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

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Sun Sep 08, 2019 6:47 pm

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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

OA D

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Sun Sep 08, 2019 6:47 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

by Jay@ManhattanReview » Sun Sep 08, 2019 9:01 pm

BTGmoderatorDC 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

OA D

Source: Veritas Prep

Given that Rachel wishes to start by at least 2 hours before the deadline, she would have 2*60 = 120 minutes to type. Given that for every two minutes beyond 3 pm that she waits before starting, her constant typing speed will increase by one word per minute, let's assume that she starts after n 2-minutes intervals, i.e. she starts type 2n minutes after 3 pm; thus, she types 1950 words in (120 - 2n) minutes. The speed at (120 - 2n) minutes before the finish of task would be (20 + n) words per minute.

Thus, the total number of words types = (120 - 2n)(20 + n) = 1950 => n = 45

Thus, Rachel can start by the latest (120 - 2n) = (120 - 2*45) = 120 - 90 = 30 minutes before 5 pm, or by 4:30 pm.

The correct answer: D

Hope this helps!

-Jay
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swerve: Legendary Member; Posts: 2548; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Mon Sep 09, 2019 2:46 am

BTGmoderatorDC 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

OA D

Source: Veritas Prep

Let $m=$ minimum minutes before 5 pm needed by Rachel
$m\left(20+\frac{1}{2}\cdot (120-m)\right)=1950$
$m^2-160m+3900=0$
$(m-30)(m-130)=0$
$m=30$ minutes
5 pm - 30 minutes $=$ 4:30 pm

Hence, __D__

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8157; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Sep 12, 2019 10:21 am

BTGmoderatorDC 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

OA D

Source: Veritas Prep

Let's analyze the answer choices (in reverse order).

If Rachel starts at 4:42 pm (and notice that 4:42 pm is 102 minutes after 3 pm), she has to type 20 + 102/2 = 20 + 51 = 71 words per minute (wpm). Since she has only 18 minutes left until 5 pm, she can type 18 x 71 = 1278 words, which means she will miss the deadline of 5 pm. If Rachel starts at 4:30 pm (and notice that 4:30 pm is 90 minutes after 3 pm), she has to type 20 + 90/2 = 20 + 45 = 65 words per minute (wpm). Since she has only 30 minutes left until 5 pm, she can type 30 x 65 = 1950 words, which means she will just make the deadline of 5 pm.

Answer: D

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