In 1980 Johns salary was $15,000 a year and Dons salary

Question

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?

Bunuel · Accepted Answer

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.

ravitejar · Answer

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:

If you like my explanation give me +1 kudos.

EMPOWERgmatRichC · Answer

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.

GMAT assassins aren't born, they're made,
Rich

laddaboy · Answer

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.

Shrikirti · Answer

15000 + 2450x = 20000 + 2000x

The approximate x value is 11.something. In this year it will be equal so round off to 12 and 1980 + 12 years is  1992.

GmatPoint · Answer

Given that in 1980,
John's salary = $15,000
Don's salary = $20,000

Let us consider that John's salary will be more than that of Don after x years.
Since John's salary is increasing $2,450 per year, after x years,
John's salary = $(15,000 + 2,450x)

Similarly, after x years,
Don's salary = $(20,000 + 2,000x)

Thus, if John's salary is greater than that of Don,

$15,000 + $2,450x > $20,000 + $2,000x
$450x > $5,000

Thus, x > 5,000/450
or, x > 11.11.

Thus in the 12th year after 1980, John's salary will be more than that of Don.
Or, in 1992, John will be earning more than Don.

achloes · Answer

An efficient approach is to backsolve using the years in the answer choices.

Setting up an equation for John and Don's future salaries will let us know when John's salary exceeds Don's.

John's salary = Don's salary 
$2450 (future year - 1980) = $5000 + $2000 (future year - 1980)

In 1992.. 
$2450 (12 years) = $5000 + $2000 (12 years)

John's salary is $29,400 while Don's salary, along with the $5000 (salary in excess of John's salary), works out to $29,000

Therefore, D is the correct answer

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

In 1980 Johns salary was $15,000 a year and Dons salary

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

In 1980 Johns salary was $15,000 a year and Dons salary

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards