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shashwats: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Mon Apr 29, 2013 4:42 am

by shashwats » Mon Apr 29, 2013 4:55 am

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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Source: Beat The GMAT — Problem Solving | Mon Apr 29, 2013 4:55 am

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Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members; Location: Delhi, India; Thanked: 344 times

by Anju@Gurome » Mon Apr 29, 2013 5:19 am

shashwats 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?

Let us assume initially there was 100 gm of nuts.
So, there was 100*4/(4 + 1) = 80 gm almonds and (100 - 80) = 20 gm walnuts.

Let us assume x gm of walnut was removed.
So, in the remaining mixture, there is (80 - x) gm almonds and 20 gm walnuts.

So, 20/(100 - x) = 25/100 = 1/4
--> (100 - x) = 80
--> x = 100 - 80 = 20

So, 20 gm almonds was removed.
--> 20 = (20/80)*100 % of 80 = 25% of 80

The correct answer is D.

Last edited by Anju@Gurome on Mon Apr 29, 2013 5:35 am, edited 1 time in total.

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srcc25anu: Master | Next Rank: 500 Posts; Posts: 423; Joined: Fri Jun 11, 2010 7:59 amFollowed by: 2 members; Location: Seattle, WA; Thanked: 86 times

by srcc25anu » Mon Apr 29, 2013 5:21 am

Let Total Mixture be 100
Almonds = 4/5 * 100 = 80
Nuts = 1/5 * 100 = 20
If we remove Y amount of nuts, Nuts / Total Mixture ratio becomes 75%
Lets plug in answer choices to see what results.

A. we remove 10% or 8 units of almonds.
Now ALMONDS to Total % = (80-8) or 72 / 92 NOT EQUAL TO 75%

C. we remove 20% or 16 units of almonds
Almonds / Total = 64 / 86 (NOT EQUAL TO 75%)

D. lets remove 25% of almonds or 20 units
Almonds / Total = 60 / 80 or 3/4 or 75% (CORRECT ANSWER)

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fifafreak: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Wed Jan 27, 2010 3:47 am; Thanked: 2 times

by fifafreak » Mon Apr 29, 2013 6:26 am

Almonds = 80; Walnuts = 20

80 + 20 = 100....[1]
80-x + 20 = 100-x ...[2]

[80-x]/[100-x]= 75/100 => x = 20 which is 25% of 80. Ans. D

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Apr 29, 2013 7:06 am

shashwats 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%

Let number of almonds = 4 and the number of walnuts = 1.
After some of the almonds are removed, the remaining almonds must constitute 75% of the remaining total.
Thus, the number of walnuts must constitute 25% = 1/4 of the remaining total.
Thus, after the almonds are removed, the total number of nuts = 4, so that walnuts/total = 1/4.
Since the total number of nuts decreases from 5 to 4, only 1 almond was removed.
Thus:
(almonds removed)/(original number of almonds) = 1/4 = 25%.

The correct answer is D.

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