P.S. - Question source, from GMAT Hacks!
If x is a positive integer, what is the result when (x + 1)! is divided by (x - 1)! ?
(1) (x - 1)! = 720
(2) x(x + 1) = 56
(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.
Answer with explanation -
[spoiler]Answer: D
While factorials can be time-consuming to calculate, we don't need to find the exact answer on a Data Sufficiency question. In this case, it is sufficient to know that we could solve. To do so, all we would need is the value of x.
Statement (1) is sufficient. Given one variable, as we are here, we can determine which value of x - 1 has a factorial equivalent to 720. (It turns out that if x = 7, x - 1 = 6, and 6! = 720.)
Statement (2) is also sufficient. We can determine from the statement that x = 7. (Remember, x must be positive.) That's enough to answer the question. Choice (D) is sufficient.
One more note. On more advanced questions, it might be handy to recognize that (x + 1)! = (x + 1)(x)(x - 1)!, so when it is divided by (x - 1)!, the result is (x + 1)(x)--statement (2). If you needed to solve for (x + 1)! divided by (x - 1)!, that would be a simple way of reaching a solution.[/spoiler]
If x is a positive integer, what is the result when (x + 1)! is divided by (x - 1)! ?
(1) (x - 1)! = 720
(2) x(x + 1) = 56
(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.
Answer with explanation -
[spoiler]Answer: D
While factorials can be time-consuming to calculate, we don't need to find the exact answer on a Data Sufficiency question. In this case, it is sufficient to know that we could solve. To do so, all we would need is the value of x.
Statement (1) is sufficient. Given one variable, as we are here, we can determine which value of x - 1 has a factorial equivalent to 720. (It turns out that if x = 7, x - 1 = 6, and 6! = 720.)
Statement (2) is also sufficient. We can determine from the statement that x = 7. (Remember, x must be positive.) That's enough to answer the question. Choice (D) is sufficient.
One more note. On more advanced questions, it might be handy to recognize that (x + 1)! = (x + 1)(x)(x - 1)!, so when it is divided by (x - 1)!, the result is (x + 1)(x)--statement (2). If you needed to solve for (x + 1)! divided by (x - 1)!, that would be a simple way of reaching a solution.[/spoiler]
