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

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A company produces a certain toy in only 2 sizes, small or large, and  [#permalink]

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New post 26 Apr 2019, 02:51
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A company produces a certain toy in only 2 sizes, small or large, and in only 2 colors, red or green. If, for each size, there are equal numbers of red and green toys in a certain production lot, what fraction of the total number of green toys is large?

(1) In the production lot, 400 of the small toys are green.
(2) In the production lot, 2/3 of the toys produced are small.


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A company produces a certain toy in only 2 sizes, small or large, and  [#permalink]

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New post Updated on: 09 May 2019, 02:41
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1
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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Originally posted by DavidTutorexamPAL on 26 Apr 2019, 15:56.
Last edited by DavidTutorexamPAL on 09 May 2019, 02:41, edited 1 time in total.
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Re: A company produces a certain toy in only 2 sizes, small or large, and  [#permalink]

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New post 27 Apr 2019, 12:46
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Bunuel wrote:
A company produces a certain toy in only 2 sizes, small or large, and in only 2 colors, red or green. If, for each size, there are equal numbers of red and green toys in a certain production lot, what fraction of the total number of green toys is large?

(1) In the production lot, 400 of the small toys are green.
(2) In the production lot, 2/3 of the toys produced are small.


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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
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Re: A company produces a certain toy in only 2 sizes, small or large, and  [#permalink]

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New post 07 May 2019, 18:39
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Bunuel wrote:
A company produces a certain toy in only 2 sizes, small or large, and in only 2 colors, red or green. If, for each size, there are equal numbers of red and green toys in a certain production lot, what fraction of the total number of green toys is large?

(1) In the production lot, 400 of the small toys are green.
(2) In the production lot, 2/3 of the toys produced are small.


DS61602.01
OG2020 NEW QUESTION



We are given that the number of green large = red large and green small = red small.

We need to determine the value of (large green)/(total green).

Statement One Alone:

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

Only knowing that we have 400 green small toys is not enough information to determine large green/green.

Statement one alone is not sufficient to answer the question.

Statement Two Alone:

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

Since 2/3 of the total are small, 1/3 are large. 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.

Answer: B
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Re: A company produces a certain toy in only 2 sizes, small or large, and  [#permalink]

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New post 08 May 2019, 11:19
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?
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Re: A company produces a certain toy in only 2 sizes, small or large, and  [#permalink]

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New post 15 May 2019, 20:48
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

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Re: A company produces a certain toy in only 2 sizes, small or large, and  [#permalink]

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New post 28 Jul 2019, 16:41
rnn wrote:
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?


+1 , thanks a lot in advance ScottTargetTestPrep
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Re: A company produces a certain toy in only 2 sizes, small or large, and  [#permalink]

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New post 06 Aug 2019, 17:53
GMATestaker wrote:
rnn wrote:
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?


+1 , thanks a lot in advance ScottTargetTestPrep



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.
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Re: A company produces a certain toy in only 2 sizes, small or large, and   [#permalink] 06 Aug 2019, 17:53
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