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
Answer: D
Source: Official guide
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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
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BTGModeratorVI
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ssrivastava
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The No. X *2 = 2X
on division by 3, we have 2X/3
sqrt(2X/3) = X
on squaring both sides,
2X/3= x^2
solving for X, X= 2/3
Ans B
on division by 3, we have 2X/3
sqrt(2X/3) = X
on squaring both sides,
2X/3= x^2
solving for X, X= 2/3
Ans B
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A positive number x is multiplied by 2...BTGModeratorVI wrote: ↑Fri Jul 03, 2020 6:58 amA 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
Answer: D
Source: Official guide
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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