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Brand W nut mix contains 24% cashews by weight, and Brand X

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Brand W nut mix contains 24% cashews by weight, and Brand X [#permalink]

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Brand W nut mix contains 24% cashews by weight, and Brand X nut mix contains 9% cashews by weight. If w pounds of Brand W nut mix are combined with x pounds of Brand X nut mix to produce y pounds of nut mix that is 15% cashews by weight, what is the value of x?

(1) w = 30
(2) y = 75

NOTE: kudos for all correct solutions.

[Reveal] Spoiler:
[Reveal] Spoiler: OA

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Brand W nut mix contains 24% cashews by weight, and Brand X [#permalink]

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New post 06 Oct 2016, 10:41
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w : x :y = 6:9:15

St1:

If w=30,

Ratio multiplier=30/6=5

x=5*9=45

Sufficient

St1:

If y=75

Ratio multiplier=75/15=5

x=5*9=45


Sufficient

D

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Re: Brand W nut mix contains 24% cashews by weight, and Brand X [#permalink]

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w(0.24) + x(0.09) = 0.15(x + w)
0.09w = 0.06x
3w = 2x

St1: w = 30 --> x = 45
Sufficient

St2: y = 75 --> x + w = 75
x + (2/3)x = 75
5x = 225
x = 45
Sufficient

Answer: D
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Re: Brand W nut mix contains 24% cashews by weight, and Brand X [#permalink]

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New post 06 Oct 2016, 11:40
acegmat123

Thanks for the post. But I couldn't get how accurate the ratio w:x:y = 6:9:15 is...can you elaborate how number 6 arrives?
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Brand W nut mix contains 24% cashews by weight, and Brand X [#permalink]

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New post 06 Oct 2016, 13:43
9------15-------------24

15 is closer to 9 than to 24. So x contributed more than w.

We just have to reverse their differences to get values.

w=| final % - % in x |

=15-9=6

Similarly

x=|final % - % in w |

=24-15=9

y= x+w= 6+9= 15

w : x : y = 6:9:15

It works for all mixture problems where two components are mixed to get final component.


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Re: Brand W nut mix contains 24% cashews by weight, and Brand X [#permalink]

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New post 09 Oct 2016, 19:43
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GMATPrepNow wrote:
Brand W nut mix contains 24% cashews by weight, and Brand X nut mix contains 9% cashews by weight. If w pounds of Brand W nut mix are combined with x pounds of Brand X nut mix to produce y pounds of nut mix that is 15% cashews by weight, what is the value of x?

(1) w = 30
(2) y = 75

NOTE: kudos for all correct solutions.

[Reveal] Spoiler:

Avg weighted formula=W1/W2=(A2-Avg.)/(Avg.-A1)
W1=w; W2=x
A1=24; A2=9
Avg= 15

(1) W1=30
substituting respective values in W1/W2=(A2-Avg.)/(Avg.-A1)
w2=x=45.........suff..

(2) W1+W2=y=75
W1=75-W2
substituting respective values in W1/W2=(A2-Avg.)/(Avg.-A1)
w2=x=45.........suff..

Ans D
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Re: Brand W nut mix contains 24% cashews by weight, and Brand X [#permalink]

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By following allegation method we know that the mixtures W and X have been mixed in ratio:

W:X = 6:9
which is 2:3

1) From first equation W = 30 we know that 2 parts of W are equal to 30 so 3 parts would be equal to 45. -- Sufficient

2) From second equation Y = 75 we know that y is made up of W and X in ratio 2:3 so total 5 parts of Y = 75, 1 part is equal to 15 and 3 parts is 45. -- Sufficient.

Option D.
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Re: Brand W nut mix contains 24% cashews by weight, and Brand X [#permalink]

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Re: Brand W nut mix contains 24% cashews by weight, and Brand X   [#permalink] 16 Jan 2018, 05:29
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