BTGmoderatorDC 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

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

Cheers,
Brent

Hi All,

We're told that 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. We're asked how many miles Rafael drove. This question can be solved in a number of different ways; using the Average Formula (as Brent did) is arguably the easiest. You can also use the 'differences' between the three given values and the average to calculate the difference between the fourth value and the average.

With an average of 80....
Carmen drove 8 miles LESS than the average
Juan drove 2 miles LESS than the average
Maria drove 3 miles MORE than the average

The 'net effect' of those differences is (-8) + (-2) + (+3) = -7... meaning that the total of those 3 values is 7 LESS than the average. This means that Rafael has to drive far enough to 'offset' that difference. Thus, Rafael drove 7 MORE than the average (re: 80+7 = 87 miles).

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorDC 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