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# M21-34

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Math Expert
Joined: 02 Sep 2009
Posts: 48096

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16 Sep 2014, 01:15
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Difficulty:

25% (medium)

Question Stats:

72% (01:10) correct 28% (01:30) wrong based on 141 sessions

Arabica coffee costs $0.4 per ounce while Robusta coffee costs$0.3 per ounce. If the blend of Arabica and Robusta costs $0.33 per ounce, what is the share of Arabica in this blend? A. 20% B. 24% C. 30% D. 33% E. 40% _________________ Math Expert Joined: 02 Sep 2009 Posts: 48096 Re M21-34 [#permalink] ### Show Tags 16 Sep 2014, 01:15 Official Solution: Arabica coffee costs$0.4 per ounce while Robusta coffee costs $0.3 per ounce. If the blend of Arabica and Robusta costs$0.33 per ounce, what is the share of Arabica in this blend?

A. 20%
B. 24%
C. 30%
D. 33%
E. 40%

If the blend contains $$A$$ ounces of Arabica and $$R$$ ounces of Robusta then $$\frac{A0.4 + R0.3}{A + R} = 0.33$$ or $$0.07A = 0.03R$$ or$$\frac{A}{R} = \frac{3}{7}$$.

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Intern
Joined: 03 Jun 2013
Posts: 1

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15 Dec 2014, 01:25
Hi, I agree the solution is 3/7, but wonder how 3/7 equals to 30%.It should be 42 %.Can someone explain
Math Expert
Joined: 02 Sep 2009
Posts: 48096

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17 Dec 2014, 06:57
gmatgary wrote:
Hi, I agree the solution is 3/7, but wonder how 3/7 equals to 30%.It should be 42 %.Can someone explain

A/R = 3/7, hence A/(A + R) = A/(TOTAL) = 3/(3 + 7) = 3/10 = 30%.
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Manager
Joined: 14 Jul 2014
Posts: 94

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02 Jan 2015, 04:41
1
Hi Bunuel,

I used the Alligation method

A R
0.40 0.30
0.33
0.03 0.07

Hence share of Arabica in this blend = 0.03/0.10 = 30%

Can this method be applied to ALL Mixture problems? What does the red part technically mean
I blindly use this concept - hope my approach is correct

Thanks
Intern
Joined: 10 Jul 2014
Posts: 1

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26 Feb 2015, 07:54
Bunuel wrote:
gmatgary wrote:
Hi, I agree the solution is 3/7, but wonder how 3/7 equals to 30%.It should be 42 %.Can someone explain

A/R = 3/7, hence A/(A + R) = A/(TOTAL) = 3/(3 + 7) = 3/10 = 30%.

I have solved the problem with a different method, but it gave the same answer.

.4 ---> x
.3 ---> 1-x

.33 = .4(x) + .3(1-x)
.33 =.4x + .3 -.3x
.03 =.1x
percentage of Arabica is x= (.03/.1) * 100 = 30% of the blend.
Director
Joined: 07 Aug 2011
Posts: 560
GMAT 1: 630 Q49 V27

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28 Mar 2015, 11:33
1
Bunuel wrote:
Arabica coffee costs $0.4 per ounce while Robusta coffee costs$0.3 per ounce. If the blend of Arabica and Robusta costs \$0.33 per ounce, what is the share of Arabica in this blend?

A. 20%
B. 24%
C. 30%
D. 33%
E. 40%

applying weighted average methodology

Robus W.Avg Arabia
0.30---0.33--------0.40
lets get rid of decimals for simplicity
30---33--------40
As weighted average is 3 unit away from Robusta and 7 units away from Arabia , we know that A:R=3:7 or A is 30% .

Alternately , Setting this question stem on equation
0.4*A + 0.3*(1-A) = 0.33
multiply by 10 and solve A for 0.3 in 1 ounce or 30% .
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Manager
Joined: 05 Jul 2015
Posts: 104
GMAT 1: 600 Q33 V40
GPA: 3.3

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20 Feb 2016, 22:05
My allegation looked like this:

Arabica is 7cents away from the average. Robusta is only 3cents away. So there is a lot more Robusta. So out of the 7+3 =10 total parts, Arabica is only 3 out of the 10 or 30%
Intern
Joined: 19 Feb 2012
Posts: 4

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04 Nov 2017, 14:04
I am getting the following.

Substituting Arabica = 1/3 and Robusta = 2/3;

I get, (0.4 * 1/3 + .3 * 2/3)/ (1/3 + 2/3) = 0.33

This implies that arabica is 33% in the blend and robusta is 66.67% in the blend.

Math Expert
Joined: 02 Sep 2009
Posts: 48096

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05 Nov 2017, 01:16
srinivasbr2009 wrote:
I am getting the following.

Substituting Arabica = 1/3 and Robusta = 2/3;

I get, (0.4 * 1/3 + .3 * 2/3)/ (1/3 + 2/3) = 0.33

This implies that arabica is 33% in the blend and robusta is 66.67% in the blend.

(0.4 * 1/3 + 0.3 * 2/3)/ (1/3 + 2/3) = 1/3 NOT 0.33.

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Re: M21-34 &nbs [#permalink] 05 Nov 2017, 01:16
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# M21-34

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