The Old Knewton Blog

The Halls and the Oateses

with one comment

Try your hand at this question:

Two family reunions are happening at the same hotel, the Oates reunion and the Hall reunion. All 100 guests at the hotel attend at least one of the reunions. If 40 people attend the Oates reunion and 62 people attend the Hall reunion, how many people attend both reunions?

(A)  2
(B)  5
(C)  10
(D)  16
(E)  22

Answer after the jump.

Explanation:

The question asks us to determine the number of people who attend both the Hall and Oates reunions. Since this is a question about overlapping sets, we will find it useful to draw a Venn diagram.

We will call the number of people who attend only the Hall reunion h, the number of people who attend only the Oates reunion o, and the number of people who attend both b. The information provided in the prompt allows us to set up three equations:

o + h + b = 100
40 – b = h
62 – b = o

If we add the second and third equations together, we get: 102 – 2b = h + o.

Rearranging the first equation, we get: 100 – b = h + o.

Now subtracting this equation from the equation above it, we find: 2 – b = 0, or b = 2.

As expected, 2 people attend both the Hall and Oates reunions. They play all of their hits and a few new songs.

Answer choice A is correct.

Advertisements

Written by Knewton

November 6, 2009 at 4:01 PM

One Response

Subscribe to comments with RSS.

  1. […] the full article: The Halls and the Oateses AKPC_IDS += "5185,"; Share this […]


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: