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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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Manager
Joined: 01 Sep 2016
Posts: 193
GMAT 1: 690 Q49 V35
If x^3.5 > y^2.5 > z^1.5, then which of the following cannot be true?  [#permalink]

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17 Jun 2017, 12:31
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65% (hard)

Question Stats:

56% (01:39) correct 44% (02:09) wrong based on 138 sessions

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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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Director
Joined: 04 Dec 2015
Posts: 750
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
If x^3.5 > y^2.5 > z^1.5, then which of the following cannot be true?  [#permalink]

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17 Jun 2017, 12:34
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bkpolymers1617 wrote:
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

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

Converting decimal power to fraction powers we get;

$$3.5 = \frac{35}{10} = \frac{7}{2}$$

$$2.5 = \frac{25}{10} = \frac{5}{2}$$

$$1.5 = \frac{15}{10} = \frac{3}{2}$$

$$x^{\frac{7}{2}} > y^{\frac{5}{2}} > z^{\frac{3}{2}}$$

Cancelling common term $$\frac{1}{2}$$ from the powers, we get;

$$x^{7} > y^{5} > z^{3}$$

Therefore (D) $$x^7 < y^5 < z^3$$ cannot be true. Answer (D)...
Manager
Joined: 01 Sep 2016
Posts: 193
GMAT 1: 690 Q49 V35
Re: If x^3.5 > y^2.5 > z^1.5, then which of the following cannot be true?  [#permalink]

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17 Jun 2017, 12:36
This is perfect. Yes D is the answer. Since we are dealing in positive numbers, i think square of the elements would not change signs. However, i was not able to understand C. Can you please help me understand how is C possible please. thanks.
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we shall fight on the beaches,
we shall fight on the landing grounds,
we shall fight in the fields and in the streets,
we shall fight in the hills;
we shall never surrender!
Director
Joined: 04 Dec 2015
Posts: 750
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
Re: If x^3.5 > y^2.5 > z^1.5, then which of the following cannot be true?  [#permalink]

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17 Jun 2017, 12:44
1
bkpolymers1617 wrote:
This is perfect. Yes D is the answer. Since we are dealing in positive numbers, i think square of the elements would not change signs. However, i was not able to understand C. Can you please help me understand how is C possible please. thanks.

Question says which option could not be true.
I didn't check for all options which will be true or not.
After simplifying the given exponents , we have $$x^7>y^5>z^3$$
Hence we cannot have (D) $$x^7<y^5<z^3$$. Hence D could not be true.
Manager
Joined: 05 Dec 2015
Posts: 109
Re: If x^3.5 > y^2.5 > z^1.5, then which of the following cannot be true?  [#permalink]

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18 Jun 2017, 18:06
How do we know the #s are positive? I simplified to X^7 etc like you did, but thought the #s could be negative and thus D could be true.

Thanks!

sashiim20 wrote:
bkpolymers1617 wrote:
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

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

Converting decimal power to fraction powers we get;

$$3.5 = \frac{35}{10} = \frac{7}{2}$$

$$2.5 = \frac{25}{10} = \frac{5}{2}$$

$$1.5 = \frac{15}{10} = \frac{3}{2}$$

$$x^{\frac{7}{2}} > y^{\frac{5}{2}} > z^{\frac{3}{2}}$$

Cancelling common term $$\frac{1}{2}$$ from the powers, we get;

$$x^{7} > y^{5} > z^{3}$$

Therefore (D) $$x^7 < y^5 < z^3$$ cannot be true. Answer (D)...
Director
Joined: 04 Dec 2015
Posts: 750
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
Re: If x^3.5 > y^2.5 > z^1.5, then which of the following cannot be true?  [#permalink]

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29 Jun 2017, 17:39
mdacosta wrote:
How do we know the #s are positive? I simplified to X^7 etc like you did, but thought the #s could be negative and thus D could be true.

Thanks!

sashiim20 wrote:
bkpolymers1617 wrote:
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

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

Converting decimal power to fraction powers we get;

$$3.5 = \frac{35}{10} = \frac{7}{2}$$

$$2.5 = \frac{25}{10} = \frac{5}{2}$$

$$1.5 = \frac{15}{10} = \frac{3}{2}$$

$$x^{\frac{7}{2}} > y^{\frac{5}{2}} > z^{\frac{3}{2}}$$

Cancelling common term $$\frac{1}{2}$$ from the powers, we get;

$$x^{7} > y^{5} > z^{3}$$

Therefore (D) $$x^7 < y^5 < z^3$$ cannot be true. Answer (D)...

$$x^{\frac{7}{2}} > y^{\frac{5}{2}} > z^{\frac{3}{2}}$$ $$= \sqrt{x^{7}} > \sqrt{y^{5}} > \sqrt{z^{3}}$$

After simplification of the expression we get that terms are square root of x, y and z, and square roots cannot have negative value. Hence the values must be positive number. Therefore D 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]

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27 Feb 2019, 03:09
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Re: If x^3.5 > y^2.5 > z^1.5, then which of the following cannot be true?   [#permalink] 27 Feb 2019, 03:09
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