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A tiara is studded with a mixture of gems. The ratio of

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by BTGmoderatorDC » Thu Jan 09, 2020 7:06 pm
A tiara is studded with a mixture of gems. The ratio of sapphires to emeralds is 3:1. If 6 emeralds are added, the tiara will contain an equal number of sapphires and emeralds. How many emeralds must be added to the original tiara so that the ratio between emeralds and sapphires is 3:1?

(A) 9

(B) 12

(C) 18

(D) 24

(E) 27




OA D

Source: Magoosh
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by Jay@ManhattanReview » Thu Jan 09, 2020 9:17 pm
BTGmoderatorDC wrote:A tiara is studded with a mixture of gems. The ratio of sapphires to emeralds is 3:1. If 6 emeralds are added, the tiara will contain an equal number of sapphires and emeralds. How many emeralds must be added to the original tiara so that the ratio between emeralds and sapphires is 3:1?

(A) 9

(B) 12

(C) 18

(D) 24

(E) 27

OA D

Source: Magoosh
Given the ratio of sapphires to emeralds is 3 : 1. Say there are 3x sapphires and x emeralds in the original tiara.

Thus, after the addition of 6 emeralds, we have 3x = x + 6 => x = 3. Thus, in the original tiara, there are 9 sapphires and 3 emeralds.

Say y emeralds were added such that the ratio between emeralds and sapphires is 3 : 1.

Thus, (3 + y)/9 = 3/1 => y = 24

The correct answer: D

Hope this helps!

-Jay
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