In each production lot for a certain toy, 25 percent of the

Question

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

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

Bunuel · Accepted Answer

Double-set matrix solution: https://gmatclub.com/forum/download/file.php?id=22172 Yellow box corresponds to the number of the toys that are blue and size B. Answer: D. Untitled.png

GMATBLACKBELT · Answer

D. 50-15=35. Best to use a double set matrix.

yogachgolf · Answer

What is double set matrix?

GMATBLACKBELT · Answer

There is a thread on here about double and triple matrix's by Killersquirrel.

pmenon · Answer

Got B. I quite like drawing trees for these type of questions. Allows me to visualize things much easier.

We know 10 toys are red and size a out of 100. Moving up the tree, we can find out that overall 25 toys are red, because 25% of toys are red, and 25% of 100 is 25. That leaves 15 red and size B

Moving to the blue side, overall we must have 25 blue. Since 50% of toys are size b, and we already have 15 size b of red, we need size b red + size b blue = 50, and 50-15=35

JeffTargetTestPrep · Answer

We are given that we have 100 toys, and we see that 50 are size A and 50 are size B.

We also see that 75 toys are blue and 25 are red.

Since 10 toys are red and size A, 50 - 10 = 40 are blue and size A.

Since 40 toys are blue and size A, 75 - 40 = 35 are blue and size B.

Answer: D

ayakik · Answer

Hi  KarishmaB   avigutman  I tried to use a different approach and I'm wondering what I did wrong.

I saw that 1/4 = R and 1/2 = A so I thought I could set this up as 10 = (1/4)(1/2)x 
Therefore, x = 80 
(3/4)(1/2)(80) = 30 
Therefore, answer choice C.

Why, in this case, do we need to use a matrix to solve this question? Why does my approach not work? Does my approach only work for conditional probability questions?

Thank you.

avigutman · Answer

ayakik  Your equation would be correct if we were told that 1/4 of the size A toys are red. But, we were told that 1/4 of ALL the toys are red.

KarishmaB · Answer

You are implying that (1/4)th of (1/2)x i.e. (1/4)th of the size A toys are red. But what we are given is that 1/4th of all toys are red. 
1/4th of all toys are red and 1/2 of all toys are size A. This does not automatically tell us how many toys are red and size A. 
Say if there are 100 toys, 25 are red and 50 are size A. How many are both red and size A? We can't say. Perhaps all 25 red toys are size A or perhaps only 10 red toys are size A or perhaps none of the red toys are size A etc.

The question then gives us that 1/10th of the toys are red and size A so now we know that 10 of the toys are red and size A. This means the other 15 red toys are size B. And the other 40 size A toys are blue. Since out of the 75 blue toys, 40 are size A, it means the other 35 are size B. 
 
Answer (D)

We are discussing two characteristics of toys - colour and size. You can use a double set matrix as used by  Bunuel  above.

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In each production lot for a certain toy, 25 percent of the

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