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Rachel needs to type up her 1950-word paper by its 5 pm deadline. If

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Rachel needs to type up her 1950-word paper by its 5 pm deadline. If  [#permalink]

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New post 21 Apr 2017, 07:44
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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

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Re: Rachel needs to type up her 1950-word paper by its 5 pm deadline. If  [#permalink]

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New post 21 Apr 2017, 10:40
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Her constant typing speed at 3PM = 20 words/minute

For every two minute delay after 3 PM constant typing speed increased by 1 word

So if she starts at 3:02 PM her speed will be 21 words/minute

So if she starts at 3:22 PM her speed will be 31 words/minute

So if she starts at 3:30 PM her speed will be 35 words/minute

So if she starts at 4:00 PM her speed will be 50 words/minute

So if she starts at 4:30 PM her speed will be 65 words/minute

So if she starts at 4:42 PM her speed will be 70 words/minute

Going by options,

Option E: if she starts at 4:42 PM with a constant speed of 70 words/minute, she will have 18 minutes to complete. So 1950/70 should be less than equal to 18. But 1950/70 comes to 27.9 minutes. So Option E is ruled out.

Option D: if she starts at 4:30 PM with a constant speed of 65 words/minute, she will have 30 minutes to complete. So 1950/65 should be less than equal to 30. 1950/65 comes to 30 minutes. So Option D is the correct choice.

Answer D. 4:30 pm
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Rachel needs to type up her 1950-word paper by its 5 pm deadline. If  [#permalink]

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New post 21 Apr 2017, 16:24
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Bunuel 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


let m=minimum minutes before 5pm needed by Rachel
m[20+1/2*(120-m)]=1950
m^2-160m+3900=0
(m-30)(m-130)=0
m=30 minutes
5pm-30 minutes=4:30pm
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Rachel needs to type up her 1950-word paper by its 5 pm deadline. If  [#permalink]

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New post 06 May 2017, 18:16
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Bunuel 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


OFFICIAL EXPLANATION


Back-solving is a good option for this problem. It is best to begin by checking the last time and then work backwards, since we want the latest time at which Rachel can start.

Starting at 4:42 pm would give Rachel 18 minutes to write at a rate of \(20+\frac{102}{2}=71\) words per minute. This is approximately 20∗70=1400 words, which is well short of the 1950 necessary to complete the assignment.

Starting at 4:30 pm would give Rachel 30 minutes to write at a rate of \(20+\frac{90}{2}=65\) words per minute. This is 30∗65=1950 words. Perfect. This must be the correct answer. D.

Could someone help to explain the rate in this problem? constant typing speed will increase by one word per minute.
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Re: Rachel needs to type up her 1950-word paper by its 5 pm deadline. If  [#permalink]

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New post 12 Jan 2018, 14:20
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Hi All,

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:

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Rachel needs to type up her 1950-word paper by its 5 pm deadline. If  [#permalink]

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New post 13 Jan 2018, 02:18
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Hi everyone,

In my opinion, to make an equation is the easiest way to solve this problem.
x - additional speed for every 2 minutes, after 3 pm
(120-2x) - time left for writing
(20+x) - speed
The equation is the following:
(120-2x)(20+x)=1950
x^2-40x+450=0
x=45
Meaning that she can start writing 45*2=90 min after 3pm, or, in other words, 4:30pm.
ANS: D

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Re: Rachel needs to type up her 1950-word paper by its 5 pm deadline. If  [#permalink]

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New post 06 Jun 2019, 18:02
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Bunuel 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


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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Re: Rachel needs to type up her 1950-word paper by its 5 pm deadline. If  [#permalink]

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New post 28 Jun 2019, 19:39
ScottTargetTestPrep wrote:
Bunuel 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


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


ScottTargetTestPrep EMPOWERgmatRichC have you assumed that while writing her speed remains constant? What I understood from the question stem was that her speed increases by 1 word / min. every 2 mins. after 3 PM, so let's say she's started writing at 4:30 PM, assuming her speed would be some 20 + a, won't her speed increase to 20 + a + 1 at 4:32 PM and then 20 + a + 2 at 4:34 PM nd 20 + a + 3 at 4:36 PM and so on?

Please help!
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Re: Rachel needs to type up her 1950-word paper by its 5 pm deadline. If  [#permalink]

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New post 29 Jun 2019, 15:07
Hi RJ7X0DefiningMyX,

The prompt refers to her "constant typing speed" once she STARTS typing. There's nothing in the wording that describes how she would get 'faster' over time (as she keeps typing), so that's a misinterpretation on your part.

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Rachel needs to type up her 1950-word paper by its 5 pm deadline. If  [#permalink]

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New post Updated on: 04 Jul 2019, 01:23
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This approach is the quickest and simplest and one that I too adopted. However, although your answer is the right one, there is a mistake in your calculations: The equation [(120-2x)(20+x)=1950] does NOT simplify to: [x^2 - 40x +450 = 0].

Following is the detailed breakdown of the calculations:

(120-2x)(20+x)=1950....> 2400+120x-40x-2x^2=1950...> 2x^2-80x-450=0...> x^2-40x-225=0...> x^2-45x+5x-225...>
x(x-45)+5(x-45)=0...> (x-45)(x+5)=0...> x=45
Therefore, the latest that Rachel can start is 90(45*2) minutes after 3 pm i.e. at 4:30 pm. ANS: D

Originally posted by effatara on 01 Jul 2019, 23:30.
Last edited by effatara on 04 Jul 2019, 01:23, edited 1 time in total.
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Re: Rachel needs to type up her 1950-word paper by its 5 pm deadline. If  [#permalink]

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New post 02 Jul 2019, 18:45
RJ7X0DefiningMyX wrote:
ScottTargetTestPrep wrote:
Bunuel 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


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


ScottTargetTestPrep EMPOWERgmatRichC have you assumed that while writing her speed remains constant? What I understood from the question stem was that her speed increases by 1 word / min. every 2 mins. after 3 PM, so let's say she's started writing at 4:30 PM, assuming her speed would be some 20 + a, won't her speed increase to 20 + a + 1 at 4:32 PM and then 20 + a + 2 at 4:34 PM nd 20 + a + 3 at 4:36 PM and so on?

Please help!


Actually, according to the question stem, Rachel’s typing speed does not increase every minute; that’s the reason the question is emphasizing that her typing speed is constant. Depending on how much time she has until the deadline, she determines a typing speed and types at that constant speed until she finishes. That’s why we take her writing speed to be constant once she begins typing.
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Re: Rachel needs to type up her 1950-word paper by its 5 pm deadline. If   [#permalink] 02 Jul 2019, 18:45
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