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04 Aug 2017, 02:20
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E
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Difficulty:
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Question Stats:
83% (01:13) correct
17%
(01:15)
wrong
based on 146
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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.
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.
sashiim20
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Schools: ISB '19 IIMB IIMA XLRI HEC Sept19 intake Rotman '21 NUS '21 NTU '20 Trinity MBA '20 Bocconi '21 Smurfit "21
Posts: 608
04 Aug 2017, 03:26
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MathRevolution
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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06 Aug 2017, 18:15
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==> If you modify the original condition and the question, it is a 2 by 2 question which appears most frequently on current GMAT math.
8.4.png [ 2.09 KiB | Viewed 2749 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
Attachment:
8.4.png [ 2.09 KiB | Viewed 2749 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
