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Word Problem

by phoenix9801 » Sat May 26, 2012 3:34 am
Can Someone show me how to solve using plugging in numbers not in algebraically. It looks like a GMAT that would be on real test day.

picked 4 and -4 as a plug in number? I? get b and c as an answer. Not sure why. Any ideas.
Also what is the difference between (x^2) vs. (x)^2 ????



Which of the following statements must be true?

Indicate all such statements.

a) (square root(x))^3 = x^-1
b) (x^2) = (x)^2
c) x^-2 = x^2
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by Anurag@Gurome » Sat May 26, 2012 8:48 pm
phoenix9801 wrote:Which of the following statements must be true?

Indicate all such statements.

a) (square root(x))^3 = x^-1
b) (x^2) = (x)^2
c) x^-2 = x^2
Whenever comparison of powers and/or roots of a variable is involved, always check with positive and negative numbers both greater and less than 1 and or -1. (No need to check with negatives when comparing roots).
  • A. Take x = 4 ---> (√4)³ = 8 ≠ 4^(-1) = 1/4 ---> FALSE
    B. x² and (x)² are identical. So this is always TRUE
    C. Take x = 2 --> 2^(-2) = 1/4 ≠ 2² = 4
Only B is true.
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by phoenix9801 » Sat May 26, 2012 9:13 pm
Thank You, but I made typo error on answer choice c it supposed to be less then. SO C) x^-2 < x^2

If I use -4 as plug in. I would get 1/16 < 16 True
If I use 4 as plug in. I would get 1/16 < 16 True

So my argument is then B and C is correct. ????

Anurag@Gurome wrote:
phoenix9801 wrote:Which of the following statements must be true?

Indicate all such statements.

a) (square root(x))^3 = x^-1
b) (x^2) = (x)^2
c) x^-2 = x^2
Whenever comparison of powers and/or roots of a variable is involved, always check with positive and negative numbers both greater and less than 1 and or -1. (No need to check with negatives when comparing roots).
  • A. Take x = 4 ---> (√4)³ = 8 ≠ 4^(-1) = 1/4 ---> FALSE
    B. x² and (x)² are identical. So this is always TRUE
    C. Take x = 2 --> 2^(-2) = 1/4 ≠ 2² = 4
Only B is true.
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