In order to complete a reading assignment on time, Terry planned to read 90 pages per day.However,she read only 75 pages per day at first, leaving 690 pages to be read during the last 6 days before the assignment was to be completed. How many days in all Terry have to complete the assignment on time?
A.15
B.16
C.25
D.40
E.46
OG #119
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This solution is in the OG. What's your question?
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This is a weighted average/mixture question.shivshankar054 wrote:In order to complete a reading assignment on time, Terry planned to read 90 pages per day.However,she read only 75 pages per day at first, leaving 690 pages to be read during the last 6 days before the assignment was to be completed. How many days in all Terry have to complete the assignment on time?
A.15
B.16
C.25
D.40
E.46
First set of days: Average number of pages per day = 75.
Last 6 days: Average number of pages per day = 690/6 = 115.
Mixture of the two sets of days: Average number of pages per day = 90.
Let F = the first set of days and L = the last 6 days.
To determine the ratio of F to L in the mixture, use ALLIGATION:
Step 1: Plot the 3 averages on a number line, with the averages for the two ingredients on the ends and the mixture average in the middle.
F 7590115 L
Step 2: Calculate the distances between the averages.
F 75159025115 L
Step 3: Determine the ratio in the mixture.
The required ratio of F to L is the RECIPROCAL of the distances in red.
F:L = 25:15 = 5:3.
Since the actual value of L is 6 days, and F:L = 5:3 = 10:6, F = 10 and L = 6.
Thus, the total number of days = F+L = 10+6 = 16.
The correct answer is B.
For two similar problems, check here:
https://www.beatthegmat.com/ratiosfract ... 15365.html
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An alternate approach is to plug in the answers, which represent the total number of days.wied81 wrote:From OG #119  Problem solving:
119) In order to complete a reading assignment on time, Terry planned to read 90 pages per day. However, she read only 75 pages per day at first, leaving 690 pages to be read during the last 6 days before the assignment was to be completed. How many days in all did Terry have to complete the assignment on time?
A) 15
B) 16
C) 25
D) 40
E) 46
OA: B
Since the planned rate was 90 pages per day, the total number of pages must be a multiple of 10.
Over the last 6 days, the total number of pages read = 690.
Thus, the total number of pages read at a rate of 75 pages per day must be a multiple of 10.
Answer choice A (15 days) implies 9 days at 75 pages per day.
Answer choice C (25 days) implies 19 days at 75 pages per day.
Neither of these answers will yield a total number of pages that is a multiple of 10.
Eliminate A and C.
Answer choice B: 16 days
10 days at 75 pages per day + 690 pages over the last 6 days = 10*75 + 690 = 1440.
16 days at 90 pages per day = 16*90 = 1440.
Success!
The correct answer is B.
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Well ok then! I submit a third solution, based on the number of days D.
The plan was to read 90*D pages, but instead of that we read 75*(D6) pages and then had 690 pages left.
So 90*D=75*D+240
And D=16
Kind Regards,
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The plan was to read 90*D pages, but instead of that we read 75*(D6) pages and then had 690 pages left.
So 90*D=75*D+240
And D=16
Kind Regards,
Misterholmes
www.gmatdojo.com
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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 earlyon (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: B
GMAT Assassins aren’t born, they’re made,
Rich
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 earlyon (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: B
GMAT Assassins aren’t born, they’re made,
Rich