Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 22 Apr 2011
Posts: 145
Schools: Mccombs business school, Mays business school, Rotman Business School,

Does the equation y = (x – p)(x – q) intercept the xaxis at
[#permalink]
Show Tags
09 Jun 2012, 17:24
Question Stats:
77% (01:03) correct 23% (01:15) wrong based on 564 sessions
HideShow timer Statistics
Does the equation y = (x – p)(x – q) intercept the xaxis at the point (2,0)? (1) pq = 8 (2) 2 – p = q
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
some people are successful, because they have been fortunate enough and some people earn success, because they have been determined.....
please press kudos if you like my post.... i am begging for kudos...lol




Math Expert
Joined: 02 Sep 2009
Posts: 50003

Re: Does the equation y = (x – p)(x – q) intercept the xaxis at
[#permalink]
Show Tags
10 Jun 2012, 02:13




Senior Manager
Joined: 13 Jan 2012
Posts: 286
Weight: 170lbs
GMAT 1: 740 Q48 V42 GMAT 2: 760 Q50 V42
WE: Analyst (Other)

Re: coordinate
[#permalink]
Show Tags
09 Jun 2012, 18:19
y=(xp)(xq)
Basically, when y=0 and x=2, does equation balance?
0 = (2p)(2q) 0 = 42q2p+qp
In order to know this, we need to know q & p
1) pq = 8 This only tell us p or q, but not both.
[strike]AD[/strike] BCE
2) 2  p = q This only tell us p or q, but not both.
1+2) We can determine both p & q through these two independent equations.
Answer is C.



Senior Manager
Joined: 13 Jan 2012
Posts: 286
Weight: 170lbs
GMAT 1: 740 Q48 V42 GMAT 2: 760 Q50 V42
WE: Analyst (Other)

Re: Does the equation y = (x – p)(x – q) intercept the xaxis at
[#permalink]
Show Tags
10 Jun 2012, 02:15
Bunuel wrote: Does the equation y = (x – p)(x – q) intercept the xaxis at the point (2,0)?
xintercepts of the graph \(y=(xp)(xq)\) is the values of \(x\) for which \((xp)(xq)=0\). So, the xintercepts are \((p, 0)\) and \((q, 0)\). The question basically asks whether either \(p\) or \(q\) equals 2. (1) pq = 8. Not sufficient to say whether p or q equals 2. (2) 2 – p = q. Not sufficient to say whether p or q equals 2.
(1)+(2) Solving \(pq=8\) and \(2p=q\) gives us that either \(p=4\) and \(q=2\) OR \(p=2\) and \(q=4\). In ether case one of the unknowns is 2, so \(y=(xp)(xq)\) intercepts the xaxis at the point (2,0). Sufficient.
Answer: C.
Hope it's clear. Damn, you're good! Was my approach right at all? Sometimes I wish a had an identical twin who could just get a 50 on my Quant section for me while I do the Verbal section, haha.



Manager
Joined: 28 Dec 2012
Posts: 104
Location: India
Concentration: Strategy, Finance
WE: Engineering (Energy and Utilities)

Does the equation y = (x – p)(x – q) intercept the xaxis at the
[#permalink]
Show Tags
13 Jan 2013, 12:30
C. If y = 0, this reduces to a quadratic equation. sum of roots = 2, product of roots = 8. Thus the roots are 4 and 2. Line passes through (4,0) and (2,0) Hence the answer is NO
_________________
Impossibility is a relative concept!!



Intern
Joined: 02 Jan 2015
Posts: 32
GMAT Date: 02082015
GPA: 3.7
WE: Management Consulting (Consulting)

Re: Does the equation y = (x – p)(x – q) intercept the xaxis at
[#permalink]
Show Tags
30 May 2015, 06:51
You can also distribute the given equation straight away: y = x^2  xq  px + pq This can be factored to: y = x^2  x(p+q) + pq From this, it's easy to recognise that if we know 'p + q' AND 'pq' then we know the line's equation, and can figure out the answer. No further calculation is necessary. As is often the case with Manhattan GMAT questions, rearranging the question is heavily rewarded.



