Problem Solving

AAPL wrote:P={40, 50, 60, 60, 70, x}

For what value of x are the mode, the median and the average of set P above equal?

A. 20
B. 35
C. 60
D. 80
E. 90

The OA is D.

The mode is absolutely equal to 60. So, the average should be equal to 60.

So, 40+50+60+60+70+x = 6*60 = 360 --> x = 80.

Has anyone another strategic approach to solve this PS question? Regards!

I sincerely doubt that there's a better (i.e., faster) approach than the one you describe.
One option would be to test the answer choices, but your approach is likely faster.

The key concept (which you have identified) is that the mode MUST be 60, since we already have two 60's.

Cheers,
Brent

Hi AAPL,

You've correctly deduced that the Mode would have to be 60. You might be able to save on some 'calculation time' if you use the patterns in the numbers to your advantage (meaning that you don't technically have to calculate the entire average by hand to find the value of X).

The numbers are 40, 50, 60, 60, 70 and X.

Notice that 50 is "10 below" the average and 70 is "10 above" the average. Those 'differences' essentially cancel out. 40 is "20 below" the average, so the missing number would have to be '20 above' the average - so that those differences also cancel out...

Final Answer: D

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

AAPL wrote:P={40, 50, 60, 60, 70, x}

For what value of x are the mode, the median and the average of set P above equal?

A. 20
B. 35
C. 60
D. 80
E. 90

We see that in order for the mode, median and average to be equal, the mode has to be 60. So we can create the equation:

(40 + 50 + 60 + 60 + 70 + x)/6 = 60

280 + x = 360

x = 80

Answer: D