BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

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

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 394
Joined: Sun Jul 02, 2017 10:59 am
Thanked: 1 times
Followed by:5 members

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

by AbeNeedsAnswers » Wed May 01, 2019 12:50 pm
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.

B

Source: Official Guide 2020
Top
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Thu May 02, 2019 1:59 am
AbeNeedsAnswers 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.

B

Source: Official Guide 2020
Say the company produces x numbers of small and y numbers of large toys. Thus,

Number of red toys = Number of green toys =x/2 + y/2 = (x + y)/2

We have to get the value of y / [(x + y)/2] = 2y / (x + y) = 2 / (x/y + 1)

If we get the value of x/y, we get the answer.

Let's take each statement one by one.

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

=> x/2 = 400 => x = 800. Can't get the value fo x/y. Insufficient.

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

=> 2/3(x + y) = x
2x/3 + 2y/3 = x
2y/3 = x/3

x/y = 2. Sufficient.

The correct answer: B

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: GRE Manhattan | ACT Tutoring San Antonio | GRE Prep Courses Boston | Houston IELTS Tutoring | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Wed May 15, 2019 6:36 pm
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: B

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Senior | Next Rank: 100 Posts
Posts: 62
Joined: Wed Nov 13, 2019 9:42 pm

matrix representation

by SampathKp » Wed Dec 18, 2019 9:28 am
AbeNeedsAnswers 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.

B

Source: Official Guide 2020
Given information can be represented in the following matrix

S . L . T
R . X . Y . X+Y
G . X . Y . X+Y
T . 2X . 2Y . 2(X+Y)

Question asked is 2Y/X+Y = Y/X+Y. we need to see from which options we get answer Y/X+Y

From (1) , X=400 , we have no information on Y, so this is NOT Sufficient to get value of Y/X+Y
From (2) , 2x = 2/3 , X= 1/3 also if 2/3 of Total no: of toys is small, then 1/3 of the toys will be large. so 2Y = 1/3 , Y= 1/6
so we have value of X and Y , hence we can compute Y/X+Y. Hence (2) is sufficient to answer the question.

Answer is B
PS Y/X+Y = 1/6/1/3+1/6 . = 1/3. so 1/3 of total numbers are toys are green colour.
    Top
    Post new topic Post Reply
    • Page 1 of 1