GMAT Quant: Question of the Day!

Today let’s work on a sets problem using Venn diagrams!

In 1997, N people graduated from college. If 1/3 of them received a degree in the applied sciences, and, of those, 1/4 graduated from a school in one of six northeastern states, which of the following expressions represents the number of people who graduated from college in 1997 who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states?

(A) 11N/12
(B) 7N/12
(C) 5N/12
(D) 6N/7
(E) N/7

This question can be solved using a Venn diagram or a matrix to make sense of the information:

The key to understanding this question lies in the last sentence:

who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states?

We have two categories to sum: the people who ONLY received a science degree but NOT from one of the 6 schools, and the people who ONLY went to the 6 schools but did NOT receive a science degree. I made up variables for these categories (x and y).

If N = 12, there are 4 applied science students, 1 of which is both. That means x = 3. If 4 students are applied science, then 12-4 = 8 are from one of the six states but NOT applied science. y = 8.

3 + 8 = 11

So we are looking for an answer choice that gives us 11 when N = 12; the answer is (A).

Tough GMAT: Quant Question of the Day

Today, we’ll take a look at a question from the Official Guide from GMAC dealing with sets! As always, try it on your own, then scroll down for an explanation! 🙂

Of the 200 students at College T majoring in one or more of the sciences, 130 are majoring in chemistry and 150 are majoring in biology. If at least 30 of the students are not majoring in either Chemistry or Biology, then the number of students majoring in both chemistry and biology could be any number from:

A) 20 to 50
B) 40 to 70
C) 50 to 130
D) 110 to 130
E) 110 to 150

The question asks what “x” could be.

150 = B + X

130 = C + X

B + C + X = 170

The MAXIMUM overlap is 130, since the Chemistry circle cannot be GREATER than 130. From there we know the answer must be either (C) or (D).

Plugging in our first two equations:

(150 – X) + (130 – X) + X = 170

150 – X + 130 – X + X = 170

150 – X + 130 = 170

150 – X = 40

– X = 40 – 150

-X = -110

X = 110

The answer is (D).