Problem Solving

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 amount of his paychecks for the year?

A) $752
B) $755
C)$765
D) $773
E) $775

The answer explanation only shows how you could solve this by calculating it out in full... i.e. working out (6(750)+20(780))/26. I can ballpark it down to 2 answers right off the bat, noticing that the average is weighted on the 780 paycheck side, but that is as far as I can go w/o calculation. Is there a better way, not involving time consuming calculation, to find the answer here?

I guess we can do this w/o calculation.

if each month he had received 750, hen the average wud be 750. He received 30*20 =600 hundred dollars extra.
this 600 dollars must be divided into 26 parts to egt the average.600/26= 23.something
answer is 750+23=773

phaedrus82 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 amount of his paychecks for the year?

A) $752
B) $755
C)$765
D) $773
E) $775

The answer explanation only shows how you could solve this by calculating it out in full... i.e. working out (6(750)+20(780))/26. I can ballpark it down to 2 answers right off the bat, noticing that the average is weighted on the 780 paycheck side, but that is as far as I can go w/o calculation. Is there a better way, not involving time consuming calculation, to find the answer here?

Let's start with rapid elimination:

765 is the midpoint between 750 and 780. 780 "weighs more" in the average, so the answer MUST be more than 765... eliminate A, B and C.

Now let's think about D and E. 775 (the easier number) is 5/6 of the way from 750 to 780. 775 would only be the right answer if 5/6ths of the paychecks were for 780. Does 20/26=5/6? No! Therefore, 775 cannot be the right answer... eliminate E.

Only one choice left - choose D!