kanha81 wrote:Last year Manfred received 26 paychecks. Each of his first 6 paychecks was $750; each of his remaining paychecks was $30 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his paychecks for the year?
(A) $752
(B) $755
(C) $765
(D) $773
(E) $775
Great algebraic solutions from dmateer! However, as with many GMAT questions, there are other approaches which may be much quicker.
If we were in a rush, we could give ourselves a 50/50 shot at this question almost immediately and then use some strategic guessing to answer with no big calculations at all.
In a weighted average, the total average will always be closer to the group with the most weight.
In this question, we have a lot more checks for $780 than for $750. Therefore, the overall average will be weighted toward $780: eliminate (a), (b) and (c).
In fact, in many weighted average questions the answer choice pattern will be:
a) closer to group 1
b) closer to group 1
c) right in the middle
d) closer to group 2
e) closer to group 2
so if you can figure out which group "weighs more" you can often give yourself a quick 50/50 shot (the answer right in the middle is almost always a sucker bet).
Going one step further:
$775 is 25/30 or 5/6 of the way between $750 and $780. For $775 to be correct, the weight of group 2 would have to be 5 times the weight of group 1.
We have 20 checks for $780 and 6 for $750. Is 20:6 = 5:1? Nope, so we can eliminate (e) as well: choose (d).
