Percentage Problem

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N:Dure: Master | Next Rank: 500 Posts; Posts: 181; Joined: Sat Oct 16, 2010 1:57 pm; Thanked: 4 times

by N:Dure » Tue Nov 16, 2010 1:36 am

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Source: Beat The GMAT — Problem Solving | Tue Nov 16, 2010 1:36 am

beat_gmat_09: Master | Next Rank: 500 Posts; Posts: 437; Joined: Sat Nov 22, 2008 5:06 amFollowed by: 1 member; Location: India; Thanked: 50 times; GMAT Score:580

by beat_gmat_09 » Tue Nov 16, 2010 1:48 am

N:Dure wrote:??

Total in Jan - J
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: 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 » Tue Nov 16, 2010 9:16 am

N:Dure wrote:??

I would multiply all the percentages by 10 to make the math easier. The problem then becomes:

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: Senior | Next Rank: 100 Posts; Posts: 80; Joined: Mon Jan 31, 2011 10:08 pmFollowed by: 2 members

by kamalakarthi » Sat Mar 19, 2011 1:19 pm

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.

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shayam: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Wed Mar 16, 2011 12:31 pmFollowed by: 1 member; Thanked: 3 times

by shayam » Mon May 16, 2011 6:58 am

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...

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