Question

Stu counted the lines of a page in his book. Counting by threes gave a remainder of 2. Counting by threes gave a remainder of 2, counting by fives also gave a remainder of 2, and counting by sevens gave a remainder of 5. How many lines were on the page?

Answer 1

counting by 3's r 2....5,8,11,14,17,20,23,26,29,32,35,38,41,44,47,50,53

counting by 5's r 2...7,12,17,22,27,32,37,42,47

counting by 7's r 5....12,19,26,33,40,47

now whats common.....that would be 47...so there are 47 lines on the page

Answer 2

There are 47 lines in the page.

Explanation:

First condition is: counting by threes gave a remainder of 2. So, starting with 2 and adding 3 again and again.

Possible number of lines: 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53 and so on...

Second condition is: counting by fives also gave a remainder of 2. Here, starting with 2 and adding 5 again and again.

So, possible number of lines: 2, 7, 12, 17, 22, 27, 32, 37, 42, 47, 52, 57, 62 and so on..

Third condition is: counting by sevens gave a remainder of 5. Here, starting with 5 and adding 7 again and again.

Possible number of lines: 5, 12, 19, 26, 33, 40, 47, 54, 61 and so on..

Therefore, the first number that appears in all three lists is 47 that fits in all three conditions.

So, 47 is your answer.

Note: These conditions are eligible for all the multiples of 47.

And we are taking 47 as the answer, because 47 is the most feasible number of lines in a page. Multiples of 47 will be much larger than 47.