A taxicab driver worked exactly 18 shifts ...

[Night reader]

A taxicab driver worked exactly 18 shifts in a month. He used an average of 10 1/4 gallons of gasoline for each of the Â…rest 10 shifts, and an average of 12 1/8 gallons of gasoline for each of the rest of his shifts. What is the average amount of gasoline, in gallons, that the taxicab driver used per shift?

(A) 11
(B) 11 1/12
(C) 11 3/16
(D) 11 1/6
(E) 11 7/24

Please show a solution.

[trangle]

For the first 10 shilfts, he uses total 102 2/4 (10 1/4*10) gallons. For the rest 8 shifts, he uses 97 (12 1/8*8) gallons. So, the average amount of gas that the taxi driver uses per shift is (102 2/4 + 97)/18 = 11 1/12 gallons. The answer is B.

[Night reader]

For the first 10 shilfts, he uses total 102 2/4 (10 1/4*10) gallons. For the rest 8 shifts, he uses 97 (12 1/8*8) gallons. So, the average amount of gas that the taxi driver uses per shift is (102 2/4 + 97)/18 = 11 1/12 gallons. The answer is B.

Thank you. The reason I had posted this problem to show much better and faster solution unlike one described in GMAT math books and residing in your answer above.

Look, how many tedious calculations you have done here

102 2/4 (10 1/4*10)

97 (12 1/8*8)

(102 2/4 + 97)/18 = 11 1/12


I understand that some people like to employ the mental math and to double check an answer to the problem, but it eats our time on GMAT

You may know the concept of weighted averages, no need to repeat. And do you agree - every single (sample) average's value is as much different from another single average's value as the difference of their values in the samples?

By taking this into consideration, next time you may wish to employ this shortcut

[10*(10 1/4 )+8(12 1/8 )] : 18 = ?

Subtract 10 1/4 from each of the single averages: [10*(0)+8*(1 7/8 )] : 18 = 15/18

Add 10 1/4 back to the result (we subtracted 10 1/4 from the nominator quantities, so we must return this value):

15/18 + 10 1/4 = 30/36 + 10 9/36 = 10 + 39/36 = 11 + 3/36 = 11 1/12 , choice (B).

p.s. the number of single averages can be 5 or 6 and they might contain terribly fractional values. So this short-cut is very handy once you get used to it.