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x is a non-negative number and the square root of (10 – 3x)

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x is a non-negative number and the square root of (10 – 3x) [#permalink] New post 17 Sep 2017, 03:55
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x is a non-negative number and the square root of (10 – 3x) is greater than x.

Quantity A
Quantity B
\(|x|\)
\(2\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: x is a non-negative number and the square root of (10 – 3x) [#permalink] New post 21 Sep 2017, 08:35
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We need to solve the equation \(sqrt(10-3x)>x\). Squaring both sides we get \(10-3x>x^2\) that can be rewritten as \(x^2+3x-10<0\). The left hand side can be rewritten as \((x-5)(x+2)\), thus the solution of the equation is \(-5<x<2\).

Since x is non negative, among the solutions we must consider only those between 0 and 2, excluded. Thus, no matter the absolute value, column A is always smaller than 2.

Answer B
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Re: x is a non-negative number and the square root of (10 – 3x) [#permalink] New post 28 Feb 2018, 14:56
IlCreatore wrote:
We need to solve the equation \(sqrt(10-3x)>x\). Squaring both sides we get \(10-3x>x^2\) that can be rewritten as \(x^2+3x-10<0\). The left hand side can be rewritten as \((x-5)(x+2)\), thus the solution of the equation is \(-5<x<2\).

Since x is non negative, among the solutions we must consider only those between 0 and 2, excluded. Thus, no matter the absolute value, column A is always smaller than 2.

Answer B

Good explanation.
Yes I will go with B as well.
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Re: x is a non-negative number and the square root of (10 – 3x) [#permalink] New post 04 Mar 2018, 02:11
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Re: x is a non-negative number and the square root of (10 – 3x) [#permalink] New post 05 Mar 2018, 14:47
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Please boxing,

your replies are very delightful. However, please as a test and not as a screenshot.

Thank you so much for your collaboration. The board is cleaner that way.

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Re: x is a non-negative number and the square root of (10 – 3x) [#permalink] New post 29 Mar 2018, 00:39
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Short & Quick way to get the Answer is :

3x has to be less than 10 as we can't find out the Sqaure root of a a negative number so x can only take values of 0,1,2 & exclude non negative solutions so 2 is rejected. Answer b
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Re: x is a non-negative number and the square root of (10 – 3x) [#permalink] New post 01 Apr 2018, 17:21
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Answer: B
Sure root of 10 - 3x is greater than x and x is a non-negative integer.
First, as x is non-negative, thus |x| equals x in A.
We try numbers. The minimum value for x can be 0.
If x = 0, square root of 10-3x equals 10, which is greater than x.
If x = 1, 10-3 is greater than 1
If x = 2, 10- 6 is not greater than 2.
So, x can be either 0 or 1 and always less than 2.
The answer is B.

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Re: x is a non-negative number and the square root of (10 – 3x) [#permalink] New post 04 Apr 2018, 07:38
Yiddo_Bhushan wrote:
Short & Quick way to get the Answer is :

3x has to be less than 10 as we can't find out the Sqaure root of a a negative number so x can only take values of 0,1,2 & exclude non negative solutions so 2 is rejected. Answer b


However, it is not mentioned that x has to be an integer. x can be just less than 10/3 or 3 for that matter.
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Re: x is a non-negative number and the square root of (10 – 3x) [#permalink] New post 04 Apr 2018, 07:41
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Given: x>0
and
\sqrt{(10-3x)} > x gives -5<x<2

Ignoring negative solutions. 0<x<2 and |x| would be less than 2
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Re: x is a non-negative number and the square root of (10 – 3x) [#permalink] New post 07 Dec 2018, 15:23
Hey guys, I understand your solution, but could you point out the fallacy or mistake in my solution.

sqrt(10-3x) > x
x>=0 so sqrt(10-3x)>0
then 10-3x >0
Thus x < (10/3)

So D because the absolute value of x can be greater than 2 or smaller than 2.
Re: x is a non-negative number and the square root of (10 – 3x)   [#permalink] 07 Dec 2018, 15:23
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