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Math Expert V
Joined: 02 Sep 2009
Posts: 58445

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Difficulty:   25% (medium)

Question Stats: 83% (00:44) correct 17% (01:35) wrong based on 6 sessions

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If $$p$$ is a positive integer ($$p ≠ 3, 4$$), which of the following expressions is equivalent to $$\frac{(p – 4)}{(p – 4)!}×\frac{(p – 3)!}{(p – 3)}$$ ?

A. $$p-2$$
B. $$p-3$$
C. $$p-4$$
D. $$p-5$$
E. $$p-6$$

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Math Expert V
Joined: 02 Sep 2009
Posts: 58445

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1
Official Solution:

If $$p$$ is a positive integer ($$p ≠ 3, 4$$), which of the following expressions is equivalent to $$\frac{(p – 4)}{(p – 4)!}×\frac{(p – 3)!}{(p – 3)}$$ ?

A. $$p-2$$
B. $$p-3$$
C. $$p-4$$
D. $$p-5$$
E. $$p-6$$

We’ll go for ALTERNATIVE because it’s easiest to solve the question using numbers.

With an expression with variables, we can just pick any number. If we pick $$p = 5$$, it gives us $$\frac{1}{1!}×\frac{2!}{2} = 1 × 1 = 1$$. Let’s check the answer choices: (A) 3 – Nope! (B) 2 – No! (C) 1 – possible, let’s see the other answer choices. (D) 0 and (E) –1 are eliminated! Only (C) remains.

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Intern  B
Joined: 08 Dec 2017
Posts: 8

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if I do not substitute value and solve expression we get 1/(p-3).

can anyone show how to solve expression n determine value.
Intern  B
Joined: 10 May 2018
Posts: 47

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I solved it like this :

the key is that the when we expand the factorial of (p-3)! it will be (p-3) (p-4)! as (p-3) (p-3-1)!

so the equation will become

((p-4)/(p-4)!) *((p-3)(p-4)!/(p-3))

so the answer becomes (p-4)

Thanks
Intern  B
Joined: 13 Jun 2019
Posts: 1

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I think this is a high-quality question.

Posted from my mobile device Re M70-06   [#permalink] 18 Oct 2019, 04:00
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