December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. December 16, 2018 December 16, 2018 03:00 PM EST 04:00 PM EST Strategies and techniques for approaching featured GMAT topics
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 11 Feb 2011
Posts: 114

If p^2 – 13p + 40 = q, and p is a positive integer between 1
[#permalink]
Show Tags
Updated on: 01 Feb 2012, 13:00
Question Stats:
62% (02:19) correct 38% (02:39) wrong based on 593 sessions
HideShow timer Statistics
If p^2 – 13p + 40 = q, and p is a positive integer between 1 and 10, inclusive, what is the probability that q < 0? A. 1/10 B. 1/5 C. 2/5 D. 3/5 E. 3/10
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
target:810 out of 800!
Originally posted by AnkitK on 09 Mar 2011, 06:56.
Last edited by Bunuel on 01 Feb 2012, 13:00, edited 1 time in total.
Edited the question and added the OA




Math Expert
Joined: 02 Sep 2009
Posts: 51218

Re: ___probability____
[#permalink]
Show Tags
09 Mar 2011, 07:37
Question moved to PS subfourm. AnkitK wrote: if p^213p+40=q ,and p is a positive integer between 1 and 10 ,inclusive what is the probability that q<0? please suggest the answers guys.Also provide explanation.I would appreciate the efforts. thnkx in advance.! Welcome to Gmat Club. Please read and follow: howtoimprovetheforumsearchfunctionforothers99451.html So please: Provide answer choices for PS questions.Also please post PS questions in the PS subforum: gmatproblemsolvingps140/and DS questions in the DS subforum: gmatdatasufficiencyds141/ No posting of PS/DS questions is allowed in the main Math forum. Question should read: If p^2 – 13p + 40 = q, and p is a positive integer between 1 and 10, inclusive, what is the probability that q < 0?A. 1/10 B. 1/5 C. 2/5 D. 3/5 E. 3/10 \(p^213p+40=(p5)(p8)\) > \(p^213p+40<0\) for \(5<p<8\): Attachment:
MSP51419ef17g8chg8g5ch00002g8ag3h1ba7ibee0.gif [ 3.69 KiB  Viewed 9320 times ]
Now, as \(p\) is an integer then \(p^213p+40=q<0\) for two values of \(p\) out of 10: 6 and 7, which means that: \(P=\frac{2}{10}=\frac{1}{5}\). 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




Manager
Joined: 11 Feb 2011
Posts: 114

Re: ___probability____
[#permalink]
Show Tags
09 Mar 2011, 07:55
Thnkx a ton bunuel for quick solution.Excellent!! Cheers:P
_________________
target:810 out of 800!



Retired Moderator
Joined: 16 Nov 2010
Posts: 1425
Location: United States (IN)
Concentration: Strategy, Technology

Re: ___probability____
[#permalink]
Show Tags
10 Mar 2011, 00:32
(p5)(p8) = q p = 6 or 7 for this to be true, so 2/10 = 1/5
_________________
Formula of Life > Achievement/Potential = k * Happiness (where k is a constant)
GMAT Club Premium Membership  big benefits and savings



Intern
Joined: 04 May 2013
Posts: 44

Re: If p^2 – 13p + 40 = q, and p is a positive integer between 1
[#permalink]
Show Tags
08 Jul 2013, 18:23
P is any integer between 110, inclusive. Plug in the each values. It took me about 1:30 min to substitute all the values.
I did this because I can't visualize the graph of the equation other than I know it will be a parabola because of the X^2.
When p = 1, 2, 3, 4, 5, 8, 9, 10 the value of q is not negative. Only time q is negative is when p = 6 or 7. Probability 2/10 = 1/5 = B



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 611

Re: If p^2 – 13p + 40 = q, and p is a positive integer between 1
[#permalink]
Show Tags
08 Jul 2013, 20:49
jjack0310 wrote: P is any integer between 110, inclusive. Plug in the each values. It took me about 1:30 min to substitute all the values.
I did this because I can't visualize the graph of the equation other than I know it will be a parabola because of the X^2.
When p = 1, 2, 3, 4, 5, 8, 9, 10 the value of q is not negative. Only time q is negative is when p = 6 or 7. Probability 2/10 = 1/5 = B Just a thought: Even if you can't visualize the graph, just to save up some precious time, Once you factorize the quadratic as this : (p5)(p8); we have to find out the values of p, in the range [1,10] which will make it negative. Or (p5)(p8)<0 . Now this is only possible if (p5) and (p8) have opposite signs,i.e. I. p5>0 AND p8<0 \(\to\) p>5 AND p<8 \(\to\) 5<p<8 OR II.p5<0 and p8>0\(\to\) p<5 AND p>8\(\to\) Invalid range. Nonetheless, any logical way that gets you the valid answer is correct.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Manager
Joined: 29 Mar 2010
Posts: 120
Location: United States
Concentration: Finance, International Business
GPA: 2.54
WE: Accounting (Hospitality and Tourism)

Re: If p^2 – 13p + 40 = q, and p is a positive integer between 1
[#permalink]
Show Tags
16 Sep 2013, 00:22
Is this question not just easy enough and factor and then plug in numbers?? if: \(p^213p+40\) Factors out to (p8)(p5)=q, which can easily be done in your head very quickly. Then make a list of numbers that would give a negative result. It can only be 2 numbers 6 and 7, since anything over 7 yields either 0 or a positive number, and anything less than 6 yields a positive number, there can only be two cases which would satisfy the solution. Is making a graph really necessary? Making it 2/10 or 1/5
_________________
4/28 GMATPrep 42Q 36V 640



