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

Question

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)

A. 80

B. 82

C. 85

D. 87

E. 89

NEW question from GMAT® Official Guide 2019 
(PS10002)

SSM700plus · Accepted Answer

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)

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.

avigutman · Answer

Video solution from Quant Reasoning:
 https://www.youtube.com/watch?v=VjzYgFPa6Uo

BrentGMATPrepNow · Answer

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

RELATED VIDEO
 https://www.youtube.com/watch?v=Y9f_0QJU1ug

chetan2u · Answer

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

D

ScottTargetTestPrep · Answer

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

kanakdaga · Answer

A little confusion here! 
Isn't the average speed equal to total distance / total time ?

How can we divide the sum of miles traveled by 4?

Posted from my mobile device

Kamika · Answer

Arithmetic mean for 4 people was 80, so we multiply 80*4=320, and 320 is the sum of results for 4 people. now we subtract 320-(72+78+83)=87

mikeross2694 · Answer

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)

A. 80

B. 82

C. 85

D. 87

E. 89

Hi,

According to stem, total miles driven: 80*4=320 miles

Now,
subtract the miles driven of the other drivers to find the miles driven for Rafael

320 miles - (72+78+83) miles= 87 miles. 
OA: D

aryansingh26 · Answer

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)

A. 80

B. 82

C. 85

D. 87

E. 89

Total miles driven = 80*4 people = 320 miles
Miles driven by Carmen, Juan and Maria = 72+78+83 = 233 miles
Miles driven by Rafael = 320 - 233 = 87 miles
Hence, OA: D

shaonkarim · Answer

Total =80*4=320
=>72+78+83+R=320
=>R=320-233=87

Answer is D

Posted from my mobile device

Shubhi09 · Answer

Calculate mean for 4 people was 80, multiply 80*4=320, and 320 is the sum of results for 4 people. now we subtract 320-(72+78+83)=87

Posted from my mobile device

AndrewN · Answer

30-second approach :

1) Figure out the sum from the average, as others have outlined above.

80*4=320

2) Add  just the units digits  of three of the four drivers.

2+8+3=13

3) Scan the answers. Since the units digit (of the total miles driven) must end in 0, we have to add 7 to the xx3 from before.  The answer must be (D), 87 .

Good luck with your studies, everyone.

- Andrew

Abhishek009 · Answer

80*4 =xx  0   (Units digit is 0)
72+78+83 = xxx  3   (Units digit is 3)

Now using units digit rule xx  0   - xxx  3   = xxx  7   ,Among the given options only (D) satisfies....

GMATinsight · Answer

Answer: Option D

Video solution by  GMATinsight

https://www.youtube.com/watch?v=xVdpX8BBrC4

D3N0 · Answer

Ans: D (87)

This method is good to use when you have only a few numbers or smaller calculations.
For the average, we know that the sum of the differences of each number from the average has to be zero.
So here, the given numbers are 72, 78, 83, and x, with an average of 80, and we need to find x 
(80-72) + (80-78) + (80-83)+ (80-x) = 0
8 + 2 + (-3) + (80-x) = 0
7 + 80 - x = 0 
 x = 87

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

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