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

Question

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

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

KarishmaB · Accepted Answer

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.

dave13 · Answer

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

niks18 · Answer

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

ScottTargetTestPrep · Answer

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

Archit3110 · Answer

use 2x2 matrix to solve

-------red------green----total
smal---10------40-------50
large--30------20--------50
total--40------60--------100

30/50 * 100= 60%
IMO B

Karastoyanov · Answer

For those who don't understand where the 200 comes from - read carefully: the given numbers are  %  and  #  of toys... I missed that too so...

minustark · Answer

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

A. 40
B. 60
C. 70
D. 80
E. 90
Red : 40%
Red and small : 10%, so the remaining are red and large, which is 30%

Green: 60% 
Green and small : 40%, green and large: 20%(as 50% large, 50% small)
Given, 20% = 40, so total toys = 200, red and large toys= 60.
B is the answer

bumpbot · Answer

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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

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