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

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04 Aug 2017, 02:20
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82% (00:53) correct 18% (01:07) wrong based on 45 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.
[Reveal] Spoiler: OA

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

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

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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:

8.4.png [ 2.09 KiB | Viewed 236 times ]

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

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