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Half of the shirts in a closet are white and 30% of the rema

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GMAT Club Legend
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Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Half of the shirts in a closet are white and 30% of the rema [#permalink] New post 10 Jun 2018, 05:12
Expert's post
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Question Stats:

71% (00:42) correct 28% (00:00) wrong based on 21 sessions
Half of the shirts in a closet are white and 30% of the remaining shirts are gray

Quantity A
Quantity B
The percent of the shirts in the closet that are not white or gray
20%


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Sandy
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Re: Half of the shirts in a closet are white and 30% of the rema [#permalink] New post 16 Jun 2018, 15:35
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The trick here is to read the question carefully. For this problem, I used 100 shirts since percents are out of 100, making it a direct conversion.

Half of the shirts in a closet are white and 30% of the remaining shirts are gray


Half of the shirts are white = 50
30% of the remaining shirts are gray = .3 * 50 = 15
Remainder of shirts that are \(not\) white or gray = 35.

Quantity A: The percent of the shirts in the closet that are not white or gray
Quantity B: 20%

Quantity A: 35%
Quantity B: 20%

Quantity A is greater.

The answer is A.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1613 [0], given: 375

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Re: Half of the shirts in a closet are white and 30% of the rema [#permalink] New post 14 Jul 2018, 04:35
Expert's post
Explanation

Choose a smart number for the total number of shirts in the closest; this is a percent problem, so 100 is a good number to pick. Out of 100 shirts, half, or 50, are white.
You know 30% of the remaining shirts are gray.

If there are 50 white shirts, there are also 50 remaining shirts and so (0.3)(50) = 15 gray shirts. Therefore, there are 50 + 15 = 65 total shirts that are white or gray, and 100 – 65 = 35 shirts that are neither white nor gray. Since 35 out of 100 shirts are neither white nor gray, exactly 35% of the shirts are neither white nor gray.

Alternatively, use algebra, though that is trickier on a problem such as this one. Set a variable, such as x, for the total number of shirts. The number of white shirts is 0.5x and the remaining shirts would equal

x – 0.5x = 0.5x.

The number of gray shirts, then, is (0.5x)(0.3) = 0.15x. Thus, there are

0.5x + 0.15x = 0.65x white or gray shirts, and

x – 0.6x = 0.35x shirts that are neither white nor gray.

Therefore, 0.35x ÷ x = 0.35, or 35%.
_________________

Sandy
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Re: Half of the shirts in a closet are white and 30% of the rema   [#permalink] 14 Jul 2018, 04:35
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