## At a certain university, there are s students, $$w$$ of whom are female and m of whom are male. The number of female phy

##### This topic has expert replies
Legendary Member
Posts: 1622
Joined: 01 Mar 2018
Followed by:2 members

### At a certain university, there are s students, $$w$$ of whom are female and m of whom are male. The number of female phy

by Gmat_mission » Sun Jun 06, 2021 10:15 am

00:00

A

B

C

D

E

## Global Stats

At a certain university, there are s students, $$w$$ of whom are female and m of whom are male. The number of female physics students is denoted by $$p_w$$ and is exactly $$12\%$$ of the female enrollment. Similarly, the number of male physics students is denoted by $$p_m$$ and is exactly $$25\%$$ of the male enrollment. If the overall number of physics students is denoted by $$p,$$ which of the following must be true?

A. $$p_w<p_m$$

B. $$w>0.06s$$

C. $$w<p<m$$

D. $$p_m=0.125s$$

E. $$0.12s<p<0.25s$$

Source: Veritas Prep

### GMAT/MBA Expert

GMAT Instructor
Posts: 2618
Joined: 02 Jun 2008
Location: Montreal
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

### Re: At a certain university, there are s students, $$w$$ of whom are female and m of whom are male. The number of female

by Ian Stewart » Tue Jun 08, 2021 5:13 am
It's just a weighted average or mixtures situation. We know 12% of one group (women) and 25% of another group (men) are in physics. So overall, when we look at men and women together, somewhere between 12% and 25% are in physics. So the number of physics students p is somewhere between 12% of all students (which is 0.12s) and 25% of all students (which is 0.25s), and E is the correct answer.

The other answers can all be false. Answer A is false if we have far more female students than male students overall. Answer B is false if only a tiny fraction of the student population is female. Answer C can clearly be false, just ignoring the middle of the inequality, because w > m can be true. Answer D will only be true in the one case where men make up exactly half of the entire student body.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

• Page 1 of 1