vehicles

[grandh01]

Worldwide production of motor
vehicles was 3.9 million vehicles in
1946 and 45.7 million in 1987. Of the
following, which is closest to the
average (arithmetic mean) annual
increase, in millions, in worldwide
production of motor vehicles during
this period?
(A) 0.08
(B) 1.0
(C) 1.1
(D) 10.5
(E) 41.8

OA is B

[theCEO]

Worldwide production of motor
vehicles was 3.9 million vehicles in
1946 and 45.7 million in 1987. Of the
following, which is closest to the
average (arithmetic mean) annual
increase, in millions, in worldwide
production of motor vehicles during
this period?
(A) 0.08
(B) 1.0
(C) 1.1
(D) 10.5
(E) 41.8

OA is B

(45.7 - 3.9) / [(1987 - 1946) + 1]
41.8 / 42 = 1
ans = b

[Ian Stewart]

(45.7 - 3.9) / [(1987 - 1946) + 1]
41.8 / 42 = 1
ans = b

While it doesn't turn out to affect the answer, the denominator here should be 41, and not 42. While there are indeed 42 different years from 1946 to 1987 inclusive, that isn't quite what we want in our denominator. We want to divide by the number of times the year changed from one to the next in that period, and from 1946 to 1987 the year changes only 41 times.

If that's not clear, I probably haven't explained myself well, but you could imagine a simpler situation. If we had the following three years of auto production:

2005: 10 cars
2006: 20 cars
2007: 40 cars

then the average increase year-on-year in auto production for this period is 30/2 = 15. We wouldn't want to divide by 3 here.

But either way the closest answer is still B.