GMAT Math

A poll asked 60 people what their favorite ice cream was between Vanilla, Chocolate, and Strawberry. 1/3 had Vanilla in last place. 1/2 had Vanilla ahead of Chocolate. 1/10 preferred Vanilla to Strawberry. How many people had vanilla in first place?

This question has me stumped.

Slappy Sanchez wrote:A poll asked 60 people what their favorite ice cream was between Vanilla, Chocolate, and Strawberry. 1/3 had Vanilla in last place. 1/2 had Vanilla ahead of Chocolate. 1/10 preferred Vanilla to Strawberry. How many people had vanilla in first place?

This question has me stumped.

I'm stumped too. I did the following.

First I broke it down into permutations of ways the people could rank them.

1 2 3

V S C
V C S
C V S
C S V
S V C
S C V

To account for the people who ranked vanilla last, CSV and SCV should add up to 20. That leaves 40 more.

Then to maximize the other two I chose 6 CVS and 30 SVC. That way there is no overlap between those who prefer vanilla to chocolate and those who prefer vanilla to strawberry.

So we have a total of 20 with vanilla in last place and 30 and 6 with vanilla in the middle. We can't have any more vanilla in last place or in the middle or at the top. So we don't even get to sixty people. We get a total of 56 and we're short 4.

At least that's my take.

Yes, this was a GMAT question. I am going off memory, so I can't remember the answers they presented. But the question (while not written the same)is one that I am sure others will see. How do you work such a problem?

The correct question is:
"A poll asked 60 people what their favorite ice cream was between Vanilla, Chocolate, and Strawberry. There were no ties, meaning every person was asked to rank the flavors in order. 3/5 had Vanilla in last place, 1/10 had Vanilla ahead of Chocolate, and 1/3 ranked Vanilla ahead of Strawberry. How many people ranked Vanilla in the first place?"

Please attempt this question again before seeing my solution below.

This is a hard question.

There are 6 possible ways in which the people rank the ice creams. We are given that there are no ties. Let's assign X1 as the number people who rank Vanilla first, Strawberry second, and Chocolate last. We can do a similar assignment to the rest of the categories.

VSC = X1
VCS = X2
CVS = X3
CSV = X4
SVC = X5
SCV = X6

The key step after this is to translate the given information algebraically. We get the following three equations:

X4+X6 = 36

X1+X2+X5 = 6

X1+X2+X3 = 20

Now our goal is to get a value for X1+X2, look to see how we could combine these equations to yield X1+X2. If we add all of them we get:

X1+X2+X1+X2+X3+X4+X5+X6 = 36+6+20

We also know that X1+X2+X3+X4+X5+X6 =60, therefore

X1+X2+60=62

or X1+X2=2

It is a tough problem. I don't know if I can do this quickly in the exam under pressure.

Dabral

Whoops, just saw this might be a GMAT question. Deleted my post.

Whoops, just saw this might be a GMAT question. Deleted my post.

Slappy Sanchez wrote:A poll asked 60 people what their favorite ice cream was between Vanilla, Chocolate, and Strawberry. 1/3 had Vanilla in last place. 1/2 had Vanilla ahead of Chocolate. 1/10 preferred Vanilla to Strawberry. How many people had vanilla in first place?

This question has me stumped.

This, as written, has more than one solution:
1. There are 3 line-ups for Vanilla ahead of Chocolate. Label these X+Y+Z=30
2. There are three line-ups for Vanilla ahead of Strawberry, but two of them showed up in 1. So we have X+Y+W=6
3. Seeing that these are two equations in three unknowns, there's a good chance of finding more than one solution. It's not an automatic "insufficient" because there is already one obvious restriction on the kinds of solutions, i.e. must be positive integers - and there may be others hiding. But we can plug in numbers and quickly see that yes there are several solutions for Vanilla in first.

Regards!
Mike Miagi
www.google.com/+MikeMiagi