Page Progression

Logic Level 2

Krishna always reads some (at least 2) pages of "Harry Potter" before going to school. One good day, Agnishom asked him - "Krishna, what is the sum of all the page numbers you read today?"

Krishna replied "It is either 512 or 412."

What is it?

Data Insufficient 512 412 None of the rest

1 solution

Ayan Jain
Feb 24, 2015

I did it by proving that the answer cannot be 512 while 412 is possible. Only way it can be 512 is that if he reads only page number 512, but then it is highly unlikely that he won't remember the number.

Let n be the number of pages he has read total. And x be the number of pages he had read earlier.

Let us assume that the sum was 512. We will prove that this isn't possible.

Then, sum of pages is -

n(n + 1)/2 - x(x + 1)/2 = 512

n(n+1) - x(x+1) = 1024

(n-1)(n+x+1) = 1024. Now, 1024 is 10^2, and so it cannot have any odd number as it's factor.

Making 2 cases -

1 - If 'n' is even.

a)x is odd. Then, (n-x)(n+x+1) becomes (odd)(even)

b)x is even. Then, it is (even)(odd)

2.If 'n' is odd.

a) x is even. Then, (odd)(even)

b) x is odd. Then (Even)(Odd).

As stated above, 1024 cannot have any odd factor other than 1, so it is not possible to get 512 as the answer. At the same time, 412 is a valid option since it can be written as (103)*4.

First assumption: When reading a book, you read the pages in order. Second assumption: For two pages to be in order (n, n+1), the sum will always be an odd number.

Since 512 is 2^8 power, it has no factor which is an odd number. For 412, we have (4,103) where 103 is the sum of the two pages (n, n+1). Hence; (51,52) (50,53) (49,54) (48,55).

Therefore the pages she read were from 48 to 55 whose sum is 412.

Geo Ferrolino - 3 years, 11 months ago

Same approach. She read from page 48 to 55.

Cleres Cupertino - 5 years, 7 months ago

Better approach will be using impolite numbers.

Rajdeep Dhingra - 5 years, 7 months ago

In the question it is not mentioned that he read the pages sequentially.He could have read any random pages. So the data here is insufficient. There could be more assumptions like the book may have more than 600 pages.

Tushar Pal - 4 years, 1 month ago

It so happens that 512 is the only three figure number ending in 12 that cannot be the sum of pages read in sequence - all the others have at least one odd factor that is not one.

Thomas Sutcliffe - 3 years, 7 months ago

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