Intern
Joined: 27 Apr 2015
Posts: 8

Why is Statement (1) NOT sufficient? "Does the equation y = ( x – p)(
[#permalink]
Show Tags
31 May 2015, 19:18
Does the equation y = ( x – p)( x – q) intercept the xaxis at the point (2,0)? (1) pq = 8 (2) 2 – p = q The answer is but: My analysis tells me that (1) should be sufficient based on these steps: Plug in (2,0) in the equation and expand: 0 = (2  p)(2  q) 0 = 2^2  2q  2p + pq Now, sub in (1) pq = 8 0 = 4  2q  2p 8 4 = 2q  2p 2 = q + p Hence: 2  p = q > same as statement (2)... so if I'm able to derive statement (2) just using information in (1), can't I plug "2 = q + p" into pq = 8 and solve? Isn't this the same as using both statements except you can only use the first one to get the info in the second, thus making (1) sufficient? What am I missing here? Kudos for any help please!



Veritas Prep GMAT Instructor
Joined: 23 Oct 2013
Posts: 144

Re: Why is Statement (1) NOT sufficient? "Does the equation y = ( x – p)(
[#permalink]
Show Tags
31 May 2015, 23:24
Great question. The problem is that you are presupposing the truth of what you are trying to figure out. The fact that statement 2 equals what you get when you manipulate statement 1 means that together they prove that the equation does intercept the xaxis at this point. Think about what you did, but using the random point (4,0). That would give you: 0 = (4p)(4q) 0 = 4^2  4q  4p + pq Sub in (1) 0 = 16  4q  4p  8 8 = 4q  4p 2 = q + p 2p = q This now leaves you with a different equation, when we assume that the equation intercepts at point (4,0). Therefore the fact that this equation equals what is given in statement 2 when you plug in (2,0) indicates that the equation intercepts at the point (2,0), and thus you need both statements in order to know that. I hope this helps!
_________________
Brandon Veritas Prep  GMAT Instructor
If you found this post helpful, please give me kudos!!!
Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.
Veritas Prep Reviews



Intern
Joined: 24 Jun 2014
Posts: 49
Concentration: Social Entrepreneurship, Nonprofit

Re: Why is Statement (1) NOT sufficient? "Does the equation y = ( x – p)(
[#permalink]
Show Tags
31 May 2015, 23:32
Hello,
Statement(2) is derived while substituting answer in Statement (1). So we are assuming y=(xp) (xq) at (2,0) to be true.It will only be possible if and only if Statement (2) is true as you have already derived. Hence we need both .



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2069

Re: Why is Statement (1) NOT sufficient? "Does the equation y = ( x – p)(
[#permalink]
Show Tags
31 May 2015, 23:47
Hi torontoclub15, When you say that statementI is sufficient to answer the question, you mean that information given in the question statement along with the information given in stI is adequate to give you a unique answer. When you are analyzing any one of the statements, pretend the other statement to be nonexistent to avoid carrying over of the information. Any dependency on the other statement is never going to give you the answer as A or B. In this question, since you are putting (2,0) in the equation ,you are assuming that the equation intercepts the xaxis at (2,0). This assumption and using the information given in stI results in the equation 2 p = q. For the equation to intercept the xaxis at (2,0), the above equation of 2  p = q should be true. But you don't know the values of p and q or p + q and hence can't say for sure if the equation is true or not. Hence you can't say if the equation intercepts the xaxis at (2,0). Similarly for stII, if you assume that the equation passes through (2,0) and use the information given in stII you would end up at pq= 8. Again using stII alone you can't say for sure if pq = 8?. Hence stII also is not sufficient to answer the question. You would observe that both the statements need each other to give you a definite answer if the equation passes through (2,0). Hence the answer has to be C. For avoiding such errors we recommend the following 5step process to solve a DS question StepI: List down the given infoStepII: Analyze the given infoStepIII: Analyze statementI independentlyStepIV: Analyze statementII independentlyStepV Combine both statements if neededFollowing these steps have the following advantages: a. You analyze the question statement to narrow down to the exact information you are looking in the statements. This helps in avoiding unnecessary analysis.
b. By analyzing statements independently you make sure that there is no carrying over of the information from one statement to the other before you reach stepV
Hope this helps Regards Harsh
_________________
Register for free sessions Number Properties  Algebra Quant Workshop
Success Stories Guillermo's Success Story  Carrie's Success Story
Ace GMAT quant Articles and Question to reach Q51  Question of the week
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2 Word Problems – Percentage 1  Percentage 2  Time and Work 1  Time and Work 2  Time, Speed and Distance 1  Time, Speed and Distance 2 Advanced Topics Permutation and Combination 1  Permutation and Combination 2  Permutation and Combination 3  Probability Geometry Triangles 1  Triangles 2  Triangles 3  Common Mistakes in Geometry Algebra Wavy line  Inequalities Practice Questions Number Properties 1  Number Properties 2  Algebra 1  Geometry  Prime Numbers  Absolute value equations  Sets
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com



