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word problem

by GRV99 » Sat Sep 17, 2011 12:12 pm
. In each production lot for a certain toy, 25 percent of the toys are red and 75 percent of the toys are blue. Half the toys are size A and half are size B. If 10 out of a lot of 100 toys are red and size A, how many of the toys are blue and size B?

(A) 15
(B) 25
(C) 30
(D) 35
(E) 40

[spoiler]OA:D[/spoiler]
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by shankar.ashwin » Sat Sep 17, 2011 12:33 pm
Red = 25
Blue = 75.

Size A = 50
Size B =50

Red & Size A = 10.

Therefore, Red & Size B = 25- 10 =15.

Total Size B = Red Size B + Blue Size B

50 = 15 + Blue Size B

Blue Size B = 35


GRV99 wrote:. In each production lot for a certain toy, 25 percent of the toys are red and 75 percent of the toys are blue. Half the toys are size A and half are size B. If 10 out of a lot of 100 toys are red and size A, how many of the toys are blue and size B?

(A) 15
(B) 25
(C) 30
(D) 35
(E) 40

[spoiler]OA:D[/spoiler]
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by Brent@GMATPrepNow » Sat Sep 17, 2011 6:02 pm
GRV99 wrote:. In each production lot for a certain toy, 25 percent of the toys are red and 75 percent of the toys are blue. Half the toys are size A and half are size B. If 10 out of a lot of 100 toys are red and size A, how many of the toys are blue and size B?

(A) 15
(B) 25
(C) 30
(D) 35
(E) 40

[spoiler]OA:D[/spoiler]
For questions where there is a population, where each member of the population has two characteristics associated with it, we can use the Double Matrix Method to solve the question.

Here, we have a population of toys and the 2 characteristics are:
1) color (blue or red)
2) size (size A or size B)

More information on the Double Matrix Method can be found in this YouTube video: https://www.youtube.com/watch?v=OWD2t5jCCZQ

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by edvhou812 » Sat Sep 17, 2011 7:31 pm
I ended up using the method put forward by Brent. I find it really quick and easy since I am not a formula whiz. Here is the logic I used to get the numbers in the attached table. The red numbers are given to us in the question. The numbers that are along the very bottom and the side are given by multiplying 100 with the given fractions. The rest fills out itself.


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