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# Does the equation y = (x – p)(x – q) intercept the x-axis at

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Does the equation y = (x – p)(x – q) intercept the x-axis at  [#permalink]

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09 Jun 2012, 17:24
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Does the equation y = (x – p)(x – q) intercept the x-axis at the point (2,0)?

(1) pq = -8

(2) -2 – p = q

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Re: Does the equation y = (x – p)(x – q) intercept the x-axis at  [#permalink]

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10 Jun 2012, 02:13
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Does the equation y = (x – p)(x – q) intercept the x-axis at the point (2,0)?

x-intercepts of the graph $$y=(x-p)(x-q)$$ is the values of $$x$$ for which $$(x-p)(x-q)=0$$. So, the x-intercepts 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 $$-2-p=q$$ 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 $$y=(x-p)(x-q)$$ intercepts the x-axis at the point (2,0). Sufficient.

Hope it's clear.
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09 Jun 2012, 18:19
1
y=(x-p)(x-q)

Basically, when y=0 and x=2, does equation balance?

0 = (2-p)(2-q)
0 = 4-2q-2p+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.

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.

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Re: Does the equation y = (x – p)(x – q) intercept the x-axis at  [#permalink]

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10 Jun 2012, 02:15
1
Bunuel wrote:
Does the equation y = (x – p)(x – q) intercept the x-axis at the point (2,0)?

x-intercepts of the graph $$y=(x-p)(x-q)$$ is the values of $$x$$ for which $$(x-p)(x-q)=0$$. So, the x-intercepts 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 $$-2-p=q$$ 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 $$y=(x-p)(x-q)$$ intercepts the x-axis at the point (2,0). Sufficient.

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.
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Does the equation y = (x – p)(x – q) intercept the x-axis at the  [#permalink]

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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)
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Re: Does the equation y = (x – p)(x – q) intercept the x-axis at  [#permalink]

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30 May 2015, 06:51
2
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.
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Why is Statement (1) NOT sufficient? "Does the equation y = ( x – p)(  [#permalink]

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31 May 2015, 19:18
Does the equation y = ( x – p)( x – q) intercept the x-axis at the point (2,0)?

(1) pq = -8

(2) -2 – p = q

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?

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Re: Why is Statement (1) NOT sufficient? "Does the equation y = ( x – p)(  [#permalink]

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31 May 2015, 23:24
2
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 x-axis at this point. Think about what you did, but using the random point (4,0). That would give you:

0 = (4-p)(4-q)
0 = 4^2 - 4q - 4p + pq
Sub in (1)
0 = 16 - 4q - 4p - 8
-8 = -4q - 4p
2 = q + p
2-p = 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!
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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 1 Hello, Statement(2) is derived while substituting answer in Statement (1). So we are assuming y=(x-p) (x-q) 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 . e-GMAT 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 1 Hi torontoclub15, When you say that statement-I is sufficient to answer the question, you mean that information given in the question statement along with the information given in st-I is adequate to give you a unique answer. When you are analyzing any one of the statements, pretend the other statement to be non-existent 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 x-axis at (2,0). This assumption and using the information given in st-I results in the equation -2 -p = q. For the equation to intercept the x-axis 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 x-axis at (2,0). Similarly for st-II, if you assume that the equation passes through (2,0) and use the information given in st-II you would end up at pq= -8. Again using st-II alone you can't say for sure if pq = -8?. Hence st-II 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 5-step process to solve a DS question Step-I: List down the given info Step-II: Analyze the given info Step-III: Analyze statement-I independently Step-IV: Analyze statement-II independently Step-V Combine both statements if needed Following 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 step-V 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 | Statistics-1 | Statistics-2 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.e-gmat.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 1 torontoclub15 wrote: Does the equation y = ( x – p)( x – q) intercept the x-axis 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 x-axis 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 GMAT 1: 580 Q46 V24 GPA: 3.88 WE: Information Technology (Consulting) Does the equation y = (x – p)(x – q) intercept the x-axis at [#permalink] ### Show Tags 01 Dec 2015, 02:26 alchemist009 wrote: Does the equation y = (x – p)(x – q) intercept the x-axis at the point (2,0)? (1) pq = -8 (2) -2 – p = q Question: $$(x – p)(x – q) = x^2-x(p+q)+pq and x=2 and y=0 --> 4-2(p+q)+pq=0 --> 2(p+q)=4+pq ?$$ (1) pq=-8 -> 2(p+q)=-4, p+q=-2 Not sufficient (2) p+q=-2 -> 4-2*(-2)+pq=0, pq=-8 Not sufficient (1)+(2) 4-2*(-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 x-axis at [#permalink] ### Show Tags 01 Dec 2015, 06:52 Bunuel wrote: Does the equation y = (x – p)(x – q) intercept the x-axis at the point (2,0)? x-intercepts of the graph $$y=(x-p)(x-q)$$ is the values of $$x$$ for which $$(x-p)(x-q)=0$$. So, the x-intercepts 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 $$-2-p=q$$ 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 $$y=(x-p)(x-q)$$ intercepts the x-axis at the point (2,0). Sufficient. Answer: C. Hope it's clear. Hi Bunuel When i do a quad equation, i get (x+4)(x-2)=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 x-axis at [#permalink] ### Show Tags 01 Dec 2015, 07:45 rahulkashyap wrote: Bunuel wrote: Does the equation y = (x – p)(x – q) intercept the x-axis at the point (2,0)? x-intercepts of the graph $$y=(x-p)(x-q)$$ is the values of $$x$$ for which $$(x-p)(x-q)=0$$. So, the x-intercepts 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 $$-2-p=q$$ 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 $$y=(x-p)(x-q)$$ intercepts the x-axis at the point (2,0). Sufficient. Answer: C. Hope it's clear. Hi Bunuel When i do a quad equation, i get (x+4)(x-2)=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. _________________ Manager Joined: 09 Oct 2015 Posts: 234 Re: Does the equation y = (x – p)(x – q) intercept the x-axis at [#permalink] ### Show Tags 01 Dec 2015, 09:06 Bunuel wrote: rahulkashyap wrote: Bunuel But the solution is for "x" I don't understand what you mean by this. Can you please re-read 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)(x-2)= 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 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Does the equation y = (x – p)(x – q) intercept the x-axis 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 x-axis at the point (2,0)? (1) pq = -8 (2) -2 – p = q If we modify the qusetion, 0=(2-p)(2-q)? and 0=4-2p-2q+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=4-2(p+q)+pq? --> 0=4-2(-2)-8? --> 0=4+4-8=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 one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: Does the equation y = (x – p)(x – q) intercept the x-axis at  [#permalink]

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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.
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Re: Does the equation y = (x – p)(x – q) intercept the x-axis at  [#permalink]

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17 Jun 2017, 09:25
alchemist009 wrote:
Does the equation y = (x – p)(x – q) intercept the x-axis 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"
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Re: Does the equation y = (x – p)(x – q) intercept the x-axis at  [#permalink]

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03 Oct 2018, 19:37
Bunuel wrote:
rahulkashyap wrote:
Bunuel wrote:
Does the equation y = (x – p)(x – q) intercept the x-axis at the point (2,0)?

x-intercepts of the graph $$y=(x-p)(x-q)$$ is the values of $$x$$ for which $$(x-p)(x-q)=0$$. So, the x-intercepts 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 $$-2-p=q$$ 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 $$y=(x-p)(x-q)$$ intercepts the x-axis at the point (2,0). Sufficient.

Hope it's clear.

When i do a quad equation,

i get (x+4)(x-2)=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=(2-p)(2-q), 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?

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