There are 7 players in a bowling team with an average...

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swerve: Legendary Member; Posts: 2535; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Sat Jan 20, 2018 7:13 am

There are 7 players in a bowling team with an average weight of 85kg. If two new players join the team, one weight 110 kg and the second weight 60 kg, what will be the new average weight?

A. 75 kg
B. 80 kg
C. 85 kg
D. 90 kg
E. 92 kg

The OA is C.

Please, can any expert explain this PS question for me? I tried to solve it of the following way but I'm not sure,

Can I say that,
$$N_{avg}=\frac{85+\left(\frac{110+60}{2}\right)}{2}=85\ kg$$
I need your help. Thanks.

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Source: Beat The GMAT — Problem Solving | Sat Jan 20, 2018 7:13 am

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by [email protected] » Sat Jan 20, 2018 1:26 pm

Hi swerve,

We're told that 7 players on a bowling team have an average weight of 85kg and that two new players join the team (one weighing 110 kg and the other weighing 60 kg). We're asked for the average weight of the 'new' team.

This question be solved in a couple of different ways. Here's how you can solve it without doing too much math - focusing instead on the 'net effect' that the two 'new' weights would have on the average...

110kg is 25kg "more" than the current average (re: 85kg).
60kg is 25kg "less" than the current average (re: 85kg).

Thus, the 'increase' from the heavier person is 'cancelled out' by the 'decrease' from the lighter person... and the average weight of the group would stay the SAME.

Final Answer: C

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EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pmFollowed by: 12 members; Thanked: 180 times

by EconomistGMATTutor » Sat Jan 20, 2018 1:52 pm

There are 7 players in a bowling team with an average weight of 85kg. If two new players join the team, one weight 110 kg and the second weight 60 kg, what will be the new average weight?

A. 75 kg
B. 80 kg
C. 85 kg
D. 90 kg
E. 92 kg

The OA is C.

Please, can any expert explain this PS question for me? I tried to solve it of the following way but I'm not sure,

Hi swerve,
Let's take a look at your question.

We have three numbers, one is 85, average of 7 numbers and other two are 110 and 60.
We can find average of these three numbers as:
$$Average\ =\ \frac{85+110+60}{3}=\frac{255}{3}=85$$
Therefore, option B is correct.

Hope it helps.
I am available if you's like any follow up.

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Our average student improves 98 points.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Jan 21, 2018 3:42 am

swerve wrote:There are 7 players in a bowling team with an average weight of 85kg. If two new players join the team, one weight 110 kg and the second weight 60 kg, what will be the new average weight?

A. 75 kg
B. 80 kg
C. 85 kg
D. 90 kg
E. 92 kg

Average weight of the 7 original players = 85.
Average weight of the 2 new players = (110+60)/2 = 85.
Since the two groups have the same average weight -- 85 -- the MIXTURE of the two groups must also have an average weight of 85.

The correct answer is C.

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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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I unlock the best way for YOU to solve problems.

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

edit

by ceilidh.erickson » Mon Jan 22, 2018 1:09 pm

EconomistGMATTutor wrote:
Hi swerve,
Let's take a look at your question.

We have three numbers, one is 85, average of 7 numbers and other two are 110 and 60.
We can find average of these three numbers as:
$$Average\ =\ \frac{85+110+60}{3}=\frac{255}{3}=85$$
Therefore, option B is correct.

Hope it helps.
I am available if you's like any follow up.

EconomistGMAT - You got the right answer, but your math was faulty here. It is only because the two additional numbers average to 85 that this works out.

Imagine instead that the two new weights were 105 and 110. We could not simply take (85 + 105 + 110)/3 and get 100.

There were 7 players with a weight of 85, so there would be 9 players in total: (7(85) + 100 + 110)/9 = 90. This is weighted toward the 7 players with a lower average weight.

On this actual problem, Mitch and Rich rightly pointed out that because the 2 new weights average to the old average of 85, we don't have to do any additional math. If we didn't notice this, though, and wanted to do the math, the correct formula would be:
$$Average\ =\ \frac{7*85+110+60}{9}=85$$

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Mon Jan 29, 2018 9:52 am

swerve wrote:There are 7 players in a bowling team with an average weight of 85kg. If two new players join the team, one weight 110 kg and the second weight 60 kg, what will be the new average weight?

A. 75 kg
B. 80 kg
C. 85 kg
D. 90 kg
E. 92 kg

The sum of the weights of the 7 bowlers is 7 x 85 = 595. If we add in two new players, the new sum is 595 + 110 + 60 = 765.

So the new average is 765/9 = 85

Alternate Solution:

When looking at the two new weights, we could have noticed that one weight is 25 greater and the other is 25 less than the average, thus creating no change in the average of the weights of the members of the team.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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