30-x) = 240 - 4x

statement 1: cost of the mixture is less than 160

240 - 4x < 160 or 4x > 80 or x>20
let's say x = 21 and y = 9

cost of x in the mixture = 21 * 4 = $82
cost of y in the mixture = 9 * 8 = $72

hence : cost of x in the mixture is greater than that of y in the mixture: A
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Re: Chemical X costs $4 per ounce, and Chemical Y costs $8 per ounce. If 3  [#permalink]

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New post 29 Dec 2017, 10:42
QZ wrote:
Chemical X costs $4 per ounce, and Chemical Y costs $8 per ounce. If 30 ounces of a mixture consists of x ounces of Chemical X and y ounces of Chemical Y, does the cost of Chemical X in the mixture exceed that of Chemical Y ?

1. The cost of the 30 ounce mixture is less than $160.
2. y < 15


This is a "stolen" OG question: https://gmatclub.com/forum/material-a-c ... 82349.html
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Re: Chemical X costs $4 per ounce, and Chemical Y costs $8 per ounce. If 3  [#permalink]

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New post 29 Dec 2017, 10:53
But certainly I didn't stole it. Found it in my practice material.

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Re: Chemical X costs $4 per ounce, and Chemical Y costs $8 per ounce. If 3  [#permalink]

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Re: Chemical X costs $4 per ounce, and Chemical Y costs $8 per ounce. If 3  [#permalink]

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New post 29 Dec 2017, 11:09
A : 4x + 8y < 160
x + 2y < 40 (dividing by 4)
Also we have,
x + y = 30
Therefore,
y < 40 -30 < 10
If y < 10 , then cost of chemical Y is < 8*10 < 80.

Since x + y = 30, y < 10 -> x > 20.

Therefore cost of material X is
> 4*20 > 80

Hence (1) is sufficient.

(2) is not. So answer is A.

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Re: Chemical X costs $4 per ounce, and Chemical Y costs $8 per ounce. If 3   [#permalink] 29 Dec 2017, 11:09
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