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

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Math Expert
Joined: 02 Sep 2009
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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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35% (medium)

Question Stats:

91% (02:05) correct 9% (01:47) wrong based on 17 sessions

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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 _________________ examPAL Representative Joined: 07 Dec 2017 Posts: 704 Re: Last year Jeff received 24 paychecks. Each of his last six paychecks [#permalink] ### Show Tags 27 Dec 2017, 01:20 1 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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Joined: 22 May 2016
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Last year Jeff received 24 paychecks. Each of his last six paychecks  [#permalink]

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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 $$n = 4$$ $$A = \frac{3,050}{4} = 762.5 \approx{763}$$ 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 Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 4100 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Last year Jeff received 24 paychecks. Each of his last six paychecks [#permalink] ### Show Tags 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

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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, 04:05
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.
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Joined: 24 Nov 2016
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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 &nbs [#permalink] 28 Dec 2017, 04:08
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