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Rachel needs to type up her 1950-word paper by its 5 pm dead

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by hazelnut01 » Sat May 06, 2017 4:02 pm
Rachel needs to type up her 1950-word paper by its 5 pm deadline. If she starts at least two hours in advance, her typing speed will be a constant 20 words per minute, but for every two minutes beyond 3 pm that she waits before starting, her constant typing speed will increase by one word per minute.

What is the latest time at which Rachel can begin typing in order to finish her paper by the deadline?

(A)2:50 pm
(B)3:23 pm
(C)3:30 pm
(D)4:30 pm
(E)4:42 pm

Source : Veritas Prep
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by [email protected] » Sat May 06, 2017 5:41 pm
Hi ziyuenlau,

This question can be solved by TESTing THE ANSWERS.

This is essentially a rate question, but the rate (and the time spent at that rate) changes depending on what time Rachel begins typing.

Based on the information in the prompt, we know that if Rachel begins typing at 3pm, then she can type for up to 2 hours (re: 120 minutes) at 20 words/minute. Thus, she could type (20)(120) = 2400 total words during that time... and that would be enough time to complete the 1950 word paper. For every TWO minutes past 3pm that she gets started, her typing speed will increase by 1 word/minute (BUT keep in mind that her available typing time will decrease by 2 minutes).

For example, if she begins at 3:02pm, then she can type of up to 118 minutes at 21 words per minute, which would total (21)(118) = 2478 total words.

We're asked for the LATEST that she could begin typing and still complete the paper on time.

Let's TEST Answer E: 4:42pm --> 18 minutes at 71 words/minute = 1,278 total words. That is NOT enough. Eliminate Answer E.

Let's TEST Answer D: 4:30pm --> 30 minutes at 65 words/minute = 1,950 total words. That IS exactly enough, so this must be the answer.

Final Answer: D

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Rich
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by Jay@ManhattanReview » Sat May 06, 2017 10:03 pm
ziyuenlau wrote:Rachel needs to type up her 1950-word paper by its 5 pm deadline. If she starts at least two hours in advance, her typing speed will be a constant 20 words per minute, but for every two minutes beyond 3 pm that she waits before starting, her constant typing speed will increase by one word per minute.

What is the latest time at which Rachel can begin typing in order to finish her paper by the deadline?

(A)2:50 pm
(B)3:23 pm
(C)3:30 pm
(D)4:30 pm
(E)4:42 pm

Source : Veritas Prep
Great solution by Rich.

Here is the Algebraic route.

Say Rachel starts typing 2x minutes after 3:00 pm and finishes by 5:00 pm.

Thus, the total time Rachel typed = (120 - 2x) minutes

Typing speed during (120 - 2x) minutes = (20 + x) words per minute

Thus, the total number of words = (120 - 2x)*(20 + x) = 1950

(120 - 2x)*(20 + x) = 1950

2400 - 40x + 120x - 2x^2 = 1950

x^2 -40x - 225 = 0

x^2 -45x +5x - 225 = 0

=> x(x-45) + 5(x-45) = 0

=> x = 45 or -5

=> x = 45 as time cannot be negative.

Thus, Rachel can start typing after 2*45 = 90 minutes after 3:00 pm ie 4:30 pm.

The correct answer: D

Hope this helps!

Relevant book: Manhattan Review GMAT Math Essentials Guide

-Jay
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