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?

Question

Sarthak Singla · Accepted Answer

We need to find the units digit of p + 3 given that p is a positive even integer with a positive units digit, and the units digit of p^3 - p^2 is equal to 0.
Step 1: Understanding the problem1. p is a positive even integer with a positive units digit.2. The units digit of p^3 - p^2 is 0.
Since p is an even integer with a positive units digit, the possible values for the units digit of p are 2, 4, 6, and 8.
Step 2: Finding the units digit of p
We need to test each possible units digit of p to see which one satisfies the condition that the units digit of p^3 - p^2 is 0.
Case 1: Units digit of p is 2- p = 2- p^2 = 2^2 = 4 (units digit is 4)- p^3 = 2^3 = 8 (units digit is 8)
The units digit of p^3 - p^2 = 8 - 4 = 4This does not satisfy the condition.
Case 2: Units digit of p is 4- p = 4- p^2 = 4^2 = 16 (units digit is 6)- p^3 = 4^3 = 64 (units digit is 4)
The units digit of p^3 - p^2 = 4 - 6 = -2This does not satisfy the condition.
Case 3: Units digit of p is 6- p = 6- p^2 = 6^2 = 36 (units digit is 6)- p^3 = 6^3 = 216 (units digit is 6)
The units digit of p^3 - p^2 = 6 - 6 = 0This satisfies the condition.
Case 4: Units digit of p is 8- p = 8- p^2 = 8^2 = 64 (units digit is 4)- p^3 = 8^3 = 512 (units digit is 2)
The units digit of p^3 - p^2 = 2 - 4 = -2This does not satisfy the condition.
Step 3: Conclusion
The only units digit of p that satisfies the condition is 6.
Step 4: Finding the units digit of p + 3
- If the units digit of p is 6, then:  p + 3  The units digit of p is 6.
The units digit of p + 3 = 6 + 3 = 9
Thus, the units digit of p + 3 is 9.