Bunuel wrote:

Last year Jeff received 24 paychecks. Each of his last six paychecks was $800; this was a $50 raise from each of his earlier paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of the paychecks for the year?

A. $748

B. $750

C. $763

D. $775

E. $776

Estimation is a shrewd strategy here, as

DavidTutorexamPAL demonstrates above.

If you do not use that method, you can shorten this problem in a couple of ways.

Use the ratio of 6 : 18David gets 6 paychecks for $800. 24 checks total.

The other 18 are $50 less than $800 = $750

Express the ratio of number of checks as a fraction:

\(\frac{6}{18} = \frac{1}{3}\)1 check for $800

3 checks for $750

4 checks total

Average check amount:

\(A = \frac{S}{n}\)

\(S = (1)800 + 3(750) = (800 + 2250) = $3,050\), and

\(n = 4\)

\(A = \frac{$3,050}{4} = 762.5 \approx{$763}\)ANSWER C

Double and halve*The long route: 6 checks for $800. 18 for $750

Average check amount=

\(\frac{6($800) + 18($750)}{24}\)For (18 * $750), double $750 and halve 18:

(9 * $1,500) = $13,500. And

(6 * $800) = $4,800

Sum = ($13,500 + 4,800) = $18,300

\(n= 24\),

A =\(\frac{$18,300}{24}\)From the answers you know: 18,300/24 = 7xx

After that, the arithmetic is quick. (Though this method is the most time-consuming.)

\(\frac{$18,300}{24}

= 762.5 \approx{$763}\)ANSWER C

See GMATclub expert

mikemcgarry,

the doubling and halving trick for GMAT math
_________________

The only thing more dangerous than ignorance is arrogance.

-- Albert Einstein