At a certain university, the Psychology department hired four

Question

At a certain university, the Psychology department hired four professors, and the Economics department hired sixteen professors. In hiring those professors, the Psychology Department hired 20 percent of the women who applied and 20 percent of the men who applied. The Economics department hired 80 percent of the women who applied and 80 percent of the men who applied. However, a greater percentage of all the men who applied than of all the women who applied were hired.

Which of the following can be properly inferred from the statements above?

A. Of all the women who applied, the proportion who applied for positions in the Psychology department was greater than the proportion of all the men who applied who did.

B. The total number of men who applied was less than the total number of women who applied.

C. Among those working in the university’s Psychology and Economics departments, the total number of men is greater than the total number of women.

D. The Economics department hired men and women in the same numbers.

E. The Economics department now has more professors than does the Psychology department.

Source: TTP Beta Testing

TaN1213 · Answer

Is the option A typed correctly?I feel the highlighted portion has some typo/missed words.

MartyTargetTestPrep · Answer

I believe that A is correct.

The proportion of women who applied is greater than the proportion of men who applied.

The proportion of women who applied is greater than the proportion of men who did.

KS15 · Answer

Not a great question IMO. B can easily be the answer. Consider these numbers
Men=2/10(Psy) and 4/5(Eco)
Women=2/10(Psy) and 8/10(Eco)

MartyTargetTestPrep · Answer

On the GMAT, an inference is not something that can be true, it is something that must be true.

B does not have to be true given what the passage says.

TaN1213 · Answer

Even I had the same doubt. B could easily be justified to be correct. 
Experts  GMATNinja ,
 would anyone shed some light on the difference between A& B?
What am I missing?

Thank you

KS15 · Answer

I disagree with what you said. On the GMAT, 4 answers HAVE to be incorrect and there will be no grey areas. Now since you accepted that B 'can be true' this itself is sufficient to prove that the question is not upto GMAT standards . B needs to be eliminated to arrive at A and it is not the case here.

MartyTargetTestPrep · Answer

Given what the passage says, B may not be true. Since this is an Inference question, and, therefore, the correct answer is the one that is always true given what the passage says, B can be eliminated.

In other words, while B is not impossible, given what the passage says, the passage does not indicate that B is true. So, B is not the correct answer.

MartyTargetTestPrep · Answer

The correct answer to a GMAT Inference question is the one that the passage indicates is always true. In other words, you are not looking for an answer that does not contradict what the passage says, but rather for one that the passage indicates is true.

Consider answer E.

E. The Economics department now has more professors than does the Psychology department.

This answer could also be true given what the passage says, but since it could also be false, it is not the correct answer.

If you plug numbers into the scenario described in the passage, you will find that the only numbers that work are the ones such that a greater proportion of the women who applied applied to the Psychology department. So, A is always true given what the passage says. If A were not true, then it would not be true that a greater percentage of all the men who applied than of all the women who applied were hired.

Here are some examples:

Most Women Apply to Psychology - Most Men Apply to Economics

Psychology Department:

Women: 15 applied 3 hired

Men: 5 applied 1 hired

Economics Department:

Women: 5 applied 4 hired

Men: 15 applied 12 hired

Proportion of women who applied that were hired: 7/20

Proportion of men who applied that were hired: 13/20

Proportion of men hired is greater.

Women and Men Apply in Equal Proportions to Psychology and Economics

Psychology Department:

Women: 10 applied 2 hired

Men: 10 applied 2 hired

Economics Department:

Women: 10 applied 8 hired

Men: 10 applied 8 hired

Proportion of women who applied that were hired: 10/20

Proportion of men who applied that were hired: 10/20

Proportion of men hired is the same as the proportion of women hired.

A Greater Proportion of the Women Apply to Economics

Psychology Department:

Women: 5 applied 1 hired

Men: 15 applied 3 hired

Economics Department:

Women: 15 applied 12 hired

Men: 5 applied 4 hired

Proportion of women who applied that were hired: 13/20

Proportion of men who applied that were hired: 7/20

Proportion of women who applied that were hired is greater.

So in order for the it to be the case that a greater percentage of all the men who applied than of all the women who applied were hired, it has to be the case that most women applied for positions in the Psychology department.

Mo2men · Answer

Hi Marty,

1- What does 'who applied who did'?? I do not understand this?

2- how could I solve this question with 2-3 minutes?

MartyTargetTestPrep · Answer

1 - 1 refers to choice A.

A. Of all the women who applied, the proportion who applied for positions in the Psychology department was greater than the proportion of all the men  who applied who did.

