BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

college T

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 234
Joined: Tue May 31, 2016 1:40 am
Thanked: 3 times

college T

by Needgmat » Wed Jun 22, 2016 10:11 am
Of the 200 students at college T majoring in one or more of the science, 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

OAD

Please explain why not E?

Why 130 is the maximum?

Thanks in advance.

Kavin
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Wed Jun 22, 2016 10:20 am
There are some nice solutions here: https://qa.www.beatthegmat.com/group-pro ... 82407.html

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Wed Jun 22, 2016 8:38 pm
Hi Kavin,

This question can be solved rather handily with the Tic-Tac-Toe board, but you can also use the Overlapping Sets Formula here (although it won't be applicable on every Overlapping Sets question that you might see on Test Day).

This prompt comes with a couple of 'twists' to it:
1) The number of students who study 'neither' is NOT a fixed value - it's a range.
2) The question asks for the RANGE of students who could study both Chemistry and Biology.

Here's how you can use the Formula though...

Total = Gp.1 + Gp.2 - Both + Neither

200 = 130 + 150 - B + (>=30)
200 = 280 - B + (>=30)
200 = (>=310) - B
B = >=110

This gives you the 'lower end' of the range, but does not immediately give you the 'upper end.' To find that, you have to think about the numbers involved. Since 130 students study Chemistry and 150 study Biology, the MAXIMUM number who could study both would be 130 (and that's if EVERY Chemistry student also studied Biology). Thus, the range is 110 to 130, inclusive.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Thu Jun 23, 2016 3:53 pm
You'd have the maximum overlap if everyone in the less populated major is also in the more populated major: if every chem major is a bio major.

You'd have the minimum overlap if you have the fewest possible people in neither major: if you have exactly 30 who aren't majoring in chem or bio.

In the first case we have 130 in both, 20 only in bio, and 50 in neither.

In the second case, we have 30 in neither, leaving (130 + 150 - Overlap) = 170, or Overlap = 110.

That gives us our range: 110 to 130.
Top
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Thu Jun 23, 2016 3:54 pm
Needgmat wrote:
Please explain why not E?

Why 130 is the maximum?

Thanks in advance.
This is a great question! If you had 150 students in both, the overlap (150) would be MORE than the number of students in biology at all (130). But the overlap (dual major) is a SUBSET of the number of students in biology at all, so 130 ≥ Overlap.
Top
Post new topic Post Reply
• Page 1 of 1