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OG2016 PS A positive number x

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by lionsshare » Mon Aug 28, 2017 1:32 pm
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

OA: D

Please share the solution for this problem.
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by Brent@GMATPrepNow » Mon Aug 28, 2017 1:50 pm
lionsshare 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

OA: D
A positive number x is multiplied by 2...
We get: 2x

...and this product is then divided by 3
We get: 2x/3

If the positive square root of the result of these two operations equals x...
We get: √(2x/3) = x

From here, we can EITHER solve this equation for x, OR we can plug in the answer choices until we find a value that satisfies the equation.

Let's SOLVE the equation: √(2x/3) = x
Square both sides to get: 2x/3 = x²
Multiply both sides by 3 to get: 2x = 3x²
Subtract 2x from both sides to get: 0 = 3x² - 2x
Factor the right side: 0 = x(3x - 2)

So, EITHER x = 0 OR (3x - 2) = 0
Since we're told that x is a positive number, we can rule out the possibility that x = 0
So, it must be the case that (3x - 2) = 0
Add 2 to both sides to get: 3x = 2
Solve: x = 2/3

Answer: D

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OG2016 PS A positive number x

by Brent@GMATPrepNow » Mon Aug 28, 2017 1:52 pm
DELETED - my solution was posted twice
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by Jay@ManhattanReview » Tue Aug 29, 2017 9:09 pm
lionsshare 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

OA: D

Please share the solution for this problem.
Let's translate the word narration to math.

1. A positive number x is multiplied by 2, we get 2x.

2. this product is then divided by 3, we get 2x/3

3. the positive square root of the result of these two operations equals x, we get √(2x/3) = x

We have to get the value of x.

Let's square √(2x/3) = x, we get 2x/3 = x^2.

=> (2/3) * x = x * x

If we compare the left-hand side and the right-hand side, one of the solutions, we get x = 2/3. This will give (2/3) * (2/3) = (2/3) * (2/3).

The other possible solution is x = 0. This will give (2/3) * 0 = 0 * 0 => 0 = 0.

We see that option D = 2/3 is given as option -- the correct answer.

The correct answer: D

Hope this helps!

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by [email protected] » Wed Aug 30, 2017 9:54 am
Hi lionsshare,

We're told that X is a positive number and that it is multiplied by 2, then divided by 3. Then we're told that this result is square-rooted and the end result equals X. We're asked for the value of X.

There's a great logic 'shortcut' to this question if you focus on the square-rooting "part" of the math. Here's a simple example of that shortcut:
IF... X = 5 and then we multiply by 5, we get 25.... square-rooting 25 gets us back to 5. This means that by multiplying by the SAME number we started with, then square-rooting that result, we get back to what we started with.

This same thing happens here: the multiply by 2 and dividing by 3 is "offset" by square-rooting.

(2/3) multiplied by 2 and divided by 3 = (2/3)(2/3) = 4/9.
Square-rooting 4/9 =
√4/√9 = 2/3

Final Answer: D

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by Matt@VeritasPrep » Wed Aug 30, 2017 5:26 pm
a positive number x:

x

is multiplied by 2:

2x

then this product is divided by 3:

2x/3

and the square root of this equals x:

√(2x/3) = x

From here, square both sides:

2x/3 = x²

divide both sides by x:

2/3 = x
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by Admin1 » Tue Sep 05, 2017 4:37 pm
Just a quick comment:

ZERO is not a positive number.
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by Admin1 » Tue Sep 05, 2017 9:17 pm
lionsshare 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

OA: D

Please share the solution for this problem.
Solution:
A positive number x multiplied by 2 can be represented as:
2x

This product is then divided by 3:
2x/3

The positive square root of the result of these two operations equals x:
√(2x/3) = X

Taking square on both sides:
√(2x/3)² = x²
2x/3 = x²

Multiplying 3 on both sides:
2x = 3x²
3x² - 2x = 0
x(3x - 2) = 0
Either x = 0 or 3x - 2 = 0 => x = 2/3

Since 0 is not a positive number, therefore x = 2/3 is the correct answer.

Hence option D is true.
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by Scott@TargetTestPrep » Mon Sep 11, 2017 10:20 am
lionsshare 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

OA: D .
We need to produce an equation from the information given in the problem stem. We are given that x is multiplied by 2 and then that product is divided by 3. This gives us:

2x/3

We are given that the positive square root of this result is equal to x. This gives us:

√(2x/3) = x

2x/3 = x^2

2x = 3x^2

3x^2 - 2x = 0

x(3x - 2) = 0

x = 0

or

3x - 2 = 0

3x = 2

x = 2/3

Answer: D

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