the toys are red and large

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 am; Location: India; Thanked: 267 times; Followed by:80 members; GMAT Score:760

the toys are red and large

by sanju09 » Wed Mar 09, 2011 4:31 am

In a certain production lot, 40 percent of the toys are red and the remaining toys are green. Half of toys are small and half are large. If 10 percent of the toys are red and small, and 40 toys are green and large. How many of the toys are red and large?
A. 40
B. 60
C. 70
D. 80
E. 90

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Source: Beat The GMAT — Problem Solving | Wed Mar 09, 2011 4:31 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Wed Mar 09, 2011 4:49 am

Red toys = 40%, Green toys = 60%
Large toys = 50%, small toys = 50%
Small red toys = 10% implies Large Red toys = 30%, Small Green Toys = 40%, and Large Green Toys = 20%
Green and Large toys = 40
Let the number of toys = T and 40 toys are green and large.
Then 20% of T = 40 implies T = 200
30% toys are Red and Large, so 30% of 200 = 60

The correct answer is B.

Last edited by Anurag@Gurome on Wed Mar 09, 2011 5:03 am, edited 1 time in total.

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 am; Location: India; Thanked: 267 times; Followed by:80 members; GMAT Score:760

by sanju09 » Wed Mar 09, 2011 4:57 am

Anurag@Gurome wrote:Red toys = 40%, Green toys = 60%
Large toys = 50%, small toys = 50%
Small red toys = 10% implies Large Red toys = 30%, Small Green Toys = 40%, and Large Green Toys = 20%
Green and Large toys = 40
Let the number of toys = T and 40 toys are green and large.
Then 20% of T = 40 implies T = 200
30% toys are Red and Large, so 30% of 200 = 60

The correct answer is A.

But [spoiler]A[/spoiler] is not [spoiler]60[/spoiler]

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Wed Mar 09, 2011 5:05 am

sanju09 wrote:
But [spoiler]A[/spoiler] is not [spoiler]60[/spoiler]

Sorry, that was a typo, its B. Thanks for pointing that. Edited the previous post.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Apr 11, 2018 5:39 am

sanju09 wrote:In a certain production lot, 40 percent of the toys are red and the remaining toys are green. Half of toys are small and half are large. If 10 percent of the toys are red and small, and 40 toys are green and large. How many of the toys are red and large?
A. 40
B. 60
C. 70
D. 80
E. 90

We can let the total number of toys = n.

So 0.4n toys are red and 0.6n are green.

0.5n are large and 0.5n are small.

0.1n are red and small.

40 toys are green and large.

We can create the equation:

Total = large + green - both green and large + neither green nor large

n = 0.5n + 0.6n - 40 + 0.1n

n = -40 + 1.2n

40 = 0.2n

200 = n

Since 0.4n of the toys are red and 0.1n of the toys are red and small, then 0.3n of the toys must be red and large. Since n = 200, the number of toys that are red and large is 0.3(200) = 60.

(Note: Alternatively, we can say:

Since 0.5n of the toys are large and 40 toys are green and large, then 0.5n - 40 toys must be red and large. Since n = 200, the number of toys that are red and large is 0.5(200) - 40 = 60.)

Answer: B

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