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M70-06

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Math Expert
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Joined: 02 Sep 2009
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M70-06  [#permalink]

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New post 03 Sep 2018, 02:44
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

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

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Math Expert
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Re M70-06  [#permalink]

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New post 03 Sep 2018, 02:44
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.


Answer: C
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Re: M70-06  [#permalink]

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New post 09 Dec 2018, 09:05
if I do not substitute value and solve expression we get 1/(p-3).

can anyone show how to solve expression n determine value.
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Re: M70-06  [#permalink]

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New post 15 Dec 2018, 13:16
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
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Re M70-06  [#permalink]

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New post 18 Oct 2019, 04:00
I think this is a high-quality question.

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