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mixture problem with percents please help!

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by wawatan » Sun Jun 22, 2008 1:23 pm
A certain mixture of nuts consists of 4 parts almonds to 1 part walnuts, by weight. By removing some of the almonds, the remained nuts consist 75 percent of almonds, by weight. What percent of the almonds were removed?
(A) 10%
(B) 12.5%
(C) 20%
(D) 25%
(E) 30%
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by Nycgrl » Sun Jun 22, 2008 1:38 pm
What's OA
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by Nycgrl » Sun Jun 22, 2008 1:42 pm
Let the total amount of mixture be 20g => 16g almonds + 4G walnuts.

Now 75% of almonds are left therefore 25% are removed so almonds removed = .25*16 = 4.

percent of almonds removed 4/16 * 100 = 10%

What's OA
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by beeparoo » Sun Jun 22, 2008 1:48 pm
A/W = 4/1........ Eq 1

Let x = amount of almonds removed

(A - x)/[(A - x) + W] = 3/4......... Eq 2

Sub in W = A/4 from Eq 1 into Eq 2

A - x = (3/4)[A - x + A/4]

x/A = 1/4
Therefore, 25% of original almonds were removed. Ans D
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by wawatan » Sun Jun 22, 2008 2:35 pm
OA is C! did anyone else get C for the answer????
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by Nycgrl » Sun Jun 22, 2008 2:42 pm
Nycgrl wrote:Let the total amount of mixture be 20g => 16g almonds + 4G walnuts.

Now 75% of almonds are left therefore 25% are removed so almonds removed = .25*16 = 4.

CORRECTION

percent of almonds removed 4/20 * 100 = 20%

Its C
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Re: mixture problem with percents please help!

by beeparoo » Sun Jun 22, 2008 3:36 pm
wawatan wrote:A certain mixture of nuts consists of 4 parts almonds to 1 part walnuts, by weight. By removing some of the almonds, the remained nuts consist 75 percent of almonds, by weight. What percent of the almonds were removed?
(A) 10%
(B) 12.5%
(C) 20%
(D) 25%
(E) 30%
I don't understand what I did wrong. I will address two points of view.

Point #1: The sentence, "By removing some of the almonds, the remained nuts consist 75 percent of almonds, by weight", indicates (to ME) that the remaining almonds are 75% of total nuts after removal of almonds.

If I compare approach to NYCgrl, she interprets that, 'after removal, 75% of original almonds (not total nuts!) remain'.

Point #2: To address the Question Stem, "What percent of the almonds were removed?", my view is to solve for
(removed almonds)/(original amt of almonds).

But again, here, NYCgrl differs by calculating for
(removed almonds)/(total original nuts) - which I would have NEVER thought the question was asking...

++

Did anyone else experience similar conflict in the interpretation of this problem??
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Re: mixture problem with percents please help!

by Ian Stewart » Mon Jun 23, 2008 6:16 am
beeparoo wrote:
wawatan wrote:A certain mixture of nuts consists of 4 parts almonds to 1 part walnuts, by weight. By removing some of the almonds, the remained nuts consist 75 percent of almonds, by weight. What percent of the almonds were removed?
(A) 10%
(B) 12.5%
(C) 20%
(D) 25%
(E) 30%
I don't understand what I did wrong. I will address two points of view.

Point #1: The sentence, "By removing some of the almonds, the remained nuts consist 75 percent of almonds, by weight", indicates (to ME) that the remaining almonds are 75% of total nuts after removal of almonds.

If I compare approach to NYCgrl, she interprets that, 'after removal, 75% of original almonds (not total nuts!) remain'.

Point #2: To address the Question Stem, "What percent of the almonds were removed?", my view is to solve for
(removed almonds)/(original amt of almonds).

But again, here, NYCgrl differs by calculating for
(removed almonds)/(total original nuts) - which I would have NEVER thought the question was asking...

++

Did anyone else experience similar conflict in the interpretation of this problem??
Well, there's something wrong with the wording of the question; it talks about 'remained nuts' which is not a phrase you'd ever see on the GMAT. So perhaps some important wording in the question has been lost in the transcription here. But, as presented, I interpret the question exactly as beeparoo does above, and the correct answer should be 25%, not 20%. So I don't think you've done anything wrong!
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
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by beeparoo » Mon Jun 23, 2008 9:20 am
Hi Ian - Thanks for your comment about the wording. It helps to know that I'm not the only person having difficulty with the wording.

@wawatan: If you had difficulty getting to the OA, I can see why. The question is too ambiguous and is left open to interpretation.
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