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

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New post 17 Jun 2017, 12:31
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A
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C
D
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  65% (hard)

Question Stats:

57% (01:36) correct 43% (02:11) wrong based on 151 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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If x^3.5 > y^2.5 > z^1.5, then which of the following cannot be true?  [#permalink]

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New post 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)...
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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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New post 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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Re: If x^3.5 > y^2.5 > z^1.5, then which of the following cannot be true?  [#permalink]

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New post 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.
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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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New post 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)...
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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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New post 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? &nbs [#permalink] 29 Jun 2017, 17:39
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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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