Last visit was: 03 Nov 2024, 15:36 It is currently 03 Nov 2024, 15:36
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
655-705 Level|   Fractions and Ratios|   Word Problems|                  
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 03 Nov 2024
Posts: 96,505
Own Kudos:
Given Kudos: 87,899
Products:
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 96,505
Kudos: 673,791
 [217]
14
Kudos
Add Kudos
203
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 02 Nov 2024
Posts: 19,684
Own Kudos:
23,720
 [47]
Given Kudos: 287
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 19,684
Kudos: 23,720
 [47]
31
Kudos
Add Kudos
16
Bookmarks
Bookmark this Post
User avatar
firas92
User avatar
Current Student
Joined: 16 Jan 2019
Last visit: 24 Jan 2024
Posts: 620
Own Kudos:
1,532
 [28]
Given Kudos: 142
Location: India
Concentration: General Management
GMAT 1: 740 Q50 V40
WE:Sales (Other)
Products:
GMAT 1: 740 Q50 V40
Posts: 620
Kudos: 1,532
 [28]
15
Kudos
Add Kudos
13
Bookmarks
Bookmark this Post
General Discussion
User avatar
DavidTutorexamPAL
User avatar
examPAL Representative
Joined: 07 Dec 2017
Last visit: 09 Sep 2020
Posts: 1,048
Own Kudos:
1,844
 [10]
Given Kudos: 26
Posts: 1,048
Kudos: 1,844
 [10]
5
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
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
User avatar
ZoltanBP
Joined: 14 Apr 2017
Last visit: 03 Nov 2024
Posts: 79
Own Kudos:
898
 [3]
Given Kudos: 566
Location: Hungary
GMAT 1: 760 Q50 V42
WE:Education (Education)
GMAT 1: 760 Q50 V42
Posts: 79
Kudos: 898
 [3]
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
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

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
avatar
rnn
Joined: 27 Nov 2015
Last visit: 19 Dec 2023
Posts: 87
Own Kudos:
Given Kudos: 325
Posts: 87
Kudos: 41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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?
User avatar
EMPOWERgmatRichC
User avatar
GMAT Club Legend
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,818
Own Kudos:
11,964
 [3]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,818
Kudos: 11,964
 [3]
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 02 Nov 2024
Posts: 19,684
Own Kudos:
23,720
 [2]
Given Kudos: 287
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 19,684
Kudos: 23,720
 [2]
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
rnn
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?



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.
User avatar
Basshead
Joined: 09 Jan 2020
Last visit: 07 Feb 2024
Posts: 943
Own Kudos:
245
 [3]
Given Kudos: 432
Location: United States
Posts: 943
Kudos: 245
 [3]
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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

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.
User avatar
GMATGuruNY
Joined: 04 Aug 2010
Last visit: 03 Nov 2024
Posts: 1,333
Own Kudos:
3,352
 [1]
Given Kudos: 9
Schools:Dartmouth College
Expert reply
Posts: 1,333
Kudos: 3,352
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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

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.
User avatar
GMATinsight
User avatar
GMAT Club Legend
Joined: 08 Jul 2010
Last visit: 02 Nov 2024
Posts: 6,060
Own Kudos:
14,404
 [1]
Given Kudos: 125
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,060
Kudos: 14,404
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
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

Wanna make solving the Official Questions interesting???


Click here and solve 1000+ Official Questions with Video solutions as Timed Sectional Tests
and Dedicated Data Sufficiency (DS) Course

Answer: Option B

Video solution by GMATinsight


Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK HERE.
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub :)
User avatar
avigutman
Joined: 17 Jul 2019
Last visit: 03 Oct 2024
Posts: 1,299
Own Kudos:
1,817
 [2]
Given Kudos: 66
Location: Canada
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Expert reply
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Posts: 1,299
Kudos: 1,817
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
avatar
Engineer1
Joined: 01 Jan 2014
Last visit: 22 Oct 2024
Posts: 214
Own Kudos:
Given Kudos: 456
Location: United States (MI)
Posts: 214
Kudos: 286
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Attachments

Solution.png
Solution.png [ 408.6 KiB | Viewed 5623 times ]

User avatar
MartyMurray
Joined: 11 Aug 2023
Last visit: 03 Nov 2024
Posts: 1,209
Own Kudos:
3,060
 [1]
Given Kudos: 106
GMAT 1: 800 Q51 V51
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
GMAT 1: 800 Q51 V51
Posts: 1,209
Kudos: 3,060
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Engineer1
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).
Moderator:
Math Expert
96505 posts