If n = p² and p is a prime number greater than 5, what is the units digit of n² ?

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by Brent@GMATPrepNow » Fri Mar 13, 2020 9:47 am

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If n = p² and p is a prime number greater than 5, what is the units digit of n² ?

A. 1
B. 3
C. 4
D. 7
E. 9

Answer: A
Source: Official guide

Brent Hanneson - Creator of GMATPrepNow.com

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Source: Beat The GMAT — Problem Solving | Fri Mar 13, 2020 9:47 am

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8156; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: If n = p² and p is a prime number greater than 5, what is the units digit of n² ?

by Scott@TargetTestPrep » Fri Mar 20, 2020 6:31 am

Brent@GMATPrepNow wrote: ↑
Fri Mar 13, 2020 9:47 am
If n = p² and p is a prime number greater than 5, what is the units digit of n² ?

A. 1
B. 3
C. 4
D. 7
E. 9

Answer: A
Source: Official guide

Solution:

If p = 7, then n = 49, and the units digit of 49^2 is 1.

If p = 11, then n = 121, and the units digit of 121^2 is 1.

Alternate solution:

Since n = p^2, then n^2 = p^4. Since p is a prime number greater than 5, the units digit of p could be 1, 3, 7 or 9, but the units digit of p^4 will always be 1 (since 1^4 = 1, 3^4 = 81, 7^4 = 2401 and 9^4 = 6561).

Answer: A

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Founder and CEO
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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: If n = p² and p is a prime number greater than 5, what is the units digit of n² ?

by Brent@GMATPrepNow » Fri Mar 20, 2020 6:36 am

Brent@GMATPrepNow wrote: ↑
Fri Mar 13, 2020 9:47 am
If n = p² and p is a prime number greater than 5, what is the units digit of n² ?

A. 1
B. 3
C. 4
D. 7
E. 9

Answer: A
Source: Official guide

Let's choose a value of p that satisfies the condition that p is a prime number greater than 5.
So, it COULD be the case that p = 7

So, n = p² = 7² = 49

If n = 49, then n² = 49² = ----1

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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