In order to complete a reading assignment on time, Terry planned to re

We can solve this problem in a similar manner to solving a work problem, and we can use a table to organize our information. We can fill in what she was “supposed” to do and what she “did” do.

We are given that her initial plan was to read 90 pages per day for “T” days. We can multiply, getting 90T for the total work that was supposed to be done for the entire reading assignment.

We are next told that she actually started out reading 75 pages per day until she had 6 days left to finish the project. Since T represents the total number of days we can say she read 75 pages per day for (T–6) days. Finally, when we multiply, we see that her work done on the T–6 days was 75T–450.



To finish this problem we need to set up one final equation. We are told that she must read 690 pages in the last 6 days to complete the assignment. From the chart we see that 90T denotes a completed assignment. Thus we can say:

75T – 450 + 690 = 90T

75T + 240 = 90T

15T = 240

T = 16

Answer B.

Her original goal was to read 90pages per day.
Thus in 6 days she would have read 90*6= 540 pages.
Since she was left with 690 pages means she was 150pages short of target.
Since the difference between 90 pages and 75 pages is 15 pages.
The number of days would be 150/15 = 10 days
Total number of days to complete assignment 10 + 6 days = 16days.

Here are my 50 cents
We know that Distance = Time*Speed, thus in our case Distance is the assignment to be completed and T are those days and S is peed, the number of pages per day. From here we get:
D=90*X - according to the plan, assignment to be completed on time reading 90 pages per day for next X days. But, Terry's plans changed so she read as follow:
75 pages for first Y days and 690 pages for last 6 days, we get these equations:
75*Y+690=90*X
X-Y=6 --------->>X planned number of days, Y - actually used reading 75 pages per day and 6 leftover days used to complete a lump 690 pages
From above we find that X=Y+6 and 75Y+690=90Y+540 or 15Y=150 --->>>>> Y=10, hence X=16 (B)
Please, correct me if I went awry.

Here's my attemp..

let say she has x days to complete the task above..

1st Case:

Rate =75
Time = x-6 days
Work = 75(x-6) = 75-450

2nd Case

Rate = ?
Time = 6 days
Work = 690

so rate = 115pages/day

=> total work done => 75x-450+690 =90x

x=16

Well, How about plugging in.

Start off with C=25 days.
We know that for 6 days its 690 pgs. So 25-6=19 days left
Now we have to multiply 75 and 19=1425
Now add 1425 and 690= 2115 pgs
But the planned rate is 90 pgs. Multi ply 90 and 25 we get 2250 pgs.
This is more than 2115. So we need to plugin a lesser number.
Plugin ans choice b and get the answer.

Formula for Avg= Total/no. of units
=> Total= Avg* no. of units

Given,
Planned average reading=90 pages/day
=> Planned total pages for d days=90*d (in pages)

Actual total pages = 75pages/day*(d-6) days +690 pages

equating both since no. of pages are the same :
90d=75(d-6) + 690
d=16

Answer B

We can solve this one with weighted average method (see MGMAT)
X*(-15) + 6*(25) = 0
X = 10 --> X+6 = 16 (B)
Let be the first X days at a rate of 75 Pages - It's below planed average of 90 (-15), the last 6 days = 690/6 = 115 --> It's above the average of 90 (+25)

She loses 15 Pages / Day

Assume she read 75 pages for the last 6 days as well.

Therefore, she would be short of 240 Pages to finish.

Since she loses 15 pages / day,

The Calculation would be:

15 Pages/ Day * No Of Days = 240

No of Days = 240/15

No of Days = 16

There is really one variable in this question: other unknowns can be derived from the number of days in total Terry has to complete the reading assignment. So let x be that number of days. We have:

90x = Total number of pages = 75(x-6) + 690
So 15x = 240
x = 16

QED.

"In order to complete a reading assignment on time, Terry planned to read 90 pages per day. "
Reading 90 pages/day would have completed the assignment.

"However, she read only 75 pages per day at first,"
She read 15 fewer pages each day till ...

leaving 690 pages to be read during the last 6 days before the assignment was to be completed.
690 pages were left for 6 days. Actually as per plan only 90*6 = 540 pages should have been left for 6 days.
Why were there 690 - 540 = 150 extra pages left to read? Because she read 15 fewer pages each day. To gather 150 extra pages left unread, she must have read 15 fewer pages for 10 days.

