Three sets of English, Maths and Science books, containing 336, 240 and 96 books, respectively, each of same height have to be stacked in such a way that all the books are stored subject-wise and the height of each stack is the same. The total number of stacks will be - 14, 10, 15 or 22.

I do not want the direct answer. Please someone explain the procedure so that I would be able to do all the questions of this sort in future. I want quick answer and secondly the most quick way to DO this sum.

Thanks in advance, for reading and replying!

Kahani - I don't think I understand the question. Is this correct: you have a stack of 336 English books, a stack of 240 math books, and a stack of 96 science books, all of equal height. You want to split these into smaller equal size stacks, and you want to end up with a total of either 14, 10, 15, or 22 stacks, correct?

Well, you can see that if you divided each stack in half that would give you 6 equal size stacks, but 6 is not one of your answers. Or you could divide each of the original stacks into 3, making 9 total, but again that's not one of your answers. It's pretty clear that the total number of stacks will have to be a multiple of 3, and the only option you give that is a multiple of 3 is 15. But that would require dividing each stack into 5 of equal height, and none of the original stacks is divisible by 5, so it's impossible. Which make me think I don't understand the question!

This question was put in the test as it is and I, being a non-native user of English can't expect myself to be knowing and understanding more than you. Still, what I made of it is -

1. There are 3 sets of books - the first set of English books (numbering 336), the second set of Maths books (numbering 240 books) and the third set of Science books (numbering 96).

2. All the books, not the stacks, are of equal sizes.

3. While making the stacks, the stacks of each category of books should be different, I mean, do not mix the books. If you have a particular set A, it should have all the books of Maths, or Science or English only.

While writing it, it came to my mind that I should find the HCF of the numbers, and divide each by it, and just get the number.

Just add all the books up, and in turn, divide the total by each one of your answer options. The one that gives you a whole number is the answer.

Just add all the books up, and in turn, divide the total by each one of your answer options. The one that gives you a whole number is the answer.

Correct. But in addition you will want to check that each stack of books can be divided by the number of books per stack that you get. For example if 7 had been given as a possible answer you might conclude that each stack would have 96 books, but you can't divide the 240 math books into piles of 96 each. So even though 7 divides into the total it's not a valid answer.

ebaines and Kcomissiong,

Thanks for answers to both of you, but as I earlier said, I thought I should go for the HCF and that I did, which was 48 and then I divided the whole number (adding all books) by HCF (i.e. 48) and got the answer as 14, and checked it as RIGHT in the answer key.

Still, thanks to both, as while explaining it out to ebaines, I got the clue!

Your method worked because each pile was divided by the HCF. But they might have been divided by a lower common factor. It was a good idea to start with the HCF, but if that answer wasn't given as an option you would try a lower CF. For example it's possible that each stack could have been divided into 42 stacks of 16 books each.