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# GRE Math Challenge #55-If x^2 +2x -15 = -m

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GRE Math Challenge #55-If x^2 +2x -15 = -m [#permalink]  28 Feb 2015, 02:28
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Question Stats:

71% (00:31) correct 28% (03:56) wrong based on 7 sessions
If $$x^2 +2x -15 = -m$$, where x is an integer from -10 to 10,inclusive, what is the probability that m is greater than 0?
A. 2/7
B. 1/3
C. 7/20
D. 2/5
E. 3/7
[Reveal] Spoiler: OA

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Re: GRE Math Challenge #55 [#permalink]  05 May 2015, 23:51
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Re: GRE Math Challenge #55 [#permalink]  13 Aug 2015, 01:40
e
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Re: GRE Math Challenge #55 [#permalink]  13 Aug 2015, 04:18
Expert's post
Any intuitive explanation?
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Re: GRE Math Challenge #55 [#permalink]  13 Aug 2015, 06:09
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Explanation

B
[Reveal] Spoiler: Solution
Given that is x an integer from -10 and 10, inclusive (21 values) we need to find the probability that $$x^2 +2x -15$$is greater than zero, so the probability that $$x^2 +2x -15 >0$$.
Factorizing the expression becomes: $$(x+5)(3-x)>0$$ . The equation holds true for $$-5<x<3$$ . Therefore x is an integer that can take the following 7 values: -4, -3 , -2 ,-1 ,0 , 1 and 2.
Thus the probability is $$\frac{7}{21} = \frac{1}{3}$$ .

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Re: GRE Math Challenge #55 [#permalink]  11 Sep 2015, 10:49
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Re: GRE Math Challenge #55-If x^2 +2x -15 = -m [#permalink]  30 Jul 2016, 04:11
Can you give me solution for this. I'm unable to understand this concept.
TIA
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Re: GRE Math Challenge #55-If x^2 +2x -15 = -m [#permalink]  31 Jul 2016, 06:11
soumya, what you have shown in your solution is not correct, if m is positive, then x^2 + 2x -15 will be negative according to the equation. So for m to be positive, x^2 +2x -15 has to be negative, i.e x^2 +2x -15 < 0. After factorizing the left side, it comes as (x+5)(x-3)<0. After solving this inequality, -5<x<3, so x can be 7 values. And probability of this x out of 21 is 7/21, i.e the answer is 1/3 (B).
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Re: GRE Math Challenge #55-If x^2 +2x -15 = -m [#permalink]  12 Nov 2016, 23:45
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Re: GRE Math Challenge #55-If x^2 +2x -15 = -m [#permalink]  24 Dec 2016, 14:40
There could be 21 values of x ranging from -10 to 10.The values of x i.e. -4,-3,-2,-1,0,1,2 (total 7 values of x) could result m greater than zero. Hence , the probability is 7/21 or 1/3.
Re: GRE Math Challenge #55-If x^2 +2x -15 = -m   [#permalink] 24 Dec 2016, 14:40
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