Last year John earned $m$ dollars at company $X$ and was promised an $n$-percent raise for this year. If John is

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Sun May 31, 2020 12:40 pm

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Last year John earned $m$ dollars at company $X$ and was promised an $n$-percent raise for this year. If John is paid the promised amount and a $10,000 bonus at the end of this year, by what percent has his total salary(including his bonus) increased this year over last in terms of $n$ and $m?$

a) $\dfrac{mn + 10000}{m} \%$
b) $\dfrac{n + 10000}{m} \%$
c) $\dfrac{mn + 100,000}{100m} \%$
d) $\dfrac{mn + 1,000,000}{100m} \%$
e) $\dfrac{mn + 1,000,000}{m} \%$

[spoiler]OA=E[/spoiler]

Source: Veritas Prep

Source: Beat The GMAT — Problem Solving | Sun May 31, 2020 12:40 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

Re: Last year John earned $m$ dollars at company $X$ and was promised an $n$-percent raise for this year. If John

by Jay@ManhattanReview » Mon Jun 01, 2020 6:43 am

M7MBA wrote: ↑
Sun May 31, 2020 12:40 pm
Last year John earned $m$ dollars at company $X$ and was promised an $n$-percent raise for this year. If John is paid the promised amount and a $10,000 bonus at the end of this year, by what percent has his total salary(including his bonus) increased this year over last in terms of $n$ and $m?$

a) $\dfrac{mn + 10000}{m} \%$
b) $\dfrac{n + 10000}{m} \%$
c) $\dfrac{mn + 100,000}{100m} \%$
d) $\dfrac{mn + 1,000,000}{100m} \%$
e) $\dfrac{mn + 1,000,000}{m} \%$

[spoiler]OA=E[/spoiler]

Source: Veritas Prep

Raise = n% of m = $ nm/100

Total increment = nm/100 + 10,000

Total increment of his salary = (nm/100 + 10,000)/m]*100% = (nm + 1,000,000)/m %

The correct answer: E

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: Last year John earned $m$ dollars at company $X$ and was promised an $n$-percent raise for this year. If John

by Scott@TargetTestPrep » Fri Jun 05, 2020 11:00 am

M7MBA wrote: ↑
Sun May 31, 2020 12:40 pm
Last year John earned $m$ dollars at company $X$ and was promised an $n$-percent raise for this year. If John is paid the promised amount and a $10,000 bonus at the end of this year, by what percent has his total salary(including his bonus) increased this year over last in terms of $n$ and $m?$

a) $\dfrac{mn + 10000}{m} \%$
b) $\dfrac{n + 10000}{m} \%$
c) $\dfrac{mn + 100,000}{100m} \%$
d) $\dfrac{mn + 1,000,000}{100m} \%$
e) $\dfrac{mn + 1,000,000}{m} \%$

[spoiler]OA=E[/spoiler]

Solution:

We can express n percent as n/100. Thus, John’s salary this year is his previous salary of m plus his raise of mn/100 plus his bonus of 10,000. Thus, his income this year is m + mn/100 + 10,000 dollars. Since he earned m dollars last year, the overall increase in his salary this year is mn/100 + 10,000. In terms of percent increase, it is:

(mn/100 + 10,000)/m x 100 = (mn + 1,000,000)/m

Answer: E

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