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Nsp10
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 III

Thank you for very nice explanations:
my doubt is in case 3:
III. x>z>y
in order to make this condition true we are assuming y>y^2,
can we also make the same condition true by assuming y<y^2 ?

y < y^2 would imply 0 < y < 1.

For x > z > y we can have (x = 10) > (z = 1/2) > (y = 1/5)

y > y^2 would imply y < 0 or y > 1

For x > z > y we can have (x = 10) > (z = 1/2) > (y = -1)
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for third one we can take negative no also right like 9>1>-2?
Bunuel


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.

Answer: E.
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sakshijjw
for third one we can take negative no also right like 9>1>-2?

Yes, x = 9, y = -2, z = 1 also works to prove that III could be true.
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