the value of p?

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Tue Aug 28, 2012 1:52 am

If p is an integer, what is the value of p?

(1) (|p|!)^p = |p|!.
(2) p^p = p^2.

[spoiler]OA C[/spoiler]

Source: gmatclub

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Source: Beat The GMAT — Data Sufficiency | Tue Aug 28, 2012 1:52 am

vk_vinayak: Legendary Member; Posts: 502; Joined: Tue Jun 03, 2008 11:36 pmFollowed by: 21 members; Thanked: 99 times

by vk_vinayak » Tue Aug 28, 2012 2:10 am

sanju09 wrote:If p is an integer, what is the value of p?

(1) (|p|!)^p = |p|!.
(2) p^p = p^2.

[spoiler]OA C[/spoiler]

Source: gmatclub

Very good question. I first chose A, thinking that 0 can't be raised to the power of 0. But forgot that 0!=1

1). (|p|!)^p = |p|! => p=0 or p=1. INSUF
2). p^p = p^2 => p=1 or p=2. INSUF

Combining. p=1. SUFFICIENT.

[spoiler]Anc: C[/spoiler]

- VK

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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Tue Aug 28, 2012 3:03 am

vk_vinayak1 wrote:. (|p|!)^p = |p|! => p=0 or p=1. INSUF
2). p^p = p^2 => p=1 or p=2. INSUF

Last edited by neelgandham on Tue Aug 28, 2012 4:12 am, edited 1 time in total.

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vk_vinayak: Legendary Member; Posts: 502; Joined: Tue Jun 03, 2008 11:36 pmFollowed by: 21 members; Thanked: 99 times

by vk_vinayak » Tue Aug 28, 2012 3:57 am

neelgandham wrote:[quote="vk_vinayak1). (|p|!)^p = |p|! => p=0 or p=1. INSUF
2). p^p = p^2 => p=1 or p=2. INSUF

Some might argue that if p =0, then 0^0 = 0^2 = 0. So, p = 0,1,2 is the solution set. For all those who agree with this, read this awe-CLAP-some article here - https://www.askamathematician.com/2010/1 ... -disagree/[/quote]

Thanks, Anil. Does GMAT consider 0^0=1 ? If yes, do you remember any OG problems that shows this.

- VK

I will (Learn. Recognize. Apply)

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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Tue Aug 28, 2012 4:03 am

0^0 = Undefined (GMAT or otherwise) to the best of my knowledge and to answer your question. NO, I haven't seen any such problems.

Anil Gandham
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