There are some nice solutions here: https://qa.www.beatthegmat.com/group-pro ... 82407.html

Cheers,
Brent

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