We know that 2/3 dislike lima beans, and 3/5 of these dislike brussel sprouts. So we know what percent of the students like lima beans, (1/3) but we have no idea what ratio likes brussel sprouts. We know that 3/5ths of those that don't like lima beans also don't like brussel sprouts, but of the kids that like lima beans you could have 100% of those liking brussel sprouts, or a 100% not liking brussel sprouts.

1) Insufficient. Giving us the total number still doesn't tell us how many of those that like lima beans also like brussel sprouts. It lets us know that 40 students like lima beans, and that 2/5ths of 80, or 32, students that don't like lima beans also don't like brussel sprouts, but we still don't have a total without that number or ratio missing for the students that like lima beans.

2) Insufficient. This basically gives us the same information as 1. 40 is 1/3 of 120, so we already knew this, but again, gets us no closer to knowing how many of those 40 like or dislike brussel sprouts, no ratio, fraction or percentage was given for this 1/3 of the students.

Hope that helps, sorry if it was a little long winded.

I think the answer is D. Can you confirm? Pardon me from filling the talbe below with '-'. The formatting is getting messed up. Ignore '-' in the table below, I am trying to put down a table with two rows and two colums.

L indicates those who like lima beans
~L is those who dislike lima beans
B and ~b are similar.

------B----~B----
-L------------------40
~L----------48---- 80
-------------------120

From (1) I can fill the above information in the table. That means the 2nd row first column element must be 32.

Which is "those who like Brussel Sprouts but dislike Lima beans" = 32.

We can get the same info from (2) also, hence answer must be D.
Correct me if my answer is wrong.

Thanks,
Calista.

OA D.

Thanks.