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In 1980 John’s salary was $15,000 a year and Don’s salary

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Status: May The Force Be With Me (D-DAY 15 May 2012)
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In 1980 John’s salary was $15,000 a year and Don’s salary [#permalink]

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In 1980 John’s salary was $15,000 a year and Don’s salary was $20,000 a year. If every year thereafter. John receives a raise of $2,450 and Don receives a raise of $2,000, the first year in which John’s salary will be more than Don’s salary is

A. 1987
B. 1988
C. 1991
D. 1992
E. 2000

My approach was to divide the difference in salary by the difference of the increment, but I think this rudimentary approach is incorrect. Anyone has any idea how to solve this?
[Reveal] Spoiler: OA

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Re: Salary Issues [#permalink]

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New post 21 Apr 2012, 21:39
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boomtangboy wrote:
10. In 1980 John’s salary was $15,000 a year and Don’s salary was $20,000 a year. If every year thereafter. John receives a raise of $2,450 and Don receives a raise of $2,000, the first year in which John’s salary will be more than Don’s salary is
(A) 1987
(B) 1988
(C) 1991
(D) 1992
(E) 2000

My approach was to divide the difference in salary by the difference of the increment, but I think this rudimentary approach is incorrect. Anyone has any idea how to solve this?


Actually the way you mention is the way to solve this question.

Difference in salaries is 20,000-15,000=$5,000 and relative increase per year is 2,450-2,000=$450 --> $5,000/$450=11.11, so 12 years are needed John’s salary to be more than Don’s salary.

Or: 15,000+2,450n>20,000+2000n --> n>11.11, so n=12.

The first year in which John’s salary will be more than Don’s salary is 1980+12=1992.

Answer: D.
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Re: In 1980 John’s salary was $15,000 a year and Don’s salary [#permalink]

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New post 22 Apr 2012, 00:32
used plugging in the answers method to arrive at the answer.

Thanks,
Shreya

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Re: In 1980 John’s salary was $15,000 a year and Don’s salary [#permalink]

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we can easily solve without any equations

As the base salary of don was 20000 and john's base salary was 15000 then the difference is 5000 and the john salary is increased by 2450 and don's salary is increased by 2000, so the difference is 450 that means john can earn 450 more than don so every year and the difference between john's and don's salary is reduced by 450 then after 12 years john's salary would exceed don's salary, 5000(the difference between john's base salary and don's base salary ) and 450(difference between john's raise don's raise ) so we get

5000-(450*12)=5000-5400=-400 so in 12th year john's salary would cross or exceed don's salary .

our answer option is d:


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Re: In 1980 John’s salary was $15,000 a year and Don’s salary [#permalink]

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Hi All,

This question is a variation on the "Chase Down" prompts (e.g. A car chasing another car or a runner chasing another runner) that are in the same rare category of questions as Combined Rates. The method for solving is also the same.

Here, we need the "head start" - in this case, the "head start" is the difference in salaries in 1980 --> $5,000

Next, we need to know how much "catch up" occurs each time period - here, it's extra money earned per year by John over Don --> $450/year

Then, it's just a rate...

($450/year)(X years) = $5,000
X = a little MORE than 11 years.

In this prompt, we have to be careful NOT to round down, as 11 years exactly would be $4,950, which is NOT what we're after.

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Re: In 1980 John’s salary was $15,000 a year and Don’s salary [#permalink]

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New post 01 Dec 2017, 20:30
The difference between Don's and John's during 1980 is $5000. And we are given their salaries increase constantly, with John's have an additional $450 increase. So in 1 year the difference between there salaries would be $5000-$450 and in 2 years it will be $5000-$900 so i.e for x years it will be $5000- ($450*x). Now we can say John's salary > Don's only when $5000-($450*x) is less than 0.
i.e ($5000-($450*x)) < 0 solving we get x > 11.11 Hence it will take 12 years for John to have a better salary than Don.
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Re: In 1980 John’s salary was $15,000 a year and Don’s salary   [#permalink] 01 Dec 2017, 20:30
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