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A positive number x is multiplied by 2, and this product is
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20 Jul 2020, 05:17
20 Jul 2020, 05:17
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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
(A) 9/4
(B) 3/2
(C) 4/3
(D) 2/3
(E) 1/2
Re: A positive number x is multiplied by 2, and this product is
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20 Jul 2020, 05:17
20 Jul 2020, 05:17
Expert Reply
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Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
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GRE Prep Club - MATH Book for the GRE Exam
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
For more GRE Quant Theory and Practice, see
GRE Prep Club - MATH Book for the GRE Exam
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Re: A positive number x is multiplied by 2, and this product is
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20 Jul 2020, 10:03
20 Jul 2020, 10:03
1
Carcass 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
(A) 9/4
(B) 3/2
(C) 4/3
(D) 2/3
(E) 1/2
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
Cheers,
Brent
