Bunuel
Ana, Bruce and Carlos are on the waiting list of an MBA program. If there are 20 people in front of Ana, 3 people between Bruce and Carlos and 15 people between Ana and Carlos, what is the number of people between Ana and Bruce?
(1) Ana is ahead of Carlos.
(2) There are 40 people on the waiting list.
Breaking Down the Info:We essentially only need to know the order of Ana, Brace, and Carlos in line. Mainly whether Bruce is in front of in the back of Carlos, and whether Carlos/Brace is in front or back of Ana.
Statement 1 Alone:This tells us Ana must be in front of Bruce as well since Bruce is only 3 people away from Carlos. However, we don't know if Bruce is in front of Carlos or behind Carlos, so there can be two answers given this information. Thus statement 1 is insufficient.
Statement 2 Alone:We should check whether we are allowed to have Ana > Carlos > Bruce. Ana is #21 in line, and add 15 then add 1 to find Carlos is no.37 in line. Thus it is not possible for Bruce to be 3 people behind Carlos, and Bruce must be in front of Carlos. Therefore if Carlos is behind Ana, we must have Ana > Bruce > Carlos.
We should check also if we have Bruce > Carlos > Ana, Carlos would be #5 in this case, and Bruce could be #1. Then it is possible to have Bruce > Carlos > Ana. Thus this statement is insufficient as we have two different relative positions for Bruce. (Note if we made Anna #20 in line with only 39 people in line, this would have been sufficient since Bruce must be 11 people away from Ana, in either direction).
Both Statements Combined:Since Ana must be in front of Bruce, we have only one option. Then combined this is sufficient.
Answer: C