Computer operator question

[wayne0426]

A computer operator made x typing mistakes in one hour, where x is a positive integer greater than 30. If she corrects C of her mistakes in the next m minutes, where C < x, how many mistakes per hour has she made in the time she has worked?

A) 60(x-C) / 60+ m

B) x - C / m

C) 60(x-m) / C

D) m / 60(x-C)

E) 60(x-C)/ m

[theCEO]

A computer operator made x typing mistakes in one hour, where x is a positive integer greater than 30. If she corrects C of her mistakes in the next m minutes, where C < x, how many mistakes per hour has she made in the time she has worked?

A) 60(x-C) / 60+ m

B) x - C / m

C) 60(x-m) / C

D) m / 60(x-C)

E) 60(x-C)/ m

In 1hour, x mistakes are made
In (60+m)/60 hour, x-c mistakes are made

mistakes per hour= (x-c)/[(60+m)/60)
mistakes per hour= 60(x-c)/60+m

ans = a

[GMATGuruNY]

A computer operator made x typing mistakes in one hour, where x is a positive integer greater than 30. If she corrects C of her mistakes in the next m minutes, where C < x, how many mistakes per hour has she made in the time she has worked?

A) 60(x-C) / 60+ m

B) x - C / m

C) 60(x-m) / C

D) m / 60(x-C)

E) 60(x-C)/ m

Let x=10, implying that 10 mistakes are made in the first hour.
Let C=0 and m=60 minutes, implying that 0 mistakes are corrected in the next hour.
Mistakes per hour = (total mistakes)/(total time) = (10 mistakes)/(2 hours) = 5. This is our target.

Now plug x=10, C=0 and m=60 into the answer choices to see which yields our target of 5.
Only A works:
60(x-C) / 60+ m = 60(10-0) / (60+60) = 5.

The correct answer is A.

[wayne0426]

thank you very much for your help!

[Matt@VeritasPrep]

Just to leave an algebraic explanation for posterity:

Our operator mworked for 1 + (m/60) hours.

In that time, she made x mistakes, then corrected C of them, leaving her with (x - C) total mistakes.

This gives us

Mistakes/Hours = (x - C) / (1 + (m/60))

= (x - C) / ((60 + m)/60)

= 60*(x - C) / (60 + m)

[susheelh]

Hello @GMATGuruNY,

Thanks a ton for this approach. Need a small clarification though. The question says that x is greater than 30. Is this just a distraction? I see that in any case, we get the same answer.

Thanks in advance!

A computer operator made x typing mistakes in one hour, where x is a positive integer greater than 30. If she corrects C of her mistakes in the next m minutes, where C < x, how many mistakes per hour has she made in the time she has worked?

A) 60(x-C) / 60+ m

B) x - C / m

C) 60(x-m) / C

D) m / 60(x-C)

E) 60(x-C)/ m

Let x=10, implying that 10 mistakes are made in the first hour.
Let C=0 and m=60 minutes, implying that 0 mistakes are corrected in the next hour.
Mistakes per hour = (total mistakes)/(total time) = (10 mistakes)/(2 hours) = 5. This is our target.

Now plug x=10, C=0 and m=60 into the answer choices to see which yields our target of 5.
Only A works:
60(x-C) / 60+ m = 60(10-0) / (60+60) = 5.

The correct answer is A.

[GMATGuruNY]

Hello @GMATGuruNY,

Thanks a ton for this approach. Need a small clarification though. The question says that x is greater than 30. Is this just a distraction? I see that in any case, we get the same answer.

Thanks in advance!

As my solution above illustrates, the constraint in red can be ignored.

[Scott@TargetTestPrep]

A computer operator made x typing mistakes in one hour, where x is a positive integer greater than 30. If she corrects C of her mistakes in the next m minutes, where C < x, how many mistakes per hour has she made in the time she has worked?

A) 60(x-C) / 60+ m

B) x - C / m

C) 60(x-m) / C

D) m / 60(x-C)

E) 60(x-C)/ m

Since she corrected C mistakes, the number of her mistakes after correction is x - C and the time spent in total, typing and correcting mistakes, is 1 hour and m minutes, or 1 + m/60 hours. Thus, the number of mistakes she has made per hour is:

(x - C)/(1 + m/60) = 60(x - C)/(60 + m)

Answer: A