Intern
Joined: 27 Mar 2014
Posts: 5
Concentration: Accounting
GMAT Date: 09042014
GPA: 4

Re: If p^2 – 13p + 40 = q, and p is a positive integer between 1
[#permalink]
Show Tags
20 Aug 2014, 21:10
P(P13) plus 40 = q
while testing the values q is negative only when p is 7 or 6
thus the answer is 2/10 or 1/5



Senior Manager
Joined: 20 Aug 2015
Posts: 390
Location: India

If p^2 – 13p + 40 = q, and p is a positive integer between 1
[#permalink]
Show Tags
20 Nov 2015, 00:46
AnkitK wrote: If p^2 – 13p + 40 = q, and p is a positive integer between 1 and 10, inclusive, what is the probability that q < 0? A. 1/10 B. 1/5 C. 2/5 D. 3/5 E. 3/10 Given: \(p^2 – 13p + 40\) = q, 1< p < 10 Required: Probability of q < 0 \(p^2 – 13p + 40\) = (p 8)(p5) = q We need q < 0 Hence (p 5)(p8) < 0 Hence 5< p < 8. Only two integral values lie in the range: 6 and 7 Probability = 2/10 = 1/5 Option B. Solving an inequality with a less than sign: The value of the variable will be greater than the smaller value and smaller than the greater value. i.e. It will lie between the extremes.
Solving an inequality with a greater than sign: The value of the variable will be smaller than the smaller value and greater than the greater value. i.e. It can take all the values except the values in the range.



Intern
Joined: 07 Feb 2015
Posts: 13
GMAT 1: 650 Q46 V34 GMAT 2: 620 Q45 V30 GMAT 3: 700 Q45 V40

Re: If p^2 – 13p + 40 = q, and p is a positive integer between 1
[#permalink]
Show Tags
13 Jan 2017, 20:58
The quadratic equation could be expanded to (p5)(p8)=q If p is a member of the set [1,10], p could be one of the 10 choices. The equation (p5)(p8) will work out to < 0 for the range (5,8). The integers between 5 and 8 exclusive are 6 and 7.
The probability that q <0 = probability(p = 5 or p = 8 is selected) = 2/10 = 1/5



Director
Joined: 26 Oct 2016
Posts: 640
Location: United States
Concentration: Marketing, International Business
GPA: 4
WE: Education (Education)

Re: If p^2 – 13p + 40 = q, and p is a positive integer between 1
[#permalink]
Show Tags
13 Mar 2017, 02:44
Factor the quadratic: p^2 – 13p + 40 = q (p – 8)(p – 5) = q For p = 5 and p = 8, q = 0. Between p = 5 and p = 8, q has a negative sign, as (p – 8) is negative and (p – 5) is positive. With a total of 10 possible integer p values, only two (p = 6 and p = 7) fall in the range 5 < p < 8, so the probability is 2/10 or 1/5. The correct answer is B.
_________________
Thanks & Regards, Anaira Mitch



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4295
Location: United States (CA)

Re: If p^2 – 13p + 40 = q, and p is a positive integer between 1
[#permalink]
Show Tags
15 Mar 2017, 15:45
AnkitK wrote: If p^2 – 13p + 40 = q, and p is a positive integer between 1 and 10, inclusive, what is the probability that q < 0? A. 1/10 B. 1/5 C. 2/5 D. 3/5 E. 3/10 We can factor the given equation: p^2 – 13p + 40 = q (p  5)(p  8) = q We see that in order for q to be negative, either (p  5) is negative and (p  8) is positive OR (p  5) is positive and (p  8) is negative. Analyzing our expression a bit further, we see that it only produces a negative product when p = 6 and p = 7. Thus, the probability that q < 0 is 2/10 = 1/5. Answer: B
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Intern
Joined: 23 Jul 2013
Posts: 15

Re: If p^2 – 13p + 40 = q, and p is a positive integer between 1
[#permalink]
Show Tags
22 Jul 2018, 18:41
Bunuel wrote: Question moved to PS subfourm. Question should read: If p^2 – 13p + 40 = q, and p is a positive integer between 1 and 10, inclusive, what is the probability that q < 0?A. 1/10 B. 1/5 C. 2/5 D. 3/5 E. 3/10 \(p^213p+40=(p5)(p8)\) > \(p^213p+40<0\) for \(5<p<8\): Attachment: MSP51419ef17g8chg8g5ch00002g8ag3h1ba7ibee0.gif Now, as \(p\) is an integer then \(p^213p+40=q<0\) for two values of \(p\) out of 10: 6 and 7, which means that: \(P=\frac{2}{10}=\frac{1}{5}\). Answer: B. Thanks for showing the explanation using the parabola Bunuel. Was curious to understand how will it look like if for eg the question put the condition of q>0. In that case, the quadratic would turn out to be (p8)(p5) > 0. In such a case the parabola will open downward but then how do we make this out as the constant a (in a*p^2) is in any case +ve..




Re: If p^2 – 13p + 40 = q, and p is a positive integer between 1 &nbs
[#permalink]
22 Jul 2018, 18:41






