Data Sufficiency

You can look at Statement 1 algebraically. If m men and w women were surveyed, we know from the stem that:

m + w = 1400

We also know from Statement 1 that

0.36m + 0.5w = (0.42)(1400)

So we have two distinct linear equations in two unknowns, and we can certainly solve for m and for w (it's DS, so we don't care what the answer actually is). So Statement 1 is sufficient.

This is a 'weighted average' question, and if you're familiar with the method known as 'alligation', you'd be able to see that Statement 1 is sufficient without doing any work at all. I'll quickly summarize how alligation works, but if you're interested you might want to look elsewhere for a more detailed explanation. Here, we know the 'average' for men is 36%, the 'average' for women is 50%, and the 'average' for men and women combined is 42%. If we draw these three averages on a number line:

---36------42-------------50---

notice first that we must have more men than women, since 42 is closer to the men's average than to the women's average. It turns out that in any weighted average question, the ratio of the distances I've coloured above is always equal to the ratio of the groups. Here the red distance is 6, and the blue distance is 8. So the groups are in a 6 to 8 ratio, and since we have more men, the ratio of men to women is 8 to 6, or 4 to 3. So 4/7 of all people are men, and since there are 1400 people in total, the number of men is (4/7)(1400) = 800.

If you solve several weighted average questions using this method, you will likely begin to appreciate that whenever you know any 3 of the following 4 things:

- the average of the first group
- the average of the second group
- the average of the two groups combined
- the ratio of the sizes of the two groups

you can always find the fourth. If you know that, then reading Statement 1, you'd realize instantly that you can find the ratio of men to women from the information given and thus can answer the question, without needing to do any algebra.

Statement 2 is not sufficient here, since while we can find the number of women who will pursue higher studies, we have no information at all about women or men who will not pursue higher studies. So the answer is A.

You could also set this problem up as an overlapping sets matrix. People surveyed were either men or women, and either planned to pursue higher studies or did not. We can then fill in the given information: 1400 people total, and 42% (588) will pursue higher studies:



Now, we can fill in the information from each statement to see if it allows us to solve for the total number of women.

(1) Call the total number of women W, and the men 1400 - W:



We can see that this will be sufficient to solve for W. 36% of men + 50% of women = total pursuing higher studies, so:
0.36(1400 - W) + 0.5W = 588
We don't need to do the algebra here to see that this will give us a value for W. SUFFICIENT

(2) Make sure you erase the information from statement (1) before addressing statement (2). Now fill in the given information - 288 men will pursue higher studies. This means that 300 women will pursue higher studies... but what does that tell us about the total number of women? Nothing! INSUFFICIENT



The answer is A.