GRE Prep 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
Track
Your Progress
Practice
Pays
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
[#permalink]
Updated on: 05 Dec 2016, 08:47
Updated on: 05 Dec 2016, 08:47
2
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
(A) 6/14
(B) 2/7
(C) 6/35
(D) 6/29
(E) 6/42
Re: There are 87 balls in a jar. Each ball is painted with at le
[#permalink]
05 Dec 2016, 14:18
05 Dec 2016, 14:18
1
Expert Reply
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.
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.
Re: There are 87 balls in a jar. Each ball is painted with at le
[#permalink]
15 Apr 2020, 13:02
15 Apr 2020, 13:02
Expert Reply
Discussed here https://gre.myprepclub.com/forum/there-are ... tml#p32149