"How many days in all did Terry have to complete the assignment on time?"
She has already read for 10 days and has 6 more to go so she had total 16 days.

Answer (B)

Let's start with a word equation

We can write: (total number of pages to be read at INTENDED rate of 90 pages/day) = (total number of pages ACTUALLY read at 75 pages/day) + 690 more pages

Let x = number of days to complete reading assignment at 90 pages per day
So, x - 6 = number of days reading at 75 pages per day (since Terry spent the last 6 days reading 690 pages)

At a rate of 90 pages/day, 90x = number of pages that COULD be read in x days
At a rate of 75 pages/day, 75(x - 6) = number of pages ACTUALLY read in x-6 days

We get: 90x = 75(x - 6) + 690
Expand to get: 90x = 75x - 450 + 690
Simplify to get: 90x = 75x + 240
We get: 15x = 240
Solve: x = 240/15 = 16

Answer: B

Cheers,
Brent

VeritasKarishma, I came up with a similar approach is it correct.

nick 1816, is this approach logical in your opinion ?

If we visualize on a graph 90 is the median and 75 and 115 opp. spectrum.

So, the excess 25 pages, over and above 90 pages (115 -90) for 6 days compensates for 15 days less read for certain days.

Can we derive a formula 15D=25*6, where D is the first days she read 75 pages.
Hence, D = 10


Thanks

Yes, correct. Since she is left with 25*6 = 150 excess because she was reading 15 fewer pages every day, she read those fewer pages for 10 days to gather 150.

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Hi All,

We’re told that Terry originally planned to read 90 pages/day to complete a particular reading assignment. However, she was only able to read 75 pages/day at first (for a certain number of days), which left her 690 pages that had to be read in the last 6 days of that original timeframe. We’re asked for the TOTAL number of days needed to complete all of the reading.

The Arithmetic that this question is based on can be approached in a number of different ways – and you can actually use a ‘comparison’ to get to the final answer fairly quickly.

Since the original plan was to read 90 pages/day, the last 6 days of reading was supposed to be (6)(90) = 540 pages. Terry had to actually read 690 pages though – which is 690 – 540 = 150 more pages than she had originally planned to read during those final days.

The difference between the original rate (re: 90 pages/day) and the amount she actually read early-on (75 pages/day) is 90 – 75 = 15 pages/day. This is interesting since she needed to make up 150 pages at the end (and 150 is 10 times 15). This means that she was reading at that slower rate for the first 10 days of reading – and she had to make up the amount that she ‘fell behind’ during the final 6 days.

That’s 10 + 6 = 16 total days of reading.

Final Answer:

GMAT Assassins aren’t born, they’re made,
Rich

Great question!

let me present my approach to solving this question.

She is required to read 90 pages per day in such a way as to complete the assessment in the given time.

However, she read only 75 pages per day at first

This means that for the last few days she has to cover extra reading-related work in addition to her current rate of work, which is 75 pages per day.


Now, for the remaining days, she will do both her current rate work and her accumulated work that she missed from day one. (15 pages per day)

Our target is to calculate the extra accumulated work that she missed from day one.

She has 690 pages in the last 6 days.
let's divide this into two parts.

1. 75 pages * 6 days = 450 pages

(This mean that she missed reading 240 pages from day one at the rate of 15 pages per day)

2. Therefore, 240/15 - 16 days

Could someone tell me if the following approach is valid? I got the answer via plugging in, but if there are any fallacies in my approach please do point them out.

I decided to plug in the answers and try it out. If she planned to read 90 pages a day, that would mean that would mean that the total number of pages should be cleanly divisible by 90.
Second, the difference between the total pages and the pages left, i.e. the pages she read, should be divisible by 75(it has been given that she at first read 75 pages/day)

Plugging in 15 does not work.
Plugging in 16 gives us 16*90 = 1440 total pages she wanted to read in 16 days.
Subtracting 690, that is, the number of pages left from 1440 gives us the number of pages she read in the first how-many-ever days, i.e. 1440-690 = 750.

If she read 75 pages per day, the number we got above should be divisible by 75, and 750 is divisible by 75!

Voila! She had 16 days to complete her assignment.