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If x^3.5 > y^2.5 > z^1.5, then which of the following cannot be true?

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Bunuel
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If x^3.5 > y^2.5 > z^1.5, then which of the following cannot be true? [#permalink] New post   26 Oct 2021, 08:15
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If \(x^{3.5} > y^{2.5} > z^{1.5}\), then which of the following cannot be true?

(A) \(x > y > z\)

(B) \(x < y < z\)

(C) \(x^3 < y^2 < z\)

(D) \(x^7 < y^5 < z^3\)

(E) \(x^{10.5} > y^{7.5} > z^{4.5}\)
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D
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NischalSR
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Re: If x^3.5 > y^2.5 > z^1.5, then which of the following cannot be true? [#permalink] New post   10 Nov 2021, 12:37
Luckily the options help in this question.

Just a quick look at the options and you will notice that option D has powers that are twice 3.5, 2.5, and 1.5.
But the signs are opposite so that is the answer.

If x^3.5 > y^2.5 > z^1.5, then x^(2*3.5) > y^(2*2.5) > z^(2*1.5)
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Re: If x^3.5 > y^2.5 > z^1.5, then which of the following cannot be true? [#permalink] New post   11 Nov 2021, 03:34
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The first thing to do is switch the exponents to fractions.
We notice that:
\(\sqrt{x^7} > \sqrt{y^5} > \sqrt{z^3}\)
Since they are all under the square root, we can just compare the exponent power.
\(x^7 > y^5 > z^3 \)
This happens to be the opposite of the correct answer, choice D.
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Re: If x^3.5 > y^2.5 > z^1.5, then which of the following cannot be true? [#permalink] New post   15 Dec 2021, 00:10
NischalSR ZenJames

If someone can lease exlain me where am I going wrong,
For A, I started w dividing the question with 0.5 throughout so it was x^7>y^5>z^3 if we take y as 2 and z as 3 then this condition is satisfied 32 (i.e 2^5)>27 (i.e 3^3) but 2>3 is not satisfied hence A cannot be true
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Re: If x^3.5 > y^2.5 > z^1.5, then which of the following cannot be true? [#permalink] New post   15 Dec 2021, 00:45
Dhwanii

I think you are stopping at testing just one case. I took the theoretical approach instead, but I reckon you can do both.
The question is asking "which of the following CANNOT be true" meaning that there is no way that it can be true.
Consider this for option A: if x=3, y=2 , z=1, then A is true.
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Re: If x^3.5 > y^2.5 > z^1.5, then which of the following cannot be true? [#permalink] New post   15 Dec 2021, 01:04
ZenJames, Thanks for your help. Understood, so basically even if one value can be true, option has to be discarded. Guess I used the must be true approach.
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Re: If x^3.5 > y^2.5 > z^1.5, then which of the following cannot be true? [#permalink] New post   08 Sep 2023, 06:32
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Re: If x^3.5 > y^2.5 > z^1.5, then which of the following cannot be true? [#permalink]
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