I am never comfortable with solutions that resort to number picking. I spent some time thinking about this problem and here's what I came up with. Let's start with the fact that |a|+|b|>= |a+b|. This is always the case, with equality occurring when a>=0 and b>=0. Our question asks us to det...

a, x, and k are positive integers. k is odd. Is a divisible by 24?

(1) x^(2a) + 1/[x^(2a)]>2
(2) x^[(k^3)-k] = x^a

The answer is C: Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone. See if you can figure it out.

Hi everyone, Sorry to respond with a delay. hoxlay... you did a great job with 2 of the subtleties of this problem, but got tripped up by the third. I'll explain. Statement 1: You were perfectly right that the only thing that statement one tells us is that x is not equal to one. That may seem irrele...

Let the lowest possible integer, which satisfies these conditions, be denoted by n: Let's translate the statements into mathematical relations (where a,b,c are integers) n = 11a + 10 = 11a+11-1 = 11(a+1) - 1 n = 13b + 12 = 13b+13-1 = 13(b+1) - 1 n = 17c + 16 = 17c+17-1 = 17(c+1) - 1 Since n = 11(a+1...

Jamie,
I stated above that I composed the problem myself.
Thanks