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During a trip that they took together, Carmen, Juan, Maria, a

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During a trip that they took together, Carmen, Juan, Maria, a  [#permalink]

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New post 21 Jun 2018, 08:07
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During a trip that they took together, Carmen, Juan, Maria, and Rafael drove an average (arithmetic mean) of 80 miles each. Carmen drove 72 miles, Juan drove 78 miles, and Maria drove 83 miles. How many miles did Rafael drive?

A. 80

B. 82

C. 85

D. 87

E. 89


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During a trip that they took together, Carmen, Juan, Maria, a  [#permalink]

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New post 21 Jun 2018, 17:33
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Bunuel wrote:
During a trip that they took together, Carmen, Juan, Maria, and Rafael drove an average (arithmetic mean) of 80 miles each. Carmen drove 72 miles, Juan drove 78 miles, and Maria drove 83 miles. How many miles did Rafael drive?

A. 80

B. 82

C. 85

D. 87

E. 89


NEW question from GMAT® Official Guide 2019


(PS10002)


Let x = the number of miles Rafael drove

Average = 80
So, (72 + 78 + 83 + x)/4 = 80
Multiply both sides by 4 to get: 72 + 78 + 83 + x = 320
Simplify: 233 + x = 320
Solve: x = 87

Answer: D

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Re: During a trip that they took together, Carmen, Juan, Maria, a  [#permalink]

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New post 21 Jun 2018, 18:00
Bunuel wrote:
During a trip that they took together, Carmen, Juan, Maria, and Rafael drove an average (arithmetic mean) of 80 miles each. Carmen drove 72 miles, Juan drove 78 miles, and Maria drove 83 miles. How many miles did Rafael drive?

A. 80

B. 82

C. 85

D. 87

E. 89


NEW question from GMAT® Official Guide 2019


(PS10002)


Total distance = average * number = 80*4=320..
So C+J+R+M=320....72+78+R+83=320
R=320-233=87

D
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During a trip that they took together, Carmen, Juan, Maria, a  [#permalink]

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New post 21 Jun 2018, 18:02
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During a trip that they took together, Carmen, Juan, Maria, and Rafael drove an average (arithmetic mean) of 80 miles each. Carmen drove 72 miles, Juan drove 78 miles, and Maria drove 83 miles. How many miles did Rafael drive?

A. 80

B. 82

C. 85

D. 87

E. 89


NEW question from GMAT® Official Guide 2019


(PS10002)

This is an easy to approach problem. Let me try without using pen & paper here.

As we all know Average is \(\frac{sum of all the elements}{no of elements}\)

Average given is - 80.

We will make note of - how far each value is from average?

C - 8
J - 2
M - \(-3\) ( -ve sign denote that it is more than average)

Add up all this value - 10-3 =7.

In order to make an average of 80. the Rafael should travel 7 miles more than average.

Rafael travels : 80 + 7 = 87.

All of the above calculation can be done in mind because it is very small number.

Ans - D.

Let me know if it doesn't help, I would elaborate it.
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Re: During a trip that they took together, Carmen, Juan, Maria, a  [#permalink]

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New post 23 Jul 2018, 17:41
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Bunuel wrote:
During a trip that they took together, Carmen, Juan, Maria, and Rafael drove an average (arithmetic mean) of 80 miles each. Carmen drove 72 miles, Juan drove 78 miles, and Maria drove 83 miles. How many miles did Rafael drive?

A. 80

B. 82

C. 85

D. 87

E. 89


We can create the equation:

(72 + 78 + 83 + x)/4 = 80

233 + x = 320

x = 87

Alternate Solution:

Carmen drove 8 miles under the average, Juan drove 2 miles under the average and Maria drove 3 miles above the average. If we add these up, we get -8 + (-2) + 3 = -7; which means we are 7 miles under the average. Therefore, Rafael must drive 7 miles over the average to keep the average at 80 miles. Thus, Rafael drove 80 + 7 = 87 miles.

Answer: D
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Re: During a trip that they took together, Carmen, Juan, Maria, a &nbs [#permalink] 23 Jul 2018, 17:41
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