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M21-34

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M21-34 [#permalink]

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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%
[Reveal] Spoiler: OA

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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\(\frac{A}{R} = \frac{3}{7}\).

Answer: C
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Re: M21-34 [#permalink]

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New post 15 Dec 2014, 00:25
Hi, I agree the solution is 3/7, but wonder how 3/7 equals to 30%.It should be 42 %.Can someone explain

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New post 17 Dec 2014, 05:57

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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

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New post 26 Feb 2015, 06:54
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.

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Re: M21-34 [#permalink]

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New post 28 Mar 2015, 10:33
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% .
Answer C
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Re: M21-34 [#permalink]

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New post 20 Feb 2016, 21:05
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%

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New post 04 Nov 2017, 13:04
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.

The answer should be 33%

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New post 05 Nov 2017, 00:16
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.

The answer should be 33%


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

Please re-read the solution above more carefully.
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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: M21-34   [#permalink] 05 Nov 2017, 00:16
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