Manager
Joined: 12 Nov 2014
Posts: 63

Re: Why is Statement (1) NOT sufficient? "Does the equation y = ( x – p)(
[#permalink]
Show Tags
31 May 2015, 23:49
torontoclub15 wrote: Does the equation y = ( x – p)( x – q) intercept the xaxis at the point (2,0)? (1) pq = 8 (2) 2 – p = q The answer is but: My analysis tells me that (1) should be sufficient based on these steps: Plug in (2,0) in the equation and expand: 0 = (2  p)(2  q) 0 = 2^2  2q  2p + pq Now, sub in (1) pq = 8 0 = 4  2q  2p 8 4 = 2q  2p 2 = q + p Hence: 2  p = q > same as statement (2)... so if I'm able to derive statement (2) just using information in (1), can't I plug "2 = q + p" into pq = 8 and solve? Isn't this the same as using both statements except you can only use the first one to get the info in the second, thus making (1) sufficient? What am I missing here? Kudos for any help please! Hi, For Data Sufficiency questions, you are not required to find answers. You just have to tell whether the statements given are sufficient to answer the questions or not. At first you have to treat each statements independently. You should not take any information from statement 2 when you are trying to figure out if statement 1 alone is sufficient and vice versa. (Basically you have to assume the other statement is not there when you are solving for one statement alone.) If each statement alone does not give you answer then you have to combine both and check. Please look at the answer choices: A. Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question. B. Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question C. Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient D. Each statement alone is sufficient E. Statements 1 and 2 together are not sufficient. What is the question here? Does the equation y = ( x – p)( x – q) intercept the xaxis at the point (2,0)? You are required to tell if the statements given are sufficient to answer the questions. i.e. y = x^2  x(p+q) + pq . You need information about both 'p+q' and 'pq' to solve for this. Take statement 1 alone. Are you able to answer the above question just by taking statement 1 alone.? No. Because you know pq = 8.But you don't know what is p+q. When you are checking for statement 1 alone you should not take any info from statement 2. Take statement 2 alone. Are you able to answer the above question just by taking statement 2 alone.? No.Because you know p+ q = 2 But you don't know what is pq. When you are checking for statement 2 alone you should not take any info from statement 1. When each statement alone is not giving you any answer. You have to combine both. Now you will see that there is information about p+q AND pq which is sufficient to answer the question. Hope you understood.
_________________
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Kindly press Kudos if the explanation is clear. Thank you Ambarish



Director
Joined: 10 Mar 2013
Posts: 518
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

Does the equation y = (x – p)(x – q) intercept the xaxis at
[#permalink]
Show Tags
01 Dec 2015, 02:26
alchemist009 wrote: Does the equation y = (x – p)(x – q) intercept the xaxis at the point (2,0)? (1) pq = 8 (2) 2 – p = q Question: \((x – p)(x – q) = x^2x(p+q)+pq and x=2 and y=0 > 42(p+q)+pq=0 > 2(p+q)=4+pq ?\) (1) pq=8 > 2(p+q)=4, p+q=2 Not sufficient (2) p+q=2 > 42*(2)+pq=0, pq=8 Not sufficient (1)+(2) 42*(2)+(8)=0 Yes Answer C
_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.
Share some Kudos, if my posts help you. Thank you !
800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660



