It is currently 21 Apr 2019, 12:47
My Tests

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

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

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Director
Director
User avatar
Joined: 16 May 2014
Posts: 595
GRE 1: Q165 V161
Followers: 94

Kudos [?]: 461 [0], given: 64

GRE Math Challenge #55-If x^2 +2x -15 = -m [#permalink] New post 28 Feb 2015, 02:28
Expert's post
00:00

Question Stats:

56% (01:11) correct 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
[Reveal] Spoiler: OA

_________________

My GRE Resources
Free GRE resources | GRE Prep Club Quant Tests
If you find this post helpful, please press the kudos button to let me know ! :)

Manager
Manager
Joined: 17 Feb 2015
Posts: 107
Followers: 3

Kudos [?]: 28 [0], given: 6

Re: GRE Math Challenge #55 [#permalink] New post 05 May 2015, 23:51
C
Intern
Intern
Joined: 12 Aug 2015
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: GRE Math Challenge #55 [#permalink] New post 13 Aug 2015, 01:40
e
Director
Director
User avatar
Joined: 16 May 2014
Posts: 595
GRE 1: Q165 V161
Followers: 94

Kudos [?]: 461 [0], given: 64

Re: GRE Math Challenge #55 [#permalink] New post 13 Aug 2015, 04:18
Expert's post
Any intuitive explanation?
_________________

My GRE Resources
Free GRE resources | GRE Prep Club Quant Tests
If you find this post helpful, please press the kudos button to let me know ! :)

1 KUDOS received
Director
Director
User avatar
Joined: 16 May 2014
Posts: 595
GRE 1: Q165 V161
Followers: 94

Kudos [?]: 461 [1] , given: 64

Re: GRE Math Challenge #55 [#permalink] New post 13 Aug 2015, 06:09
1
This post received
KUDOS
Expert's post

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 \(\frac{7}{21} = \frac{1}{3}\) .

_________________

My GRE Resources
Free GRE resources | GRE Prep Club Quant Tests
If you find this post helpful, please press the kudos button to let me know ! :)

Intern
Intern
Joined: 11 Sep 2015
Posts: 5
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: GRE Math Challenge #55 [#permalink] New post 11 Sep 2015, 10:49
C
Intern
Intern
Joined: 15 Mar 2016
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: GRE Math Challenge #55-If x^2 +2x -15 = -m [#permalink] New post 30 Jul 2016, 04:11
Can you give me solution for this. I'm unable to understand this concept.
TIA
Intern
Intern
Joined: 03 Jun 2016
Posts: 37
Followers: 0

Kudos [?]: 27 [0], given: 4

Re: GRE Math Challenge #55-If x^2 +2x -15 = -m [#permalink] New post 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).
Intern
Intern
Joined: 04 May 2016
Posts: 6
Followers: 0

Kudos [?]: 2 [0], given: 3

Re: GRE Math Challenge #55-If x^2 +2x -15 = -m [#permalink] New post 12 Nov 2016, 23:45
The answer is (B).
1 KUDOS received
Intern
Intern
Joined: 04 May 2016
Posts: 6
Followers: 0

Kudos [?]: 2 [1] , given: 3

Re: GRE Math Challenge #55-If x^2 +2x -15 = -m [#permalink] New post 24 Dec 2016, 14:40
1
This post received
KUDOS
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.
Manager
Manager
User avatar
Joined: 01 Nov 2018
Posts: 87
Followers: 0

Kudos [?]: 43 [0], given: 22

Re: GRE Math Challenge #55-If x^2 +2x -15 = -m [#permalink] New post 04 Jan 2019, 23:07
Expert's post
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(n-1)
20=n-1
21 = n

that being taken care of...

we have x^2+2x-15= -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+2x-15 <0

factor

(x-3)(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
Supreme Moderator
Joined: 01 Nov 2017
Posts: 370
Followers: 5

Kudos [?]: 110 [0], given: 4

Re: GRE Math Challenge #55-If x^2 +2x -15 = -m [#permalink] New post 05 Jan 2019, 05:06
Expert's post
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..
\(x^2+2x-15=-m.....x^2+5x-3x-15=-m........(x+5)(x-3)=-m\)
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 \((x+5)(x-3)=0\) are -5 and 3.
Now if we take any value less than -5, both (x+5) and (x-3) 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 (x-3) 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 (x-3) 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
\(x^2+2x-15=-m.....x^2+2x=15-m........(x)(x+2)=15-m......m=15-x(x+2)\)
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
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Re: GRE Math Challenge #55-If x^2 +2x -15 = -m   [#permalink] 05 Jan 2019, 05:06
Display posts from previous: Sort by

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

  Question banks Downloads My Bookmarks Reviews Important topics  


GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.