November 20, 2018 November 20, 2018 09:00 AM PST 10:00 AM PST The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat. November 20, 2018 November 20, 2018 06:00 PM EST 07:00 PM EST What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50627

Question Stats:
42% (01:36) correct 58% (03:07) wrong based on 184 sessions
HideShow timer Statistics



Math Expert
Joined: 02 Sep 2009
Posts: 50627

Official Solution:If \(x^2 + 2x 15 = m\), where \(x\) is an integer from 10 and 10, inclusive, what is the probability that \(m\) is greater than zero? A. \(\frac{2}{7}\) B. \(\frac{1}{3}\) C. \(\frac{7}{20}\) D. \(\frac{2}{5}\) E. \(\frac{3}{7}\) Rearrange the given equation: \(x^22x+15=m\). Given that \(x\) is an integer from 10 and 10, inclusive (21 values) we need to find the probability that \(x^22x+15\) is greater than zero, so the probability that \(x^22x+15>0\). Factorize: \((x+5)(3x) \gt 0\). This equation holds true for \(5 \lt x \lt 3\). Since \(x\) is an integer then it can take the following 7 values: 4, 3, 2, 1, 0, 1, and 2. So, the probability is \(\frac{7}{21}=\frac{1}{3}\). Answer: B
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 11 Aug 2014
Posts: 5

Re: M2811
[#permalink]
Show Tags
08 Nov 2014, 11:24
Bunuel wrote: Official Solution:
If \(x^2 + 2x 15 = m\), where \(x\) is an integer from 10 and 10, inclusive, what is the probability that \(m\) is greater than zero?
A. \(\frac{2}{7}\) B. \(\frac{1}{3}\) C. \(\frac{7}{20}\) D. \(\frac{2}{5}\) E. \(\frac{3}{7}\)
Rearrange the given equation: \(x^22x+15=m\). Given that \(x\) is an integer from 10 and 10, inclusive (21 values) we need to find the probability that \(x^22x+15\) is greater than zero, so the probability that \(x^22x+15>0\). Factorize: \((x+5)(3x) \gt 0\). This equation holds true for \(5 \gt x \gt 3\). Since \(x\) is an integer then it can take the following 7 values: 4, 3, 2, 1, 0, 1, and 2. So, the probability is \(\frac{7}{21}=\frac{1}{3}\).
Answer: B This equation doesn't look right −5>x>3 . Function wouldn't hold true for values greater than 3.



Math Expert
Joined: 02 Sep 2009
Posts: 50627

Re: M2811
[#permalink]
Show Tags
09 Nov 2014, 05:09
parameswaranprasad wrote: Bunuel wrote: Official Solution:
If \(x^2 + 2x 15 = m\), where \(x\) is an integer from 10 and 10, inclusive, what is the probability that \(m\) is greater than zero?
A. \(\frac{2}{7}\) B. \(\frac{1}{3}\) C. \(\frac{7}{20}\) D. \(\frac{2}{5}\) E. \(\frac{3}{7}\)
Rearrange the given equation: \(x^22x+15=m\). Given that \(x\) is an integer from 10 and 10, inclusive (21 values) we need to find the probability that \(x^22x+15\) is greater than zero, so the probability that \(x^22x+15>0\). Factorize: \((x+5)(3x) \gt 0\). This equation holds true for \(5 \gt x \gt 3\). Since \(x\) is an integer then it can take the following 7 values: 4, 3, 2, 1, 0, 1, and 2. So, the probability is \(\frac{7}{21}=\frac{1}{3}\).
Answer: B This equation doesn't look right −5>x>3 . Function wouldn't hold true for values greater than 3. There was a typo. Should have been \(5 \lt x \lt 3\). Edited. Thank you.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 24 Jun 2015
Posts: 46

Re: M2811
[#permalink]
Show Tags
06 Jul 2015, 04:08
Bunuel wrote: parameswaranprasad wrote: Bunuel wrote: Official Solution:
If \(x^2 + 2x 15 = m\), where \(x\) is an integer from 10 and 10, inclusive, what is the probability that \(m\) is greater than zero?
A. \(\frac{2}{7}\) B. \(\frac{1}{3}\) C. \(\frac{7}{20}\) D. \(\frac{2}{5}\) E. \(\frac{3}{7}\)
Rearrange the given equation: \(x^22x+15=m\). Given that \(x\) is an integer from 10 and 10, inclusive (21 values) we need to find the probability that \(x^22x+15\) is greater than zero, so the probability that \(x^22x+15>0\). Factorize: \((x+5)(3x) \gt 0\). This equation holds true for \(5 \gt x \gt 3\). Since \(x\) is an integer then it can take the following 7 values: 4, 3, 2, 1, 0, 1, and 2. So, the probability is \(\frac{7}{21}=\frac{1}{3}\).
Answer: B This equation doesn't look right −5>x>3 . Function wouldn't hold true for values greater than 3. There was a typo. Should have been \(5 \lt x \lt 3\). Edited. Thank you. Hi Bunuel, Could you explain hoy do you factorize: (x+5)(3−x)>0. ? I have the doubt because x^2 is negative in the original equation x^22x+15. *** Also I thought that when inequalitie is >0 (Like this exercise), the solution for x are OUT ranges (x<5 and x>3), not IN ranges (5<x<3) . So I am confused in both things, how do you factorize the inequalitie and also why the solutions for the inequalitie are 5<x<3 (I already studied the inequalities section and I read what I mention in ***). I appreciate your help. Thanks a lot. Regards. Luis Navarro Looking for 700



