Number System

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CaptainHaddock: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Tue Sep 20, 2011 7:40 pm; Thanked: 1 times; Followed by:1 members

Number System

by CaptainHaddock » Mon Oct 31, 2011 10:25 am

P and N are natural numbers. If P^N has the same unit's digit as P, how many possibilities exist for the unit's digit of P?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Would like to know the methodology. OA is D

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Source: Beat The GMAT — Problem Solving | Mon Oct 31, 2011 10:25 am

gmatblood: Master | Next Rank: 500 Posts; Posts: 489; Joined: Tue Jul 05, 2011 11:10 am; Thanked: 28 times; Followed by:5 members

by gmatblood » Mon Oct 31, 2011 10:32 am

CaptainHaddock wrote:P and N are natural numbers. If P^N has the same unit's digit as P, how many possibilities exist for the unit's digit of P?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Would like to know the methodology. OA is D

the digits are 0,1,5,6 = 4(d)

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saketk: Legendary Member; Posts: 608; Joined: Sun Jun 19, 2011 11:16 am; Thanked: 37 times; Followed by:8 members

by saketk » Thu Nov 03, 2011 11:17 am

CaptainHaddock wrote:P and N are natural numbers. If P^N has the same unit's digit as P, how many possibilities exist for the unit's digit of P?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Would like to know the methodology. OA is D

Well I have a concern here-

1) what is the source of this question?
2) I can give you many more examples in addition to 1,5,6, and 0.

For example if p =3 and N = 5 then 3^5 = 243. this also satisfies the given condition.

If p= 7 and N= 5 then 7^5 = 16807. this also satisfies the given condition.

NONE OF THE OPTIONS SATISFY THIS CONDITION

Again, what is the source of this question?

NONE OF THE OPTIONS SATISFY THIS CONDITION

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sam2304: Legendary Member; Posts: 1239; Joined: Tue Apr 26, 2011 6:25 am; Thanked: 233 times; Followed by:26 members; GMAT Score:680