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If n = p^2 and p is a prime number greater than 5, what is

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by Jay@ManhattanReview » Mon Dec 30, 2019 9:23 pm
BTGmoderatorDC wrote:If n = p^2 and p is a prime number greater than 5, what is the units digit of n^2 ?

A. 1
B. 3
C. 4
D. 7
E. 9

OA A

Source: Official Guide
Say p = 7, then n^2 = p^4 = 7^4 = 49^2; the units digit of 49^2 is 1. The correct answer is A. There is no need to check for other prime numbers such as 11, 13, 17, etc. since this is a PS question, the correct option must be true for p = 7. As in PS questions, only one option is correct, the correct answer is A.

You may try with p = 11 => n^4 = 11^4; units digit is 1. Again, say p = 19 => n^4 = 19^4; units digit is 1.

The correct answer: A

Hope this helps!

-Jay
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by Brent@GMATPrepNow » Tue Dec 31, 2019 3:18 am
BTGmoderatorDC wrote:If n = p^2 and p is a prime number greater than 5, what is the units digit of n^2 ?

A. 1
B. 3
C. 4
D. 7
E. 9
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

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by Scott@TargetTestPrep » Sat Jan 04, 2020 7:23 pm
BTGmoderatorDC wrote:If n = p^2 and p is a prime number greater than 5, what is the units digit of n^2 ?

A. 1
B. 3
C. 4
D. 7
E. 9

OA A

Source: Official Guide
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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