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# Last year Jeff received 24 paychecks. Each of his last six paychecks

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Last year Jeff received 24 paychecks. Each of his last six paychecks [#permalink]

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27 Dec 2017, 01:01
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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 [Reveal] Spoiler: OA _________________ examPAL Representative Joined: 07 Dec 2017 Posts: 305 Re: Last year Jeff received 24 paychecks. Each of his last six paychecks [#permalink] ### Show Tags 27 Dec 2017, 01:20 1 This post received KUDOS Expert's post 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

We're given the ratio between paychecks and asked to find the average.
Before calculating, we'll estimate the answer. This is an Alternative approach.

Jeff's paychecks were all $750 or$800 so the average must be somewhere in the middle.
(A), (B) are eliminated.
Had exactly half of the paychecks been $750 and half been$800 the average would in the middle of the two - $775. But - there are more$750 paychecks than $800 so the answer must be smaller than$775.
(D), (E) are eliminated.

** Note that estimating like this requires much easier calculations than the full solution. Usually it can eliminate 2-3 of the answers and the rest can be tested directly.
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Save up to $250 on examPAL packages (special for GMAT Club members) SC Moderator Joined: 22 May 2016 Posts: 1571 Last year Jeff received 24 paychecks. Each of his last six paychecks [#permalink] ### Show Tags 27 Dec 2017, 10:36 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 : 18
David 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 $$n = 4$$

$$A = \frac{3,050}{4} = 762.5 \approx{763}$$

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.)

$$\frac{18,300}{24} = 762.5 \approx{763}$$

See GMATclub expert mikemcgarry, the doubling and halving trick for GMAT math
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Last year Jeff received 24 paychecks. Each of his last six paychecks [#permalink]

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27 Dec 2017, 11:01
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 $$\frac{18*750 + 6*800}{24}= \frac{13500 + 4800}{24}$$ ~ $$763$$ Or, The nearest dollar, what was the average (arithmetic mean) amount of the paychecks for the year is (C) 763 Answer will be (C) _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) examPAL Representative Joined: 07 Dec 2017 Posts: 305 Re: Last year Jeff received 24 paychecks. Each of his last six paychecks [#permalink] ### Show Tags 28 Dec 2017, 04:05 genxer123 wrote: Estimation is a shrewd strategy here, as DavidTutorexamPAL demonstrates above. Thanks! Estimation can do wonders for the harder or more calculation-intensive questions. Especially considering that often we just don't have the time to waste. _________________ David Senior tutor at examPAL Signup for a free GMAT course We won some awards: Join our next webinar (free) Save up to$250 on examPAL packages (special for GMAT Club members)

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Re: Last year Jeff received 24 paychecks. Each of his last six paychecks [#permalink]

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28 Dec 2017, 04:08
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

$$Average=\frac{Sum.Paychecks}{Number.Paychecks}=\frac{(6*800)+(18*750)}{24}=\frac{4800+13500}{24}=\frac{18300}{24}=\frac{9150}{12}=\frac{3050}{4}=\frac{(1525=1526)}{2}=763$$ to the nearest dollar.

Re: Last year Jeff received 24 paychecks. Each of his last six paychecks   [#permalink] 28 Dec 2017, 04:08
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