Manager
Joined: 09 Oct 2015
Posts: 234

Re: Does the equation y = (x – p)(x – q) intercept the xaxis at
[#permalink]
Show Tags
01 Dec 2015, 06:52
Bunuel wrote: Does the equation y = (x – p)(x – q) intercept the xaxis at the point (2,0)?
xintercepts of the graph \(y=(xp)(xq)\) is the values of \(x\) for which \((xp)(xq)=0\). So, the xintercepts are \((p, 0)\) and \((q, 0)\). The question basically asks whether either \(p\) or \(q\) equals 2. (1) pq = 8. Not sufficient to say whether p or q equals 2. (2) 2 – p = q. Not sufficient to say whether p or q equals 2.
(1)+(2) Solving \(pq=8\) and \(2p=q\) gives us that either \(p=4\) and \(q=2\) OR \(p=2\) and \(q=4\). In ether case one of the unknowns is 2, so \(y=(xp)(xq)\) intercepts the xaxis at the point (2,0). Sufficient.
Answer: C.
Hope it's clear. Hi BunuelWhen i do a quad equation, i get (x+4)(x2)=0 this means that either x=2 or 4 how can we conclude it to be sufficient, as it could be either 2,0 or 4,0 thanks



Math Expert
Joined: 02 Sep 2009
Posts: 50003

Re: Does the equation y = (x – p)(x – q) intercept the xaxis at
[#permalink]
Show Tags
01 Dec 2015, 07:45
rahulkashyap wrote: Bunuel wrote: Does the equation y = (x – p)(x – q) intercept the xaxis at the point (2,0)?
xintercepts of the graph \(y=(xp)(xq)\) is the values of \(x\) for which \((xp)(xq)=0\). So, the xintercepts are \((p, 0)\) and \((q, 0)\). The question basically asks whether either \(p\) or \(q\) equals 2. (1) pq = 8. Not sufficient to say whether p or q equals 2. (2) 2 – p = q. Not sufficient to say whether p or q equals 2.
(1)+(2) Solving \(pq=8\) and \(2p=q\) gives us that either \(p=4\) and \(q=2\) OR \(p=2\) and \(q=4\). In ether case one of the unknowns is 2, so \(y=(xp)(xq)\) intercepts the xaxis at the point (2,0). Sufficient.
Answer: C.
Hope it's clear. Hi BunuelWhen i do a quad equation, i get (x+4)(x2)=0 this means that either x=2 or 4 how can we conclude it to be sufficient, as it could be either 2,0 or 4,0 thanks The question asks whether either \(p\) or \(q\) equals 2. Solving gives two solution sets: 1. p=4 and q=2. Or: 2. p=2 and q=−4. So, in the first case q=2 and in the second case p=2.
_________________
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: 09 Oct 2015
Posts: 234

Re: Does the equation y = (x – p)(x – q) intercept the xaxis at
[#permalink]
Show Tags
01 Dec 2015, 09:06
Bunuel wrote: rahulkashyap wrote: BunuelBut the solution is for "x" I don't understand what you mean by this. Can you please reread the solutions given above? Well, the equation is : y=(x−p)(x−q) to find the x intercept, I plugged in y=0 this gives me the equation x^2  qx  px +pq= 0 this, on using (1) and (2) i get : x^2 + 2x  8 =0 on solving this quad eq, we get : (x+4)(x2)= 0 so, x=2 or 4 from solving the quad equation therefore, (2,0) or (4,0)



