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Question of the week - 35 (A writer gets paid $10 per page, for .....)

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Question of the week - 35 (A writer gets paid $10 per page, for .....)  [#permalink]

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New post 08 Feb 2019, 01:17
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Question Stats:

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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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Re: Question of the week - 35 (A writer gets paid $10 per page, for .....)  [#permalink]

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New post 08 Feb 2019, 01:42
EgmatQuantExpert wrote:
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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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..
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Re: Question of the week - 35 (A writer gets paid $10 per page, for .....)  [#permalink]

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New post 08 Feb 2019, 03:37
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 wrote:
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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Question of the week - 35 (A writer gets paid $10 per page, for .....)  [#permalink]

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New post 11 Feb 2019, 22:57

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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Question of the week - 35 (A writer gets paid $10 per page, for .....)   [#permalink] 11 Feb 2019, 22:57
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