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In a certain production lot, 40 percent of the toys are red

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In a certain production lot, 40 percent of the toys are red  [#permalink]

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New post Updated on: 14 Dec 2013, 04:54
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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

Hi all,

Like many of you I am in the process of preparing for the GMAT. I was going through the quant review book but I got stuck at this point. I just cannot understand how they get to the solution.

Does any of you get how they figure out that the percentage of large & green is 20%!?



Cheers
Dav

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Originally posted by dav2013 on 13 Dec 2013, 13:01.
Last edited by Bunuel on 14 Dec 2013, 04:54, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: Percentages driving me mad  [#permalink]

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New post 14 Dec 2013, 00:21
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dav2013 wrote:
Hi all,

Like many of you I am in the process of preparing for the GMAT. I was going through the quant review book but I got stuck at this point. I just cannot understand how they get to the solution.

Does any of you get how they figure out that the percentage of large & green is 20%!?



Cheers
Dav

uhm


40% toys are red.
50% toys are small - 50% are large

Red and small - 10%
Red and large must be 30% (since there are total 40% red toys)
But 50% toys are large. If 30% are red and large, the rest 20% large toys must be green. So large and green toys are 20%.
These 20% large and green toys are actually 40 so total number of toys must be 200.

Since red and large toys are 30%, they must be 60.
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In a certain production lot, 40 percent of the toys are red  [#permalink]

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New post 06 Apr 2018, 05:34
dav2013 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

Hi all,

Like many of you I am in the process of preparing for the GMAT. I was going through the quant review book but I got stuck at this point. I just cannot understand how they get to the solution.

Does any of you get how they figure out that the percentage of large & green is 20%!?



Cheers
Dav


hey niks18 can you correct my reasoning ? :)
if 40 percent of the toys are red and if 10 percent of the toys are red and small assuming the total number of toys 100. then answer must be 40-10 =30 (red and large) isnt it logical ? and how we understand that total number turns out 200 :? :)
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Re: In a certain production lot, 40 percent of the toys are red  [#permalink]

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New post 09 Apr 2018, 02:40
1
dave13 wrote:
dav2013 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

Hi all,

Like many of you I am in the process of preparing for the GMAT. I was going through the quant review book but I got stuck at this point. I just cannot understand how they get to the solution.

Does any of you get how they figure out that the percentage of large & green is 20%!?



Cheers
Dav


hey niks18 can you correct my reasoning ? :)
if 40 percent of the toys are red and if 10 percent of the toys are red and small assuming the total number of toys 100. then answer must be 40-10 =30 (red and large) isnt it logical ? and how we understand that total number turns out 200 :? :)


hi dave13

Refer to the first post for the detailed solution. You can prepare a matrix as shown in the above solution. From the matrix it is clear that 20% toys are green and large and it is also given that 40 toys are green and large. Hence we have -

20% of total toys = 40 => total toys = 40*(100/20)=200
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Re: In a certain production lot, 40 percent of the toys are red  [#permalink]

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New post 10 Apr 2018, 16:10
1
dav2013 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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Re: In a certain production lot, 40 percent of the toys are red &nbs [#permalink] 10 Apr 2018, 16:10
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