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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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New post 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

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

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New post 27 Dec 2017, 01:20
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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.
(C) is our answer.

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

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

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New post 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)

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

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

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New post 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.

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