Math Expert
Joined: 02 Sep 2009
Posts: 50627

Re: M2811
[#permalink]
Show Tags
06 Jul 2015, 06:53



Intern
Joined: 24 Jun 2015
Posts: 46

Re: M2811
[#permalink]
Show Tags
06 Jul 2015, 12:34
Bunuel wrote: luisnavarro wrote: Hi Bunuel,
Could you explain hoy do you factorize: (x+5)(3−x)>0. ? I have the doubt because x^2 is negative in the original equation x^22x+15.
*** Also I thought that when inequalitie is >0 (Like this exercise), the solution for x are OUT ranges (x<5 and x>3), not IN ranges (5<x<3) .
So I am confused in both things, how do you factorize the inequalitie and also why the solutions for the inequalitie are 5<x<3 (I already studied the inequalities section and I read what I mention in ***).
I appreciate your help.
Thanks a lot.
Regards.
Luis Navarro Looking for 700 My advice would be to brush up fundamentals before answering questions, especially such hard ones. Factoring Quadratics: http://www.purplemath.com/modules/factquad.htmSolving Quadratic Equations: http://www.purplemath.com/modules/solvquad.htmThanks a lot Bunuel, I appreciate your help. I read the information and now it is totally clear to me. Best regards. Luis Navarro Looking for 700.



Intern
Joined: 15 Apr 2015
Posts: 1

Re: M2811
[#permalink]
Show Tags
23 Apr 2017, 23:01
Hi Bunuel, why X<5 and X>3 is not considered?



Intern
Joined: 21 May 2017
Posts: 2

Re: M2811
[#permalink]
Show Tags
16 Jul 2017, 11:13
I have the same question, mkugan80 wrote: Hi Bunuel, why X<5 and X>3 is not considered?



Math Expert
Joined: 02 Sep 2009
Posts: 50627

Re: M2811
[#permalink]
Show Tags
16 Jul 2017, 20:07



Intern
Joined: 05 Oct 2018
Posts: 8

Re: M2811
[#permalink]
Show Tags
23 Oct 2018, 06:28
I tried to factor as written to (x+5)(x3) = m. I found 12 out of 21 possible values for making the left hand side positive and subtracted 12/21 from 1 and got answer E. I think my error was forgetting to subtract out the two cases for making m 0.
Thanks for the problem and explanation.



Senior Manager
Joined: 08 Jun 2013
Posts: 476
Location: India
GPA: 3.82
WE: Engineering (Other)

Re: M2811
[#permalink]
Show Tags
23 Oct 2018, 07:52
Bunuel wrote: If \(x^2 + 2x 15 = m\), where \(x\) is an integer from 10 and 10, inclusive, what is the probability that \(m\) is greater than zero?
A. \(\frac{2}{7}\) B. \(\frac{1}{3}\) C. \(\frac{7}{20}\) D. \(\frac{2}{5}\) E. \(\frac{3}{7}\) \(x^2 + 2x 15 = m\) i.e. \(x^2 + 2x +1 = 16m\) i.e \(m = 16  (x+1)^2\) For m>0 possible values x can take are 4, 3, 2, 1, 0, 1, 2, 3. Total values x can take 21 (i.e. 10 to 10) Required probability = 7/21 = 1/3
_________________
It seems Kudos button not working correctly with all my posts...
Please check if it is working with this post......
is it?....
Anyways...Thanks for trying



Intern
Status: All our dreams can come true, if we have the courage to pursue them
Joined: 03 Jul 2015
Posts: 20
Location: India
Concentration: Technology, Finance
WE: Information Technology (Computer Software)

Re: M2811
[#permalink]
Show Tags
23 Oct 2018, 13:24
Hi Bunuel, chetan2uI arrived at the correct answer but with a different approach/solution with the idea that we need to count the possible 'm' values but not 'x' values, as you did in OE . Not sure if this one is correct. Let me know if this is correct. Rewriting the given solution, (x+5)(x3)=m Now, substituting values of x from 10 to 10 gives m values as 65,48,33,20,9,0,7,12,15,16,15,12,7,0,9,20,33,36,65,84,105 respectively. Out of these, if we remove repetitions, Count of +ve values of m is 4 (7,12,15,16) Count of all m values is 12 So probability : 4/12 => 1/3If we don't remove repetitions, we get 7/21=>1/3










