Problem Solving

BTGmoderatorDC wrote:Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p + 3?

A. 3
B. 6
C. 7
D. 9
E. It cannot be determined from the given information.

OA D

Source: Manhattan Prep

Given that p is a positive even integer with a positive units digit, the units digit of p can be 2, 4, 6, or 8.

Let's try for these possible values of p.

1. Say p = 2; p^3 - p^2 = 2^3 - 2^2 = 8 - 4 = 4 ≠ 0. Unit digit of p cannot be 2;
2. Say p = 4; p^3 - p^2 = 4^3 - 4^2 = 64 - 16 = _8 ≠ 0. Unit digit of p cannot be 4;
3. Say p = 6; p^3 - p^2 = 6^3 - 6^2 = 216 - 36 = _ _0 = 0. Unit digit of p must be 6

Thus, the units digit of p + 3 = 6 + 3 = 9.

The correct answer: D

Hope this helps!

-Jay
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BTGmoderatorDC wrote:Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p + 3?

A. 3
B. 6
C. 7
D. 9
E. It cannot be determined from the given information.

OA D

Source: Manhattan Prep

The only single digit numbers for which the difference between the units digit of its cube and the units digit of its square is 0 are: 0, 1, 5, and 6. However, since p is a positive even integer with a positive units digit, its units digit must be 6. Thus, the units digit of p + 3 is 9.

Answer: D