Expression as Integer

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Expression as Integer

by EOV » Fri Nov 30, 2012 5:09 am
Hi everybody,

If a and b are positive integers, is a!/b! an integer?

(1) (b - a)(b + a) = 7! + 1
(2) b + a = 11

(A) Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
(B) Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
(C) Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.
(D) Each statement alone is sufficient to answer the question.
(E) Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.

Please, help me to find correct answer.
Source: — Data Sufficiency |

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by GMATGuruNY » Fri Nov 30, 2012 5:59 am
EOV wrote:Hi everybody,

If a and b are positive integers, is a!/b! an integer?

(1) (b - a)(b + a) = 7! + 1
(2) b + a = 11

Please, help me to find correct answer.
a!/b! will be an integer if a>b.
To illustrate:
If a=5 and b=3, then a!/b! = (5*4*3*2)/(3*2) = 5*4 = 20.

Question rephrased: Is a>b?

Statement 1: (b - a)(b + a) = 7! + 1
7! + 1 > 0.
Since a and b are positive integers, b+a>0.
Thus, the equation above implies the following:
b-a = (7! + 1)/(b+a) = positive/positive = positive.
Since b-a>0, b>a.
SUFFICIENT.

Statement 2: b+a=11
If a=10 and b=1, then a>b.
If a=1 and b=10, then a<b.
INSUFFICIENT.

The correct answer is A.
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