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Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by sukh » Wed Oct 26, 2011 12:51 am
Tom read a book containing 480 pages by reading the same number of pages each day. If he would have finished the book 5 days earlier by reading 16 pages a day more, how many days did Tom spend reading the book? (A) 10 (B) 12 (C) 15 (D) 16 (E) 18
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by neelgandham » Wed Oct 26, 2011 2:33 am
sukh wrote:Tom read a book containing 480 pages by reading the same number of pages each day. If he would have finished the book 5 days earlier by reading 16 pages a day more, how many days did Tom spend reading the book? (A) 10 (B) 12 (C) 15 (D) 16 (E) 18
Let the number of days , he finished reading the book in = x, then
the number of pages Tom read everyday = 480/x

If the number of pages Tom read everyday is 16 pages per day more than the number of pages Tom read everyday = (480/x)+16
and the number of days , he finished reading the book in = x-5,

Total number of pages is always the same = (Number of pages Tom read everyday)*(The number of days , he finished reading the book in )

=> x * (480/x) = (x-5)*((480/x)+16)
=> 480x = (x-5)*(480+16x)
=> x*x - 5*x - 150 = 0 (Simplifying)
=> (x-15)(x+10)=0
=> x = 15
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by tpr-becky » Sun Oct 30, 2011 8:18 am
This is a great problem for introducing technique - if you understand the alegebra and can consistently do it without any mistakes then you can do it the above way. However, if algebra is a problem for you you can look to the answers and work backwards in this problem

Start with the middle number:

If he took 15 days to read the book then he read 32 pages every day. If he increases that by 16 then he reads 48 pages every day and it takes him 10 days - this is 5 days faster and so this is the correct answer.

We start with the middle number becuase if the answer is wrong you can go up or down depending on whether the answer is too big or too small. Using this method you generally have to plug in two answers before you get the correct one.
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