 It is currently 26 Jun 2019, 02:23 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

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. There are 87 balls in a jar. Each ball is painted with at le  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS: Intern Joined: 22 Oct 2016
Posts: 15
Followers: 0

Kudos [?]: 3  , given: 0

There are 87 balls in a jar. Each ball is painted with at le [#permalink]
2
KUDOS 00:00

Question Stats: 100% (00:00) correct 0% (00:00) wrong based on 1 sessions
There are 87 balls in a jar. Each ball is painted with at least one of two colors, red or green. It is observed that 2/7 of the balls that have red color also have green color, while 3/7 of the balls that have green color also have red color. What fraction of the balls in the jar have both red and green colors?

(A) 6/14
(B) 2/7
(C) 6/35
(D) 6/29
(E) 6/42
[Reveal] Spoiler: OA

Last edited by Carcass on 05 Dec 2016, 08:47, edited 1 time in total.
Edited the question GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 120

Kudos [?]: 1910  , given: 397

Re: There are 87 balls in a jar. Each ball is painted with at le [#permalink]
1
KUDOS
Expert's post
Let number of red only balls be $$a$$ and green only ball be $$b$$ and both red and green be $$c$$.

So we can say $$a+b+c=87$$.

2/7 of the balls that have red color also have green color

So $$\frac{c}{(a+c)}= \frac{2}{7}$$.

3/7 of the balls that have green color also have red color

So $$\frac{c}{(b+c)}=\frac{3}{7}$$.

Inverting both fractions and adding them

$$\frac{(a+c)}{c}+\frac{(b+c)}{c}=\frac{7}{3}+\frac{7}{2}$$

Subtracting 1 from both sides

$$\frac{a+b+2c}{c}-1= \frac{35}{6}-1$$.

$$\frac{a+b+c}{c}=\frac{29}{6}$$

Inverting again

$$\frac{c}{a+b+c}=\frac{6}{29}$$.

Our objective was always to find $$\frac{c}{a+b+c}$$.

Hence option D is correct.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test Re: There are 87 balls in a jar. Each ball is painted with at le   [#permalink] 05 Dec 2016, 14:18
Display posts from previous: Sort by

There are 87 balls in a jar. Each ball is painted with at le  Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.