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There are 200 number of clothes. What is the number of clothes that ar

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Math Revolution GMAT Instructor
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New post 04 Aug 2017, 02:20
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Question Stats:

87% (01:14) correct 13% (01:37) wrong based on 58 sessions

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There are 200 number of clothes. What is the number of clothes that are red but not made of cotton?

1) 10% of the total clothes are neither red nor made of cotton.
2) 50% of the total clothes are both red and made of cotton.

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Re: There are 200 number of clothes. What is the number of clothes that ar  [#permalink]

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New post 04 Aug 2017, 03:26
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MathRevolution wrote:
There are 200 number of clothes. What is the number of clothes that are red but not made of cotton?

1) 10% of the total clothes are neither red nor made of cotton.
2) 50% of the total clothes are both red and made of cotton.


Total number of clothes \(= 200\)

Total \(=\) Red Only \(+\) Cotton Only \(-\) (Both Red and made of Cotton) \(+\) Neither (Neither Red nor made of Cotton)

We need to find the value of Red Only.

1) \(10\)% of the total clothes are neither red nor made of cotton.

\(10\)% of \(200 = \frac{10}{100} * 200 = 20\)

\(20\) clothes are neither red nor made of cotton. Therefore we have the value of Neither. We cannot find value of Red Only. Hence I is Not Sufficient.

2) \(50\)% of the total clothes are both red and made of cotton.

\(50\)% of \(200 = \frac{50}{100} * 200 = 100\)

\(100\) clothes are Both Red and Made of Cotton. Therefore we have the value of Both. We cannot find the value of Red Only. Hence II is Not Sufficient.

Combining (\(1\)) and (\(2\));

Total \(=\) Red Only \(+\) Cotton Only \(-\) (Both Red and made of Cotton) \(+\) Neither (Neither Red nor made of Cotton)

\(200 =\) Red Only \(+\) Cotton Only \(- 100 + 20\)

We do not have the value of Cotton Only or Red Only. Therefore, we cannot find the value of Red Only.

Hence Combining (\(1\)) and (\(2\)) are Not Sufficient.

Answer (E)...


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Re: There are 200 number of clothes. What is the number of clothes that ar  [#permalink]

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New post 06 Aug 2017, 18:15
==> If you modify the original condition and the question, it is a 2 by 2 question which appears most frequently on current GMAT math.

Attachment:
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As shown above, there are 4 variables (w,x,y,z) and 1 equation (W+X+Y+Z=200). In order to match the number of variables to the number of equations, there must be 3 more equations. Since there is 1 for con 1) and 1 for con 2), E is most likely to be the answer. By solving con 1) & con 2), you get z=200(10%)=20 and w=200(505)=100, but the value of y is not unique and not sufficient.

The answer is E.
Answer: E
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Re: There are 200 number of clothes. What is the number of clothes that ar   [#permalink] 06 Aug 2017, 18:15
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