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

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Joined: 04 Jan 2015
Posts: 2594
Question of the week - 35 (A writer gets paid \$10 per page, for .....)  [#permalink]

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08 Feb 2019, 01:17
00:00

Difficulty:

85% (hard)

Question Stats:

39% (03:29) correct 61% (02:58) wrong based on 33 sessions

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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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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

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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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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Joined: 04 Jan 2015
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Question of the week - 35 (A writer gets paid \$10 per page, for .....)  [#permalink]

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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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