Tom Read a Book Containing 480 Pages by Reading the Same Number GMAT Problem Solving

Question: 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?

1. 10
2. 12
3. 15
4. 16
5. 18

“Tom read a book containing 480 pages by reading the same number of pages each day" - is a topic of the GMAT Quantitative reasoning section of GMAT.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The GMAT Quant topic's problem-solving section comprises highly calculative mathematical problems that must be solved using the appropriate mathematical facts.

Answer: C

Solution and Explanation:

Approach Solution 1:

Given in the question that Tom is reading a book having 480 pages. And each day he reads the same number of pages. If he read 16 pages more each day he would’ve finished the book 5 days earlier.
Say the number of days Tom spent reading the book was d. Then:
The number of pages he read per day would be 480/d
The number of pages he would read per day with an increased speed would be 480 / (d−5);
We are told that the number of pages for the second case was 16 pages per day more, so 480/d= (480/(d−5)) −16.
At this point it's much better to plug answer choices rather than solve for d. Answer choice C fits: 480/15 = 32 = (480/(15−5)) − 16.

Hence C is the correct answer.

Approach Solution 2:

Given in the question that Tom is reading a book having 480 pages. And each day he reads the same number of pages. If he read 16 pages more each day he would’ve finished the book 5 days earlier.
Let the number of days Tom spent reading the book was x. Then:

We will have the equation as,
[480 / x] = [480 / (x+16)] + 5
the working it out
[480 / x] = [480 + 5(x + 16)] / (x+16)
480x + 7680 = 5x^2 + 560x
5x^2 + 80x -7680
finally dividing by 5
x^2 + 16x - 1536
x^2 + 16x - 1536 is…
(x + 48) (x - 32)
x = 32
So 480/x = 480/32 = 15

Hence, C is the correct choice.

Approach Solution 3:

Let the number of pages Tom reads be x.
X must be divisible by 480, as he reads the same no of pages each day.
Option E fails the divisibility test.
We are left with the options 10, 12, 15, 16 which pass the divisibility test.
Days : 10 12 15 16
X : 48 40 32 30
X+16 : 64 56 48 46
X+16 must be divisible by 480, as he would have finished the book five days earlier.

C is the correct answer.

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