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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?

Give your answer to the nearest 0.1 percent.

[Reveal] Spoiler: OA
15.8

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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.

The correct answer is 15.8.
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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.

The correct answer is 15.8.

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]  12 May 2019, 03:03
My problem:

If Arnie's salary= 1.1578 times Jack's salary,how do we calculate the answer to the nearest 0.1% and get the answer as 15.8%.
Please provide me the stepwise solution from this step if possible.
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Re: QOTD # 21 From 2011 to 2012, Jack’s annual salary increased [#permalink]  12 May 2019, 04:39
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We said that the salary is 1.158 times but you must express this number in terms of percentage. Therefore, you must express it * 100

1.15 *100 = 115.8 %

Our base (always) is 100. So, our difference is 15.8 %

Hope now is more clear to you.

For the rest of the process to come to a solution see my explanation above.

Regards
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Re: QOTD # 21 From 2011 to 2012, Jack’s annual salary increased [#permalink]  12 May 2019, 21:08
Thank you for the explanation.
My problem now is to understand this step:
Our base (always) is 100. So, our difference is 15.8 %
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Re: QOTD # 21 From 2011 to 2012, Jack’s annual salary increased [#permalink]  13 May 2019, 02:14
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Expert's post
Dear ARIJOSHI

the rule for percentage is that the base is always 100 from which you do have a percentage increase or decrease.

Now if the equation is r = 115 percent of k and the base is 100 (the rule) the difference is 15; 115-100=15

So the percent difference is 15 %

Hope this helps now.

For refence see our gmatclub math book page 15

Attachment:
GMAT Club Math Book v3 - Jan-2-2013.pdf [2.83 MiB]

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Re: QOTD # 21 From 2011 to 2012, Jack’s annual salary increased [#permalink]  19 May 2019, 11:16
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Quote:
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?

For this problem, make sure to plug in for the foundation variable to make the problem easier. Here, set they're equal salaries in 2012 = 100 each.

Then, use the calculator to solve for each of the salaries in 2011.

Jack 2011 : 100 = 1.1x = 90.91.

Arnie : 100 = .95x = 105.26

Finally, solve for the % change. (Difference = 14.35 / Original = 90.91) x 100 --> 15.79 rounded to 15.8% greater.
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Re: QOTD # 21 From 2011 to 2012, Jack’s annual salary increased   [#permalink] 19 May 2019, 11:16
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# QOTD # 21 From 2011 to 2012, Jack’s annual salary increased

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