A writer gets paid $10 per page, for the first 40 pages that she write

Question

A writer gets paid $10 per page, for the first 40 pages that she writes on a day. For every additional page that she writes on that day, she gets an extra $4 per page over the normal pay per page. She writes at least 35 pages in a single day. In a span of 3 consecutive days, she earned a total amount of $1500. What is the maximum number of pages that she wrote in a single day?

A. 40
B. 55
C. 65
D. 68
E. 80

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e-GMAT Question of the Week #35

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Official Answer

C

A. 40
B. 55
C. 65
D. 68
E. 80

e-GMAT     Question of the Week #35

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chetan2u · Answer

For max on one day, take minimum the other days, so 35 each day at the rate of 10 per page = 35*2*10=700..
On the third day 1500-700=800..
40 at the rate of 10 is 400$, so remaining 400 is at the rate of 10+4 or 14 per page... But 400 is not a multiple of 14..
So look for a multiple of 14 such that 14x=400-10y...

thus x has to be a multiple of 10 and therefore 14x=350...x=25..
Therefore the total on third day = 40+25=65..

Archit3110 · Answer

for day 1 & 2 : suppose writer has written 35 pages each on both days ; 35*2 = 70 pages and has earned ; 70 * 10 = 700 $
balance amount = 1500-700 ; 800 $
800 $ can be earned ; 40 pages * 10 $ each + 14 $ * no of additional pages

now if we see 800-400 = 400 $ amount which writer would have earned typing extra pages has to be a factor of 14 & 10 both since we have unit digit as 0 
so only nearest possible no is 25 ; 14* 25 = 350 
so it means on a single day she must have had written 40 + 25 = 65 pages in total... equal to 750 $
and on other days she must have written 40 pages , 35 pages amount to 750 $ total
IMO C 65 pages

EgmatQuantExpert · Answer

Solution 
  Given  
In this question, we are given that
 • A writer gets paid $10 per page, for the first 40 pages that she writes on a day.
• For every additional page that she writes on that day, she gets an extra $4 per page over the normal pay per page.
• She writes at least 35 pages in a single day.
• In a span of 3 consecutive days, she earned a total amount of $1500.

To Find  
From the given information, we need to determine
 • The maximum number of pages that the writer wrote in a single day

Approach & Working  
As we are trying to find the maximum number of pages that she wrote in a single day, we need to minimize the number of pages that she wrote on the other 2 days.

It is also given that the writer wrote at least 35 pages on a single day.
 • Hence, we can assume that the other 2 days she wrote 35 pages each day and earned (35 x 2 x $10) = $700 in total.
• Therefore, her earning on the day she writes maximum pages = ($1500 – $700) = $800

Now, for the first 40 pages, she is already earning ($10 x 40) = $400.
So, for the remaining pages she can earn = $800 – $400 = $400.

As in every extra page beyond 40 pages, she is earning ($10 + $4) = $14, then number of extra pages she wrote should be $400/14 = 28.57, which is not an integer!
It means, she must have written a few pages on the other 2 days.
 • If she wrote 1 page on the other 2 days, then on that day she wrote ($400 - $10)/$14 = 27.8, which is not an integer.
• If she wrote 2 pages on the other 2 days, then on that day she wrote ($400 - $20)/$14 = 27.1, which is not an integer.
• If she wrote 3 pages on the other 2 days, then on that day she wrote ($400 - $30)/$14 = 26.4, which is not an integer.
• If she wrote 4 pages on the other 2 days, then on that day she wrote ($400 - $40)/$14 = 25.7, which is not an integer.
• If she wrote 5 pages on the other 2 days, then on that day she wrote ($400 - $10)/$14 = 25, which is an integer.

Therefore, she must have written 25 extra pages on that day, and hence, the total number of pages that she wrote is 40 + 25 = 65

Hence, the correct answer choice is option C.

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Wadree · Answer

We gotta make maximum page on 1 of 3 days.... So other 2 days she wrote minimum page 35......
So those other 2 days she total earned = 35 × 2 × 10 = 700 .......
So other day she wrote..... 40 +   pages .....
So for 40 page she got = 40 × 10 = 400 ..... So far we made up = 700 + 400 = 1100 ..... but we still have to figure out how she got da rest 400 money..... 
So... For extra page after 40 page....she will get 14 dollar per page.... So lets divide 400 by 14 so we'll know how many extra pages she wrote..... 400 / 14 = 28.6 .... Actually 28 × 14 = 392 ..... So still 8 dollars left with no assigned day....
If we assume she wrote extra 28 pages on that maximum day.... Then 8 dollars will be left without any account.... And minimum per day wage is 10 dollars... So it wont be possible to assign 8 dollars to any other day......
So extra page cant be 28.... Same way..... For 27 extra page.... 22 dollars left which cant be assigned to any day....for 26 extra page..... 36 dollars left which cant be assigned to any day.... But for 25 extra page...... 50 dollars left which she might've earned writing 5 pages on other 2 minimum days...... 
So.... Maximum page she wrote on any day 40 + 25 = 65 page.......

Kinshook · Answer

A writer gets paid $10 per page, for the first 40 pages that she writes on a day. For every additional page that she writes on that day, she gets an extra $4 per page over the normal pay per page. She writes at least 35 pages in a single day. In a span of 3 consecutive days, she earned a total amount of $1500. What is the maximum number of pages that she wrote in a single day?

A. 40
B. 55
C. 65
D. 68
E. 80

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e-GMAT Question of the Week #35

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Official Answer

C

What is the maximum number of pages that she wrote in a single day?

Money earned for writing 35 pages in a single day = 35*$10 = $350

For maximum number of pages that she wrote in a single day, she should write maximum pages in a single day and 35 pages on other 2 days.

Money earned for writing 35 pages in 2 days = 2* $350 = $700

Remaining money earned on a single day = $1500 - $700 = $800

Let us image that she wrote x pages in a single day and y pages on other days where x is max and y is min. x & y are positive integers.

800 = 400 + 14(x-40) + 10y
400 = 14(x-40) + 10y
x-40 = (400-10y)/14

x-40 = 350/14 = 25
x = 40 + 25 = 65

IMO C

A writer gets paid $10 per page, for the first 40 pages that she write

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GMAT Problem Solving (PS) Questions

A writer gets paid $10 per page, for the first 40 pages that she write

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