Let \(p\) be a positive integer such that the unit digit of \(p ^ 3\) is \(4\). What are the possible unit digits of \((p + 3) ^ 3\)?

Question and options

Let

p

be a positive integer such that the unit digit of

p ^ 3

4

. What are the possible unit digits of

(p + 3) ^ 3

Correct answer: A - 3

p^3 ends in 4 only when p ends in 4 (4^3=64). Then p+3 ends in 7 and 7^3=343, so (p+3)^3 ends in 3.