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Re: If x > y^2 > z^4, which of the following statements could be true? [#permalink]

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16 Sep 2009, 08:52

E. Question asks what could be true, not what must be. in second choice the only way is to pick fractions. a very good explanation dabral gives on the link, he gave in the post above. kudos for you.
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Re: If x > y^2 > z^4, which of the following statements could be true? [#permalink]

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16 Oct 2016, 10:33

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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If x > y^2 > z^4, which of the following statements could be true?

I. x>y>z II. z>y>x III. x>z>y

A. I only B. I and II only C. 1 and III only D. II and III only E. I, II and II

As this is a COULD be true question then even one set of numbers proving that statement holds true is enough to say that this statement should be part of correct answer choice.

Given: \(x > y^2 > z^4\).

1. \(x>y>z\) --> the easiest one: if \(x=100\), \(y=2\) and \(z=1\) --> this set satisfies \(x > y^2 > z^4\) as well as given statement \(x>y>z\). So 1 COULD be true.

2. \(z>y>x\) --> we have reverse order than in stem (\(x > y^2 > z^4\)), so let's try fractions: if \(x=\frac{1}{5}\), \(y=\frac{1}{4}\) and \(z=\frac{1}{3}\) then again the stem and this statement hold true. So 2 also COULD be true.

3. \(x>z>y\) --> let's make \(x\) some big number, let's say 1,000. Next, let's try the fractions for \(z\) and \(y\) for the same reason as above (reverse order of \(y\) and \(z\)): \(y=\frac{1}{3}\) and \(z=\frac{1}{2}\). The stem and this statement hold true for this set of numbers. So 3 also COULD be true.

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