gmatusa2010 wrote:Is a^2 + b^2 > c^2?
(1) a^3 + b^3 > c^3
(2) a + b > c
Is there a non-number testing approach to this?
i can't think of any straightforward algebra approach off the top of my head, but, since all the powers in the statements are odd, you can dust this one really fast by using signs (pos/neg/zero) strategically.
first, let's try for a "Yes". that's easy to do -- just set c = 0, and let a & b be anything positive. then both statements are satisfied, and the answer to the question is "yes".
now, let's try for a "No".
if the powers in the choices were even, this would be a real pain in the neck (cf. the corresponding gprep problem, which has 4th powers in one of the choices). however, there's a quick cut here: just let a and b be small positive numbers (like 1 and 2), and let c be a HUGE negative number (like -1,000,000). then both statements are again true, and the answer to the question is very clearly "no".
so, (e).
Ron has been teaching various standardized tests for 20 years.
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