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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]  17 Sep 2017, 03:55
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43% (01:08) correct 56% (01:33) wrong based on 57 sessions

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]  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.

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Re: x is a non-negative number and the square root of (10 – 3x) [#permalink]  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.

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]  04 Mar 2018, 02:11
so
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Kudos [?]: 1027 [0], given: 4631

Re: x is a non-negative number and the square root of (10 – 3x) [#permalink]  05 Mar 2018, 14:47
Expert's post

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.

regards
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Re: x is a non-negative number and the square root of (10 – 3x) [#permalink]  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]  01 Apr 2018, 17:21
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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]  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]  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]  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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# x is a non-negative number and the square root of (10 – 3x)

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