Is the answer D?

This was my approach:

This is a yes/no question

statement 1:

Since the question is asking if a, b, and c are consecutive integers and we know that a<b<c... test the equation using:

a=a

b=a+1

c=a+2

1/a = 1/(a+1)+ 1/(a+2)

Without even solving, you can see pretty quickly that this is going to be a cubed polynomial and it won't yield an integer solution. Since it's given that a, b, and c have to be positive integers...then it follows that for this statement to be true, a, b and c cannot be consecutive integers. sufficient.

statement 2:

plug in the same variables from statement 1.

a+c=(b-1)(b+1)-1

a+a+2=a^2+2a+1-1

2a+2=a^2+2a

2=a^2

again, consecutive integers will not yield a positive integer for a, b, or c. Variables a, b, and c cannot be consecutive integers, so sufficient.

Since statement 1 and 2 are sufficient, ans should be D

_________________

Paul

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