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28 Jan 2018, 05:03
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D
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Difficulty:
95%
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Question Stats:
53% (03:11) correct
47%
(02:58)
wrong
based on 257
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There are 87 balls in a jar. Each ball is painted with at least one of the two colors, red and green. It is observed that 2/7 f 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 has both red and green colors?
a) 6/14
b)2/7
c) 6/35
d) 6/29
e) 1/5
source: NOVA GMAT
a) 6/14
b)2/7
c) 6/35
d) 6/29
e) 1/5
source: NOVA GMAT
03 Feb 2018, 22:32
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poul_249
You have to visualise the problem as set problem...
Given 87 Balls with Red and Green colour
So the set equation becomes; Total (Red & Green Balls) = #Red Balls + # Green Balls - Both (Red & Green)
Given is 2/7 of Red balls also are Green ==> Both ( Red and green) = \(\frac{2}{7}\) * # Red Balls
Also it is stated that 3/5 of Green balls are red, which is again stating that ==> Both ( Red and green) = \(\frac{3}{7}\) * # Green Balls
Essentially it means that #Red Balls = \(\frac{7}{2}\)* Both (Red and Green)
Also it means that #Green Balls = \(\frac{7}{3}\)* Both (Red and Green)
Now coming back to original equation Total (Red & Green Balls) = #Red Balls + # Green Balls - Both (Red & Green)
Substituting the values we got above
87= \(\frac{7}{2}*Both + \frac{7}{3}*Both - Both\)
So Both = 18
We are asked to find Both/Total =\(\frac{18}{87}\) = \(6/29\)
Hope it helps , pls press Kudos
ven diagram..
87=R+G-Both RG
given that ...Both = 2R/7 = 3G/7; we need to find Both/total
87= 7Both/2 + 7Both/3 - Both
Both = 18
therefore , 18/87 = 6/29 D
Corrected G in 3G/7
87=R+G-Both RG
given that ...Both = 2R/7 = 3G/7; we need to find Both/total
87= 7Both/2 + 7Both/3 - Both
Both = 18
therefore , 18/87 = 6/29 D
Corrected G in 3G/7
