Data Sufficiency

Hi ,

Please explain this by double matrix method.

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem.
Remember equal number of variables and independent equations ensures a solution.

Of the 1,4000 college teachers surveyed, 42 percent said that they considered engaging in research an a essential goal. How many of the college tehachers surveyed were women?
1) In the survey, 36 percent of the men and 50 percent of the women said they considered engaging in research an essential goal
2) In the survey, 288 men said that they considered engaging in research an essential goal

Transforming the original condition and the question, we have the below 2by2 table that are common in GMAT test

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There are 4 variables (a,b,c,d), 2 equations (a+b+c+d=1,400, a+b=1,400*0.42) and thus we need 2 more equations to match the number of variables and equations.
In case of 1), there are 2 equations (b=(b+d)*0.36, a=(a+c)*0.5) therefore the condition is sufficient.
In case of 2), there is 1 equation (b=288) therefore the condition is not sufficient. Therefore the answer is A


Normally for cases where we need 2 more equations, such as original conditions with 2 variable, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using ) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

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Hi Brent ,

Thank you sir, I got it.

Thanks,

SJ