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

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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Use a 2x2 table to solve

Let small red toys be \(x\) which makes small green toys also \(x\) (they are equal)
Similarly, large red toys and large green toys are each \(y\)

So the total number of green toys is \(x+y\)

We are asked to find \(\frac{y}{x+y}\)

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

\(x=400\)

No info about \(y\) or how \(x\) is related to \(y\). Not sufficient

(2) In the production lot, \(\frac{2}{3}\) of the toys produced are small.

So \(\frac{1}{3}\) of the total toys produced are large

This means \(\frac{2y}{2(x+y)}=\frac{1}{3}\)

Therefore, \(\frac{y}{x+y}\) is \(\frac{1}{3}\)

Sufficient

Answer is (B)

_________________

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).

Posted from my mobile device

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.
_________________

Given: 2 sizes (S=small L=large) ; 2 colors (R=red G=green) ; SR = SG ; LR = LG
Asked: LG / (LG+SG)

1.SG = 400 (insufficient - intuitively we need ratios or at least some information about the large toys)
2.(SG+SR)/(SG+SR+LG+LR) = 2/3 -> if small toys are 2/3 of total then large toys are 1/3
-> (LG+LR)/(LG+LR+SG+SR) = 1/3 -> 2LG/(2LG + 2SG) = 1/3 -> (multiply left side by .5/.5)
-> LG/(LG+SG) = 1/3 (sufficient)

B

p.s: Clear and precise algebraic inferences from the question stem are the key for GMAT mastery. Studying Bunuel 's thought process and approach to every problem can help one improve tremendously.

Cheers

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.
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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.
_________________

Fairly simple question:

Options: A, D, B, C and E.

Information in the question: There are only 2 sized toys, small and large, and each size has equal number of red:green colour.

To find: Ratio of Large Green Toys to the total Toys produced.

Statement 1: Gives information about the number of small toys produced which are green in colour. However, we are not concerned with small green toys. INSUFFICIENT.

Re: Options: A and D eliminated. B, C and E remain.

Statement 2: Total small toys produced are 2/3rds. This means that total Large toys produced are 1/3. And given that half of each sized toys are green, the ratio of Large Green Toys to Total Toys produced

= 1/3 x 1/2
= 1/6.

ANSWER: B

Answer: Option B

Video solution by GMATinsight



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A alone insuff bcoz 400 green and red small toys no information about big toys
B looks like insuff but wait if 2/3 small toys 1/3 green and 1/3 red afterwards 1/6 large green and 1/6 red we can find the ratio
IMO B

Video solution from Quant Reasoning:
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Concept being tested (notes)

if you have the same ratio for small to large in each of the colors (blue and red) , you will also have the same ratio of small to large in general (Total)
----------

Small : Large
R 1x : 3y
G 1x : 3y
----------
2x : 6y
-------------------------------------

Small : Large
R 1x : 3y
G 2x : 6y
----------
3x : 9y OR 1x : 3y
----------

however

Small : Large
R 1x : 3y
G 3x : 6y
----------
4x : 9y WHICH IS NOT EQUAL TO 1x : 3y
----------

Reason - teeter totter
case 1 - 33 % and 33 % with weights are 1 each.
case 2 - 33 % and 33 % with weights as 1 and 2
case 3 - 33 % and 50 % with weight as 1 and 2 ..

Slow and read carefully.

Posted from my mobile device

The moment I read this line "In the production lot, 400 of the small toys are green.". My first instinct was to think that 400 has to be multiplied by something to give the value of the green toys.

I understand that the question is actually saying that there are 400 small green toys.

Any tips to avoid such mistakes?
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