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A bowl contains equal numbers of red, orange, green, blue,

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A bowl contains equal numbers of red, orange, green, blue,

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A bowl contains equal numbers of red, orange, green, blue, and yellow candies. Kaz eats all of the green candies and half of the orange ones. Next, he eats half of the remaining pieces of each color. Finally, he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 15% of the original number. What percent of the red candies remain?

A. 0%
B. 5%
C. 10%
D.15%
E. 20%

OA A

Source: Manhattan Prep

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BTGmoderatorDC wrote:
A bowl contains equal numbers of red, orange, green, blue, and yellow candies. Kaz eats all of the green candies and half of the orange ones. Next, he eats half of the remaining pieces of each color. Finally, he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 15% of the original number. What percent of the red candies remain?

A. 0%
B. 5%
C. 10%
D.15%
E. 20%

OA A

Source: Manhattan Prep
Let’s let the initial number of candies of each color be 12 (and thus the total number of candies is 60). So he eats all 12 green candies and 6 orange candies at first. Next he eats 3 orange, 6 red, 6 blue and 6 yellow candies. Thus far, we have

60 - (12 + 6 + 3 + 6 x 3) = 60 - 39 = 21

candies left. At this point, there are 3 orange, 6 red, 6 blue and 6 yellow candies left. Since 15% of 60 is 9, he must eat 12 more candies to get to 9. However, since he eats an equal number of of red and yellow candies, he must eat 6 red and 6 yellow candies to have 9 candies left. Therefore, there will be no more red candies left.

Answer: A

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Founder and CEO
scott@targettestprep.com



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BTGmoderatorDC wrote:
A bowl contains equal numbers of red, orange, green, blue, and yellow candies. Kaz eats all of the green candies and half of the orange ones. Next, he eats half of the remaining pieces of each color. Finally, he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 15% of the original number. What percent of the red candies remain?

A. 0%
B. 5%
C. 10%
D.15%
E. 20%
Let R=O=G=B=Y=20, for a total of 100 marbles.

Kaz eats all of the green candies and half of the orange ones.
R=20, O=10, G=0, B=20, Y=20

He eats half of the remaining pieces of each color.
R=10, O=5, G=0, B=10, Y=10

He eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 15% of the original number.
Since only 15 of the original 100 candies must remain, Kaz must eat the 10 remaining red and 10 remaining yellow candies, leaving only O=5 and B=10:
R=0, O=5, G=0, B=10, Y=0

What percent of the red candies remain?
(new R)/(original R) = 0/20 = 0%

The correct answer is A.

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Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

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