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6390
GPA: 3.82

Re: Does the equation y = (x – p)(x – q) intercept the xaxis at
[#permalink]
Show Tags
03 Dec 2015, 08:38
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. Does the equation y = (x – p)(x – q) intercept the xaxis at the point (2,0)? (1) pq = 8 (2) 2 – p = q If we modify the qusetion, 0=(2p)(2q)? and 0=42p2q+pq?. There are 2 variables (p,q) and 2 equations are given by the 2 conditions, so there is high chance (C) will be the answer. Looking at the conditions together, 0=42(p+q)+pq? > 0=42(2)8? > 0=4+48=0? This answers the question 'yes' and is therefore sufficient and the answer becomes (C). For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



Manager
Joined: 17 Jun 2015
Posts: 220
GMAT 1: 540 Q39 V26 GMAT 2: 680 Q46 V37

Re: Does the equation y = (x – p)(x – q) intercept the xaxis at
[#permalink]
Show Tags
17 Dec 2015, 10:31
Solving the given equation takes from of a quadratic equation i.e the equation of a parabola. A parabola meets the x axis and in order to find so we need the entire quadratic equation. The equation looks as this X^2  (P+Q)X + PQ We get these two components from Statements 1 and 2. Hence, C Also, this equation is in the form of sum of roots and product of roots.
_________________
Fais de ta vie un rêve et d'un rêve une réalité



Director
Joined: 12 Nov 2016
Posts: 749
Location: United States
GPA: 2.66

Re: Does the equation y = (x – p)(x – q) intercept the xaxis at
[#permalink]
Show Tags
17 Jun 2017, 09:25
alchemist009 wrote: Does the equation y = (x – p)(x – q) intercept the xaxis at the point (2,0)? (1) pq = 8 (2) 2 – p = q Statement 1 pq= 8 P and Q could take on multiple values and these values would affect whether x intercepts the x axis at point (2,0) 4, 2 8, 1 8, 1 etc Statement 2 There are two variables; no ratio is given, no criteria is given cannot solve insuff Statement 1 & 2 With both statements we can calculate the exact values of p and q Thus "C"



Intern
Joined: 05 Sep 2018
Posts: 5

Re: Does the equation y = (x – p)(x – q) intercept the xaxis at
[#permalink]
Show Tags
03 Oct 2018, 19:37
Bunuel wrote: rahulkashyap wrote: Bunuel wrote: Does the equation y = (x – p)(x – q) intercept the xaxis at the point (2,0)?
xintercepts of the graph \(y=(xp)(xq)\) is the values of \(x\) for which \((xp)(xq)=0\). So, the xintercepts are \((p, 0)\) and \((q, 0)\). The question basically asks whether either \(p\) or \(q\) equals 2. (1) pq = 8. Not sufficient to say whether p or q equals 2. (2) 2 – p = q. Not sufficient to say whether p or q equals 2.
(1)+(2) Solving \(pq=8\) and \(2p=q\) gives us that either \(p=4\) and \(q=2\) OR \(p=2\) and \(q=4\). In ether case one of the unknowns is 2, so \(y=(xp)(xq)\) intercepts the xaxis at the point (2,0). Sufficient.
Answer: C.
Hope it's clear. When i do a quad equation, i get (x+4)(x2)=0 this means that either x=2 or 4 how can we conclude it to be sufficient, as it could be either 2,0 or 4,0 thanks The question asks whether either \(p\) or \(q\) equals 2. Solving gives two solution sets: 1. p=4 and q=2. Or: 2. p=2 and q=−4. So, in the first case q=2 and in the second case p=2. Hi Bunuel, Hope you're well. I'm in the same boat, I solved the equation by factoring & got x=2 and x=4. How would I conclude that it's sufficient if neither p nor q is identified? (My thinking) "If we're looking at (2,0) to be an intercept of the initial equation  the equation can be altered to look like this => 0=(2p)(2q), where as long as p or q is 2, it would satisfy". However, I'm struggling to see how it would be C when all I did was find x? Thanks in advance!




Re: Does the equation y = (x – p)(x – q) intercept the xaxis at &nbs
[#permalink]
03 Oct 2018, 19:37






