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

Question

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}

NischalSR · Answer

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)

ZenJames · Answer

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.

Dhwanii · Answer

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

ZenJames · Answer

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.

Dhwanii · Answer

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.

rianaamy · Answer

What set of numbers can both be true for option C and the original question? In other words, how can we eliminate option C?

GMATBusters · Answer

Since the exponents are in decimal form, 3.5 can be expressed as 7/2, representing the square root of x raised to the 7th power. Therefore, x cannot be negative, as the square root of a negative number is not defined.

similarly, x, y , and z are positive (0 is also not possible)

Now, we can take any power of the inequality as both sides of the inequality are non-negative.

If you take the square of the given inequality, you will get x^7>y^5> z^3

whereas the given relation in D is the opposite of this and hence NOT Possible.

D is the right answer.

shubhim20 · Answer

@bunuel @bb @KarishmaB

shubhim20 · Answer

KarishmaB   Bunuel   bb  please explain

KarishmaB · Answer

First step is to simplify to understand what is given.

x^{3.5} > y^{2.5} > z^{1.5}

x^{7/2} > y^{5/2} > z^{3/2}

\sqrt{x^7} > \sqrt{y^5} > \sqrt{z^3}

All terms are definitely positive since these are principal square roots. So we can square the inequality.

x^7 > y^5 > z^3 
Look at the options for any option that negates this or gives that the variables are negative. Option (D) negates this.

Answer (D)

jonatasjun · Answer

(C) x^3<y^2<z
I could not find a scenario where this is true...

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

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