Problem Solving

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: D

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

AAPL wrote:Veritas Prep

Sumanta 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 Sumanta 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

Since the problem asks for the latest time she can begin typing and still meet the deadline of 5 pm, let's check the answer choices in reverse order. That is, let's begin with choice E (4:42 pm). Since 4:42 pm is 1 hour and 42 minutes, or 102 minutes, past 3 pm, and there are 102/2 = 51 two-minute intervals between 3 pm and 4:42 pm (inclusive), her speed is 20 + 51 = 71 wpm (words per minute) if she starts at 4:42 pm. Since she has 18 minutes until the deadline, she can type 71 x 18 = 1,278 words. However, this is fewer than the 1950 words she has to type.

So let's try choice D (4:30 pm) now. Since 4:30 pm is 1 hour and 30 minutes or 90 minutes past 3 pm, and there are 90/2 = 45 two-minute intervals between 3 pm and 4:30 pm (inclusive), her speed is 20 + 45 = 65 wpm if she starts at 4:30 pm. Since she has 30 minutes until the deadline, she can type 65 x 30 = 1,950 words. This is exactly the number of words she needs to type. So choice D is the correct answer.

Answer: D