GMATPrep Quant Question: What is this?

by Stacey Koprince Jun 13, 2012

I don’t have a great title for you because I don’t have a really clean category for this question “ and that’s exactly why it caught my attention and why I’m sharing it with you today.
Try out this GMATPrep problem:

Did one of the 3 members of a certain team sell at least 2 raffle tickets yesterday?

(1) The 3 members sold a total of 6 raffle tickets yesterday.

(2) No 2 of the members sold the same number of raffle tickets yesterday.

This really does not look like a tough question does it? It looks easy! We can’t know for sure exactly how this question was rated, but consider this. I received this as the 15th question in my GMATPrep quant section. Up until that point, I had missed 2 questions, #6 and #14.

By the way, I took the test on a plane without scrap paper and the two I missed were both geometry questions for which I really needed to draw something out. Don’t try that at home! Write everything down. (After #14, I got a napkin from the flight attendant and started using that!)

So, yes, I’d missed the question right before (#14), but I had also gotten 12 of 14 questions right so far. In other words, the above question is at the upper end of the range.

So, the question is harder than it looks. Let’s talk about why. = )

The question stem is telling us that a certain team contains 3 members. Okay, write that down: team = 3 memb.

They ask about one of the members; what they’re really saying is did ANY one or AT LEAST one of those three members do some particular thing? Note that they are NOT saying did exactly one member sell at least 2 tickets. If they wanted to say exactly and only one member, then they would say exactly one member. If they say simply one member, then they mean at least one “ but possibly more than one.

Finally that particular thing is sell at least 2 raffle tickets yesterday.

How do we write that down? It’s tempting not to write anything down. Resist that temptation “ you’ll be a lot more likely to make a mistake if you don’t write anything down.

I wrote down: did at least 1 sell > 2 tickets yesterday?

Then I went to the statements.

(1) The 3 members sold a total of 6 raffle tickets yesterday.

At first glance, this looks like it tells me nothing. But wait! What are some actual possibilities?

1, 2, 3. At least one sold two or more.

0, 0, 6. At least one sold two or more.

2, 2, 2. At least one sold two or more!

In fact, there’s no way to come up with a set of three non-negative integers that add to 6 and are all less than 2. Why? Try it. The largest integer you could use would be 1, and 1+1+1 = 3.

If you want to explore this a little more deeply, there’s a math principle that says that if the average of a set of integers is also an integer, then at least one of the integers in the set must be greater than or equal to the average. In this case, the average is 6/3 = 2, therefore at least one number in the set must be greater than or equal to the average. This makes sense logically too: if the average is 2, then all of the numbers in the set can’t be less than 2.

Okay, statement 1 is sufficient! Cross off answers B, C, and E.

Let’s move on to statement 2:

(2) No 2 of the members sold the same number of raffle tickets yesterday.

Well, that doesn’t tell me how many each one did sell! No, it doesn’t. But keep thinking.

There are 3 members. One member could have sold zero tickets. The second member could have sold one ticket. What does that leave for the third member? Right. The third member has to have sold two or more tickets. It’s not possible for all three to have sold less than 2, because there are only two possible integers less than 2 for the number of tickets sold: 0 and 1.

The correct answer is D.

Do you see my dilemma about what to call this one? I could have called it a permutation / combination problem, because it does have something to do with the different possible ways in which things played out in the scenario. I finally decided, though, that I’m going to call this a logic question. That’s what they were really getting me to do “ figure out what was logically possible and logically impossible. They didn’t even use big numbers in the problem; it really was all about logic.

Key Takeaways:

(1) Some questions look easy and are actually really tricky. If you answer a quant question in less than a minute and think, wow, that was easy check your work! Also don’t play the this question looks easy so I must not be doing well game. In the heat of the moment, you really can’t tell how difficult something is.

(2) Some questions are going to require a more logical approach. In a way, this problem actually reminds me of an IR question. It has a lot less text than a typical IR question, but it’s forcing me to use similar reasoning. So, fair warning: even quant questions might require more of a logical approach!

* All quotes copyright and courtesy of the Graduate Management Admissions Council. Usage of this material does not imply endorsement by GMAC.