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A positive number x is multiplied by 2, and this product is then divid

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A positive number x is multiplied by 2, and this product is then divid  [#permalink]

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New post 13 Aug 2008, 20:33
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A positive number x is multiplied by 2, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ?

(A) 9/4
(B) 3/2
(C) 4/3
(D) 2/3
(E) 1/2

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-positive-number-x-is-multiplied-by-2-and-this-product-is-144437.html
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Re: A positive number x is multiplied by 2, and this product is then divid  [#permalink]

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New post 13 Aug 2008, 21:44
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droopy57 wrote:
A positive number x is multiplied by 2, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x?

a. 9/4
b. 3/2
c. 4/3
d. 2/3
e. 1/2


**question: what is the fastest way to solve this non-algebraically? Any clear way to choose between the two possible choices?**


((2x)/3)^0.5 = x
Square both sides
(2x)/3 = x^2
2x = 3x^2
2 = 3x
x = 2/3

Non algebraically: you can look at answer choices and see which number when multiplied into ((2x)/3)^0.5 will give you a square in numerator and denominator (so that it equals itself).

9/4 will give 18/12
3/2 will give 1 (but 1 does not = 3/2)
4/3 will give 8/9
2/3 will give 4/9 (aha!)
1/2 will give 2/6
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Re: A positive number x is multiplied by 2, and this product is then divid  [#permalink]

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New post 14 Aug 2008, 09:17
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fastest way:

I had to write it down in an equation form, but then, the answer struck me as obvious once I had done this.

\(\sqrt{\frac{2}{3}x} = x\)

square both sides gives you

\(\frac{2}{3}x = x^2\)

can also be written as:

\(\frac{2}{3}*x = x*x\)

Divide both sides by x gives you

\(\frac{2}{3} = x\)

Not sure the best way to do this is without the equation. When you reduce things to writing on the pad, it helps eliminate errors which occur when we try to keep everything straight in our heads.

droopy57 wrote:
A positive number x is multiplied by 2, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x?

a. 9/4
b. 3/2
c. 4/3
d. 2/3
e. 1/2


**question: what is the fastest way to solve this non-algebraically? Any clear way to choose between the two possible choices?**
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Re: A positive number x is multiplied by 2, and this product is then divid  [#permalink]

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New post 14 Aug 2008, 09:21
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jallenmorris wrote:
if 2/3 * x = x * x, then x must be 2/3.


just an addition
if 2/3 * x = x^2
x(x-2/3) = 0
either x = 0 or x = 2/3
x = o not possible as per question (x is positive) So x = 2/3
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Re: A positive number x is multiplied by 2, and this product is then divid  [#permalink]

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New post 14 Aug 2008, 09:25
Good point. I wish I could say I didn't consider 0 because the questions stated "positive integer" but I just got lucky ;)

durgesh79 wrote:
jallenmorris wrote:
if 2/3 * x = x * x, then x must be 2/3.


just an addition
if 2/3 * x = x^2
x(x-2/3) = 0
either x = 0 or x = 2/3
x = o not possible as per question (x is positive) So x = 2/3
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Re: A positive number x is multiplied by 2, and this product is then divid  [#permalink]

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New post 14 Aug 2008, 11:02
sqrt(2x/3) = x

square both sides ---> 2x/3 = x^2

multiply both sides by 3 ---> 2x = 3x^2

3x^ - 2x = 0

x(3x - 2) = 0

x = 0, x = 2/3
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Re: A positive number x is multiplied by 2, and this product is then divid  [#permalink]

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New post 14 Aug 2008, 20:55
Thanks all. I solved the same way but thought there may be a faster way to solve since I took a minute or two to think through the question.
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A positive number x is multiplied by 2 and this product is then divide  [#permalink]

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New post 08 Feb 2011, 01:02
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A positive number x is multiplied by 2 and this product is then divided by 3. If the positive square root of the results of these two operations equals x, what is the value of x?

A. 9/4
B. 3/2
C. 4/3
D. 2/3
E. 1/2
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Re: A positive number x is multiplied by 2 and this product is then divide  [#permalink]

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New post 08 Feb 2011, 01:38
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sq rt(2x/3) = x

=> 2x/3 = x^2

=> x = 2/3

Ans - D
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Re: A positive number x is multiplied by 2 and this product is then divide  [#permalink]

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New post 08 Feb 2011, 02:09
x multiplied by 2 = 2x
2x divided by 3= 2x/3

Positive square root of 2x/3 = \(\sqrt{\frac{2x}{3}}\)

\(\sqrt{\frac{2x}{3}} = x\)

Squaring both sides;

\(\frac{2x}{3}=x^2\)

Divide both sides by "x" (we can perform this operation since x is a +ve number)

\(\frac{2}{3}=x\)
\(x=\frac{2}{3}\)

Ans: "D"
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Re: A positive number x is multiplied by 2, and this product is then divid  [#permalink]

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New post 18 Nov 2011, 11:37
The solution given by jallenmorris seems fast and easy enough
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A positive number x is multiplied by 2, and this product is then divid  [#permalink]

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New post 09 Oct 2014, 07:23
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droopy57 wrote:
A positive number x is multiplied by 2, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ?

(A) 9/4
(B) 3/2
(C) 4/3
(D) 2/3
(E) 1/2


Given that: \(\sqrt{\frac{2x}{3}}=x\) --> \(\frac{2x}{3}=x^2\) --> \(x(3x-2)=0\) --> \(x=0\) (dscard since we are told that x is a positive number) or \(x=\frac{2}{3}\).

Answer: D.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-positive-number-x-is-multiplied-by-2-and-this-product-is-144437.html
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Re: A positive number x is multiplied by 2 and this product is then divide  [#permalink]

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Re: A positive number x is multiplied by 2 and this product is then divide   [#permalink] 28 Sep 2015, 00:38

A positive number x is multiplied by 2, and this product is then divid

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