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

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.

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:

GMAT assassins aren't born, they're made,
Rich

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

Please, kudos

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!

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.

GMAT assassins aren't born, they're made,
Rich

arshak90
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

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.

Here is the solution -

According to question the following things are certain -
1. Before 3 PM the typing speed is 20 words per min
2. After 3 PM the typing speed increases by 1 word per min with every 2 min gap or delay
3. There are total 1950 words to write before 5 PM
4. Whenever Rachel starts writing the speed of typing will be constant

So we can certainly say that after 3 PM the typing speed will be (if she starts at)
At 3.00 PM - Typing speed will be 20 per min
At 3.02 PM - Typing speed will be 21 per min
At 3.04 PM - Typing speed will be 22 per min & so on ..........

From above we can say that every 2 min there is an increase of 1 word. So the formula will be = 20 + (min after 3 PM at which Rachel starts)/2. i.e. 20+T/2

This means that Rachel typing speed will increase by 1 word with every 2 min passing time. So if we look at the answer options we can find out that -
A. 2:50 pm - Cannot be the answer as the min typing speed is 20 word per min
B. 3:23 pm - means 97 min to 5 PM. So Cannot be the answer as at 3:23 pm typing speed will be 20 + 11 = 31 and if we divide 1950 by 31 the answer will be 62 which is not equals to 97 min
C. 3:30 pm - means 90 min to 5 PM. So Cannot be the answer as at 3:30 pm typing speed will be 20 + 15 = 35 and if we divide 1950 by 31 the answer will be 55 which is not equals to 90 min
D. 4:30 pm - means 30 min to 5 PM. So it is our answer as at 4:30 pm the typing speed will be 20 + 45 = 65 and if we divide 1950 by 65 the answer will be 30 which is equals to 30 min
E. 4:42 pm - means 18 min to 5 PM. So Cannot be the answer as at 4:42 pm typing speed will be 20 + 51 = 71 and if we divide 1950 by 71 the answer will be 27 which is not equals to 18 min

So Option D is answer

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.

Answer: D