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## Factorial

If (x-1)!/(X-3)!*2 =72, what is the value of x?

what is the easiest way to solve this?

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I think something missing in the question........

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Originally Posted by gmatmix780
If (x-1)!/(X-3)!*2 =72, what is the value of x?

what is the easiest way to solve this?

Left hand side :

(x-1)!/(X-3)! *2= (x-1)(x-2)(x-3)!/(X-3)!*2

Now (x-1)(x-2)(x-3)!/(X-3)! = > (x-1)(x-2)*2

Hence :

(x-1)(x-2)*2 = 72

So , (x-1)(x-2) = 36

Now proceed....

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Good question

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Originally Posted by gmatmix780
If (x-1)!/(X-3)!*2 =72, what is the value of x?

what is the easiest way to solve this?
What are the answer choices here?

If we continue with Abhishek009's solution, we get:

(x-1)(x-2) = 36
x^2 - 3x + 2 = 36
x^2 - 3x - 34 = 0

At this point, we can't factor the quadratic equation, which means x is not an integer.
I'd be surprised if this were an actual GMAT question, since I've never seen a GMAT question require students to use the Quadratic Formula (or its cousin "Completing the Square") to solve a quadratic equation and the only way to solve x^2 - 3x - 34 = 0 is to use one of these time-consuming approaches.

What's the source of this question?

Cheers,
Brent

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