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# QOTD # 21 From 2011 to 2012, Jack’s annual salary increased

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QOTD # 21 From 2011 to 2012, Jack’s annual salary increased [#permalink]  12 Sep 2016, 02:33
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From 2011 to 2012, Jack’s annual salary increased by 10 percent and Arnie’s annual salary decreased by 5 percent. If their annual salaries were equal in 2012, then Arnie’s annual salary in 2011 was what percent greater than Jack’s annual salary in 2011?

[Reveal] Spoiler: OA
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Question: 21
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Re: QOTD # 21 From 2011 to 2012, Jack’s annual salary increased [#permalink]  12 Sep 2016, 02:36
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Explanation

Let k be Jack’s annual salary in 2011, and let r be Arnie’s annual salary in 2011. Then Jack’s annual salary in 2012 was 1.1k, and Arnie’s was 0.95r. Since their salaries in 2012 were equal to each other, you have 0.95r = 1.1k. Solving the equation for r, you get r = \frac{1.1}{0.95} * k

Since \frac{1.1}{0.95} = 1.1578 it follows that, rounded to the nearest 0.1%, Arnie’s annual salary in 2011 was 15.8% greater than Jack’s annual salary in 2011.

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Re: QOTD # 21 From 2011 to 2012, Jack’s annual salary increased [#permalink]  30 Jun 2017, 07:17
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Carcass wrote:
Explanation

Let k be Jack’s annual salary in 2011, and let r be Arnie’s annual salary in 2011. Then Jack’s annual salary in 2012 was 1.1k, and Arnie’s was 0.95r. Since their salaries in 2012 were equal to each other, you have 0.95r = 1.1k. Solving the equation for r, you get r = \frac{1.1}{0.95} * k

Since \frac{1.1}{0.95} = 1.1578 it follows that, rounded to the nearest 0.1%, Arnie’s annual salary in 2011 was 15.8% greater than Jack’s annual salary in 2011.

for the above answer, I don't think it is calculated properly according to question. I the question there is percentage increase asked. here its merely the number of times the salary is more is calculated
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Re: QOTD # 21 From 2011 to 2012, Jack’s annual salary increased [#permalink]  01 Jul 2017, 08:05
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Expert's post
Hey,

After the increase in Jacks salary and decrease in Anie's salary their salaries becam equal.

If you took the fraction of the original salaries it came out to be 1.1578.

So basically Arnies salary was 1.158 times Jacks or 115.8% of Jacks salary or 15.8% more than Jacks salary.

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Re: QOTD # 21 From 2011 to 2012, Jack’s annual salary increased   [#permalink] 01 Jul 2017, 08:05
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