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GRE Math Challenge #55If x^2 +2x 15 = m [#permalink]
28 Feb 2015, 02:28
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43% (02:47) wrong based on 16 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
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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
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Re: GRE Math Challenge #55 [#permalink]
13 Aug 2015, 04:18
Any intuitive explanation?
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Re: GRE Math Challenge #55 [#permalink]
13 Aug 2015, 06:09
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Explanation BGiven 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: \((x+5)(3x)>0\) . 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 #55If 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 #55If 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)(x3)<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 #55If x^2 +2x 15 = m [#permalink]
12 Nov 2016, 23:45
The answer is (B).



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Re: GRE Math Challenge #55If x^2 +2x 15 = m [#permalink]
24 Dec 2016, 14:40
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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.



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Re: GRE Math Challenge #55If x^2 +2x 15 = m [#permalink]
04 Jan 2019, 23:07
mosur7 wrote: Can you give me solution for this. I'm unable to understand this concept. TIA Think of it this way first, there are 21 numbers between 10 and 10, since 0 is included, if youre not sure why, use the arithmetic series formula to be sure 10= 10 +1(n1) 20=n1 21 = n that being taken care of... we have x^2+2x15= m they ask what is the change that m is greater than 0. if thats the case, then m is a negative number, which is less than zero, rewrite the inequality like this. x^2+2x15 <0 factor (x3)(x+5)<0 the solutions we see are 3 and 5 that means the solution is between 3 and negative 5, non inclusive. then the solutions can be any integer between 3 and 5, which are 2,1,0,1,2,3,4. thats seven numbers out of 21 possible solutions. so 7/21= 1/3 the answer is B



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Re: GRE Math Challenge #55If x^2 +2x 15 = m [#permalink]
05 Jan 2019, 05:06
soumya1989 wrote: 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 Two ways.. (I) Also explained above.. \(x^2+2x15=m.....x^2+5x3x15=m........(x+5)(x3)=m\) Now x can take any value from 10 to 10, but m >0. When x is 5 or 3, m is 0 as roots of quadratic equation \((x+5)(x3)=0\) are 5 and 3. Now if we take any value less than 5, both (x+5) and (x3) will be negative and their product will be positive that is m>0...m<0 Similarly, if we take any value more than 3, both (x+5) and (x3) will be positive and their product will be positive that is m>0...m<0 However for values between 5 and 3, (x+5) will be positive and (x3) will be negative and their product will be negative.. Thus m<0....m>0 So, the values 4, 3, 2, 1, 0, 1, 2 will fit in.. so 7 values out of 21 values will give a probability of \(\frac{7}{21}=\frac{1}{3}\) (II) Next could be \(x^2+2x15=m.....x^2+2x=15m........(x)(x+2)=15m......m=15x(x+2)\) So, sum of two consecutive even integers should be less than 15 for m>0.. Now, 5*3 = 15 so x>5 AND 3*5=15, so x<3 5<x<3... Rest same as above for probability B
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Some useful Theory. 1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressionsarithmeticgeometricandharmonic11574.html#p27048 2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effectsofarithmeticoperationsonfractions11573.html?sid=d570445335a783891cd4d48a17db9825 3. Remainders : https://greprepclub.com/forum/remainderswhatyoushouldknow11524.html 4. Number properties : https://greprepclub.com/forum/numberpropertyallyourequire11518.html 5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolutemodulusabetterunderstanding11281.html




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