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For which of the following positive integers is the square of that int

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For which of the following positive integers is the square of that int  [#permalink]

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New post 26 Aug 2018, 06:27
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For which of the following positive integers is the square of that integer divided by the cube root of the same integer equal to nine times that integer?

(A) 4
(B) 8
(C) 16
(D) 27
(E) 125

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Re: For which of the following positive integers is the square of that int  [#permalink]

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New post 26 Aug 2018, 06:33
729/3=(9*27)
243 = 243

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Re: For which of the following positive integers is the square of that int  [#permalink]

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New post 26 Aug 2018, 07:13
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Cube root of x has to be an integer - we can eliminate A & C and then we can substitute and find the answer.

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Re: For which of the following positive integers is the square of that int  [#permalink]

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New post 26 Aug 2018, 07:33
Bunuel wrote:
For which of the following positive integers is the square of that integer divided by the cube root of the same integer equal to nine times that integer?

(A) 4
(B) 8
(C) 16
(D) 27
(E) 125


Hi Bunuel,

I tried by taking each of the answer choices.

I started with 125 then went on to 27 and stopped.

Some other way to solve this?
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Re: For which of the following positive integers is the square of that int  [#permalink]

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New post 26 Aug 2018, 07:35
Bunuel wrote:
For which of the following positive integers is the square of that integer divided by the cube root of the same integer equal to nine times that integer?

(A) 4
(B) 8
(C) 16
(D) 27
(E) 125


Working with the options is the best strategy for solving such questions...

(A) Cube of 4 not possible ( For GMAT ) hence rejected.
(B) 8*8/2 = 32 ( Not equal to 9 times 8 = 72) , hence rejected.
(C) Cube of 16 not possible ( For GMAT ) hence rejected.
(D) 27*27/3 = 243 = 9*27 (Answer )
(E) 125*125/5 = 3125 ( Not equal to 9 times 125 = 1125) , hence rejected.

The answer must be (D)
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For which of the following positive integers is the square of that int  [#permalink]

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New post 26 Aug 2018, 11:13
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Bunuel wrote:
For which of the following positive integers is the square of that integer divided by the cube root of the same integer equal to nine times that integer?

(A) 4
(B) 8
(C) 16
(D) 27
(E) 125


Let the positive integer be x.

Given, square of integer 'x' divided by the cube root of the same integer(x) equal to nine times that integer(x).

Converting the problem from word to algebra:

\(\sqrt{x}/\sqrt[3]{x}=9x\)
Or, \(x^2/x^{\frac{1}{3}}=9x\)
Or, \(x^{2-\frac{1}{3}}=9x\)
Or, \(x^{\frac{5}{3}}=9x\)
Or, \((x^{\frac{5}{3}})^3=(9x)^3\)
Or, \(x^5=9^3*x^3\)

Since x is positive, we can cancel out common factor from both the sides, we have
\(x^2=9^3\)
Or,\(x^2=3^6=(3^3)^2\)
Or, \(x=3^3=27\)

Ans. (D)

Hi zanaik89,
I hope this helps.
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Re: For which of the following positive integers is the square of that int  [#permalink]

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New post 26 Aug 2018, 11:34
1
Bunuel wrote:
For which of the following positive integers is the square of that integer divided by the cube root of the same integer equal to nine times that integer?

(A) 4
(B) 8
(C) 16
(D) 27
(E) 125
Answer is 27
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Re: For which of the following positive integers is the square of that int  [#permalink]

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New post 26 Aug 2018, 16:38
Bunuel wrote:
For which of the following positive integers is the square of that integer divided by the cube root of the same integer equal to nine times that integer?

(A) 4
(B) 8
(C) 16
(D) 27
(E) 125


let x^3=integer
let x=cube root of integer
let x^6=square of integer
x^6/x=9x^3➡
x=3
x^3=27
D
Re: For which of the following positive integers is the square of that int &nbs [#permalink] 26 Aug 2018, 16:38
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