Hi GmatPeak,

Yes - you can approach the question Algebraically, but you have to be careful about relying on "System Algebra" with certain DS questions. Depending on what the specific prompt asks for, you might not need the same number of equations and variables to properly answer the question.

We're told that 1 book was left when a pile of books was stacked in rows of 5. We're asked for the TOTAL number of books. This question can be solved by TESTing VALUES. To start, since 1 book remained when the books were stacked in rows of 5, the total number of books COULD be... 1, 6, 11, 16, 21, 26, 31, 36, etc.

1) When the books were stacked in rows of 7, 1 book was left

Using the same logic that we used at the beginning, the information in Fact 1 tells us that the total number of books COULD be....
1, 8, 15, 22, 29, 36, 43, 50, 57, 64, 71... 106.... 141.... etc.
Combined, with the information that we started with, the possible number of books could be 36, 71, 106, 141, etc.
Fact 1 is INSUFFICIENT

2) When the books were stacked in rows of 8, 4 books were left

Using the same logic that we used at the beginning and in Fact 1, the information in Fact 2 tells us that the total number of books COULD be....
4, 12, 20, 28, 36, 44, 52, 60, 68, 76... 116.... 156.... etc.
Combined, with the information that we started with, the possible number of books could be 36, 76, 116, etc.
Fact 2 is INSUFFICIENT

Combined, we know that the total number of books must be even (and end in a 6) and must 'fit' each of the 3 patterns described above. We can already see one of the 'overlap points' (36 books) and since the numbers go on forever in a repeating pattern, it's highly likely that there will be another overlap (the next overlap is at 316 books).
Combined, INSUFFICIENT

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

GmatPeak wrote:If 1 book was left when a pile of books was stacked in rows of 5, how many books are there in all?

(1) When the books were stacked in rows of 7, 1 book was left

(2) When the books were stacked in rows of 8, 4 books were left

We can create the equation:

Number of books = 5Q + 1 where Q is a positive integer

So the numbers of books can be:

6, 11, 16, 21, 26, 31, 36, ...

Statement One Alone:

When the books were stacked in rows of 7, 1 book was left.

So the numbers of books can be:

8, 15, 22, 29, 36, ...

We see that we could have 36 books. We can also add the LCM of 5 and 7, which is 35, to 36 to obtain 71 books. Both 36 books and 71 books will have 1 book left when they were stacked in rows of 5 or 7. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

When the books were stacked in rows of 8, 4 books were left.

So the numbers of books can be:

12, 20, 28, 36, ...

We see that we could have 36 books. We can also add the LCM of 5 and 8, which is 40, to 36 to obtain 76 books. Both 36 books and 76 books will have 1 book left when they were stacked in rows of 5 and 4 books left when they were stacked in rows of 8. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Again, we see that we could have 36 books. We can also add the LCM of 5, 7 and 8, which is 280, to 36 to obtain 316 books. Both 36 books and 316 books will have 1 book left when they were stacked in rows of 5 or 7, and 4 books left when they were stacked in rows of 8. Both statements together are not sufficient to answer the question.

Answer: E