This answer compares the proportion of the all the women who applied who applied for positions in the Psychology department with the proportion of all the men  who applied who applied for positions in the Psychology department .

2 - I'm not sure that this question is quite right for answering within two minutes. All the same, here's a strategy for answering it quickly.

First go through the answers and eliminate the ones that can easily be eliminated.

A - Tough to say. Could be right. Keep for now.

B - This could somehow be correct as well.

C - Tempting, but it's a trap. We know about people who applied and were hired. There could be any number in the departments already working. So, we don't have information supporting this answer.

D. Interesting. Keep and review.

E. This one is like C. Eliminate.

OK, if we really want this done fast, we going to have to see what's going on. So, here's what we have to see.

Even though the percentage of women who applied who were hired by each department was the same as the percentage of men who applied who were hired by each department, the total percentage of the men who applied who were hired was greater.

Notice that the Economics department hired 16 people and hired 80% of those who applied, while the Psychology department hired just four and hired just 20 percent of those who applied. Perhaps these differences are key.

The best guess at this point is that the greater number hired and the greater percentage hired by the Economics department somehow skews things. Maybe men mostly applied to Economics. It may not yet be clear why, but we could go with the unconfirmed logic that, if most men applied to Economics, which hired more people and hired a greater percentage of applicants, then somehow the percentage of men hired overall could exceed the percentage of women hired overall. So, A is looking like the best answer.

To get this done in anything close to two minutes, we're going to have to test this theory with numbers that work for A but not for B or D and hope that our theory of how a greater percentage of men got hired is correct.

4 people were hired by Psychology. Let's make it 2 men and 2 women hired. So, since 20% of each were hired, a total of 10 men and 10 women applied.

16 people were hired in Economics. To eliminate D, the number of women hired and the number of men hired can't be the same. To eliminate B, we need more men than women who applied. For A, we need a greater proportion of men applying to Economics than to Psychology.

So, we have to go with 15 men applied to Economics and 12 were hired and 5 women applied to Economics and 4 were hired.

This better work, or two minutes is going to be way in the past by the time the question is answered.

So we have 14/25 men were hired, which is close to 15/25, which is 60%, and 6/15 women were hired, 40%.

A is looking good. D does not have to be the case. B does not have to be the case.

A is the correct answer.

Could the question really be answered in two minutes? Maybe if you were to nail all the numbers the first time. Otherwise, you might have to do a couple of tests.

An alternative to doing the tests is just to go with A once you see that there has to be some way in which the proportion of men hired is greater and that therefore it's likely that most men applied to Economics, which hired a greater number of people and a greater percentage of applicants and thus would have a greater effect on the percentage hired. If you were to just go with A once you saw that logic, even though you might not be 100% sure that A is correct, you could probably get the question answered in under two minutes.

The truth is that this is a practice question meant to provide people with a way to practice working with numbers in CR questions and to practice avoiding trap answers. So, perhaps the best move is to consider ways to answer it as quickly as possible, and even if they don't quite get it done in two minutes, you will have learned things that you can apply to get a more reasonable question CR question right in under two minutes.

Mo2men · Answer

Hi Marty, Thanks for great and comprehensive explanation

However, my question about A maybe different. I'm interested in understanding the construction of the sentence how come 'who applied who did' come behind each other? what does 'who applied who' mean? What 'who did' means? 'who did 'what? thanks

MartyTargetTestPrep · Answer

"who applied who did" modifies "men".

We are talking about a subset of men, "the proportion of all the men who who applied who did."

Did what?

We are comparing "the proportion of all the men who who applied who did" with "Of all the women who applied, the proportion who applied for positions in the Psychology department".

So, what the men did is "applied for positions in the Psychology Department".

So, the full version would be "the proportion of all the men who applied who applied for positions in the Psychology department".

The wording could perhaps be better.

Hope this explanation works. If not, let me know.

Mo2men · Answer

Hi Marty,

Thanks for your trial to explain. But I could not understand, although I'm not weak in English

Honestly, the question is really great but you added huge complexity that added stress and distraction in addition to the difficulty of the question itself.

I hope you can rephrase the sentence again.

MartyTargetTestPrep · Answer

Sounds good. I appreciate the feedback, and I will review the question with your input in mind and see how I can improve it.

One challenge of writing CR answer choices is writing them without using too many words. One has to figure out how to say something clearly while using only around two dozen words. Sometimes, making an answer choice clear can be quite a little puzzle.

Anyway, this discussion illustrates why beta testing questions can be super useful.

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At a certain university, the Psychology department hired four

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