Problem Solving

AAPL 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

The OA is D.

I don't have clear this PS question, I appreciate if any expert explain it for me. Thank you so much.

You could just do simple arithmetic. The first 6 paychecks were$750, for a total of 6*750 = 4500. The next 20 paychecks were all for 780 for a total of 20*780 = 15600. In all, the paychecks were worth 4500 + 15600 = 20,100. On average, the 26 checks would be worth 20,100/26 = about 773. The answer is D.

AAPL 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

The OA is D.

I don't have clear this PS question, I appreciate if any expert explain it for me. Thank you so much.

You could also use the number line. We know that the ratio of 750 checks to 780 checks is 6:20 or 3:10. So let's call the distance from each check to the overall average 10x and 3x. (We know that the overall average will be far closer to 780 than 750 as there are far more 780 checks, so the 3x will represent the gap between the 780 and the overall average and the 10x will represent the gap between 750 and the overall average.) Our number line will look like this:

750------------10x---------AVG--3x--780

10x + 3x = 780-750
13x = 30
x = 30/13
3x = 90/13, which is very close to 7.

So the AVG = 780 - 7 = 773. The answer is D