A company produces a certain toy in only 2 sizes, small or large, and

The Logical approach to this question will focus on the fact that we are asked to find the ratio, so we don't necessarily need exact numbers.
Statement (1) doesn't give us any information regarding the ratio between the groups of small vs. large toys, and is thus insufficient.
Statement (2) tells us that 2/3 are small, meaning 1/3 are large, and since the number of red and green toys is equal for each size group, then 1/3 of the green toys are large and the other 2/3 are small (as they make half of these groups).
The correct answer is (B).

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For the red category, let \(s\) and \(l\) be the numbers of small and large toys produced, respectively. For the green category, the production volumes are the same as those for the red category according to the original information. Globally, \(2s\) and \(2l\) are the numbers of small and large toys produced, respectively.

The original question: For the green category, \(\frac{l}{s+l}=?\)

1) We know that \(s=400\), but no information is given about \(l\). Thus, we can't get a unique value to answer the original question. \(\implies\) Insufficient

2) We know that \(\frac{2s}{2s+2l}=\frac{s}{s+l}=\frac{2}{3}\)

\(1-\frac{s}{s+l}=1-\frac{2}{3}\)

\(\frac{l}{s+l}=\frac{1}{3}\)

Thus, the answer to the original question is a unique value. \(\implies\) Sufficient

Answer: B

Hi ScottTargetTestPrep

I did not understand this sentence "Thus, (2/3)/2 = 1/3 are small green and (1/3)/2 = 1/6 are large green. Thus, the large green toys are (1/6)/(1/3 + 1/6) = 1/(2 + 1) = 1/3 of the total number of green toys"

Could you kindly elaborate here more please?

Hi All,

We're told that a company produces a certain toy in only 2 sizes, small or large, and in only 2 colors, red or green - and that for each size, there are EQUAL numbers of red and green toys in a certain production lot. We're asked for the fraction of the total number of GREEN toys that are LARGE. This question can be approached with a mix of logic and TESTing VALUES.

(1) In the production lot, 400 of the small toys are green.

With the information in Fact 1, we know that there are 400 small RED toys (since there are EQUAL numbers of red and green toys in each size), but we don't know how many LARGE GREEN toys there are, so the answer to the question would change depending on number.
Fact 1 is INSUFFICIENT

(2) In the production lot, 2/3 of the toys produced are small.

With Fact 2, we know that 2/3 of the toys are SMALL, so the remaining 1/3 of the toys are LARGE. The prompt tells us that there are EQUAL numbers of red and green toys in each size). These ratios are enough to answer the question; you can prove it with Algebra or by TESTing VALUES.

IF....
TOTAL toys = 6
Total Small = 4 (2 red and 2 green)
Total Large = 2 (1 red and 1 green)
Total fraction of GREEN toys that are LARGE = 1/3

IF....
TOTAL toys = 12
Total Small = 8 (4 red and 4 green)
Total Large = 4 (2 red and 2 green)
Total fraction of GREEN toys that are LARGE = 2/6 = 1/3
Etc.
The answer will ALWAYS be 1/3.
Fact 2 is SUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich

That is because in the problem stem, it says “If, for each size, there are equal numbers of red and green toys in a certain production lot.” That means, for the small size, half are green and the other half is red. Since 2/3 of the toys are small, (2/3)/2 = 1/3 of all toys are small green toys. Similarly, since 1/3 of the toys are lare, (1/3)/2 = 1/6 of all toys are large green toys. The question asks what fraction of green toys are large. So we have 1/6 of the toys are large green and (1/3 + 1/6) of the toys are green, so the fraction is (1/6)/(1/3 + 1/6) = 1/(2 + 1) = 1/3.

The wording of this question makes it challenging. We're told for each size, there are equal numbers of red and green toys.

For example, for small toys, red = green = 10. Large toys: red = green = 20.

What fraction of the total numbers of green toys is large? Notice the question is asking for a ratio -- not a specific amount.

(1) If 400 of the small toys are green, then 400 of the small toys are red. However, we have no information about the large toys; INSUFFICIENT.

(2) If 2/3 of the toys produced are small, then 1/3 of the toys produced are big.

Of the 1/3 toys, HALF will be green and HALF will be red. Therefore, we can conclude 1/6 of the green toys is large. SUFFICIENT.

Answer is B.

For each size, the number of red = the number of green.
One more approach for Statement 2:

Let the total number of toys = 6x.
Small toys \(= \frac{2}{3}*6x = 4x\) --> 2x small red, 2x small green
Large toys = 6x-4x = 2x --> x large red, x large green

Resulting fraction:
\(\frac{large-green}{total-green} = \frac{x}{2x+x} = \frac{x}{3x} = \frac{1}{3}\)
SUFFICIENT.

Answer: Option B

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How is everyone getting 1/3?


Moreover, it took me 2 mins 35 ish seconds. I did not want to take chance with no calculation. Any tips to reduce time here?

MartyMurray Thank you.

We can answer this one in under a minute using mental math.

The key to quickly answering the question is seeing the implications of the following in the passage:

for each size, there are equal numbers of red and green toys in a certain production lot

That information indicates two things:

- In the entire production lot, there are equal numbers of red and green toys. After all, if there are equal numbers of red and green toys for each size, then the numbers of red and green toys in the two sizes must add up to the same total for red and green. So, red toys and green toys each make up half the toys.

- The fraction of toys in a particular size is also the fraction of toys in a color that are in that size. After all, if there are equal numbers of red and green toys for each size, then the number of red or green toys for a size will simply be half the number of toys for that size, and red toys and green toys each make up half of the toys. So, the fraction of toys that are of a size is (number in size)/(total), and the fraction of toys in a color that are in a size is (1/2 number in size)/(1/2 total). We see that (number in size)/(total) = (1/2 number in size)/(1/2 total). So, fraction of total in a size = fraction of a color in a size.

(1) In the production lot, 400 of the small toys are green.

This information about a single absolute number does not indicate anything about the fraction of toys that are small or the fraction of toys that are large or the fraction of green toys that are small or the fraction of green toys that are large.

Insufficient.

(2) In the production lot, 2/3 of the toys produced are small.

This information indicates that 1/3 of the toys produced are large.

That information, in turn, indicates that 1/3 of the green toys are large, given what we have discussed above.

Sufficient.

The correct answer is (B).