At a certain committee meeting only associate professors and

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swerve: Legendary Member; Posts: 2545; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Sun Nov 24, 2019 3:29 am

At a certain committee meeting, only associate professors and assistant professors are present. Each associate professor has bought 2 pencils and 1 chart for the meeting, while each assistant professor bought 1 pencil and 2 charts. If a total of 10 pencils and 11 charts have been bought for the meeting, how many people are present?

A. 6
B. 7
C. 8
D. 9
E. 10

The OA is B

Source: GMAT Prep

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Source: Beat The GMAT — Problem Solving | Sun Nov 24, 2019 3:29 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Nov 24, 2019 6:30 am

swerve wrote:At a certain committee meeting, only associate professors and assistant professors are present. Each associate professor has bought 2 pencils and 1 chart for the meeting, while each assistant professor bought 1 pencil and 2 charts. If a total of 10 pencils and 11 charts have been bought for the meeting, how many people are present?

A. 6
B. 7
C. 8
D. 9
E. 10

Notice that the question asks us to find that TOTAL number of people present.
In other words, the question does NOT ask us to find the number of associate professors or assistant professors present.

Since each person brings THREE items, and since total of 21 items were brought (10 pencils and 11 charts), then the number of people = 21/3 = 7

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8154; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Nov 28, 2019 4:23 pm

swerve wrote:At a certain committee meeting, only associate professors and assistant professors are present. Each associate professor has bought 2 pencils and 1 chart for the meeting, while each assistant professor bought 1 pencil and 2 charts. If a total of 10 pencils and 11 charts have been bought for the meeting, how many people are present?

A. 6
B. 7
C. 8
D. 9
E. 10

The OA is B

Source: GMAT Prep

We can let the number of associate professors = a and the number of assistant professors = n and create two equations:

Pencil equation:

2a + n = 10

Chart equation:

a + 2n = 11

Let's add the two equations together:

3a + 3n = 21

a + n = 7

Thus, there are 7 people at the meeting.

Answer: B

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