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Percentage Problem
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beat_gmat_09
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Total in Jan - JN:Dure wrote:??
Total in Feb - F
7% rejected in Jan - 7J/100
8% rejected in Feb - 8J/100
Total rejected in Jan and Feb both = 7.8 of (J + F) /100
7J + 8F = 7.8(J + F)
Solving, F = 4J
1/4
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GMATGuruNY
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I would multiply all the percentages by 10 to make the math easier. The problem then becomes:N:Dure wrote:??
How do we combine 70% with 80% to yield a mixture that is 78%?
This is a weighted average question. An efficient approach is alligation:
The proportion needed of each of the original percentages (70% and 80%) is the difference between the other 2 percentages.
Proportion needed of 70% = 80-78 = 2.
Proportion needed of 80% = 78-70 = 8.
Thus, the ratio needed is 2:8 = 1:4.
The correct answer is C.
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kamalakarthi
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Mitch,
Thank you very much for the answer. However my doubt was 1:4 for the total rejections right. That means for every 1 peice of jan rejection there has to be 4 rejections. How this can be the total ratio of production. Can you please help me understand this.
Thank you very much for the answer. However my doubt was 1:4 for the total rejections right. That means for every 1 peice of jan rejection there has to be 4 rejections. How this can be the total ratio of production. Can you please help me understand this.
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shayam
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Hi Kamalkarthi,
The ratio coming out from Allegation would be
How much of J is used : How much of F is used in deriving 7.8% taken from J+ F.
To understand better:
Lets solve the same problem using the percentage of units produced.
Percentage of units produced in J= 93% (100-7)
Percentage of units produced in F =92% (100-8)
Percentage together j + f = 92.2 (100-7.8)
Hence using allegation . Ratio of J:F used = (92 - 92.2) /(92.2 -93)
= -0.2/-0.8
= 1/4
This is same as the one produced using defects percentage.
Hope this helps...
The ratio coming out from Allegation would be
How much of J is used : How much of F is used in deriving 7.8% taken from J+ F.
To understand better:
Lets solve the same problem using the percentage of units produced.
Percentage of units produced in J= 93% (100-7)
Percentage of units produced in F =92% (100-8)
Percentage together j + f = 92.2 (100-7.8)
Hence using allegation . Ratio of J:F used = (92 - 92.2) /(92.2 -93)
= -0.2/-0.8
= 1/4
This is same as the one produced using defects percentage.
Hope this helps...
