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# M61-03

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6815
GMAT 1: 760 Q51 V42
GPA: 3.82

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17 Jun 2018, 23:43
00:00

Difficulty:

35% (medium)

Question Stats:

62% (01:22) correct 38% (01:37) wrong based on 13 sessions

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Let $$f(x)= (x-p)(x-q)$$. If $$f(11)=f(20)=0$$, then $$f(10)=$$?

A. -5
B. -1
C. 1
D. 5
E. 10

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6815 GMAT 1: 760 Q51 V42 GPA: 3.82 Re M61-03 [#permalink] ### Show Tags 17 Jun 2018, 23:43 Official Solution: Let $$f(x)= (x-p)(x-q)$$. If $$f(11)=f(20)=0$$, then $$f(10)=$$? A. -5 B. -1 C. 1 D. 5 E. 10 Since 11 and 20 are roots of $$f(x) = 0$$, we must have $$f(x) = (x-11)(x-20)$$. Thus, $$f(10) = (10-11)(10-20) = (-1)(-10) = 10$$. Answer: 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$149 for 3 month Online Course"
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Manager
Joined: 18 Jan 2018
Posts: 68
GPA: 3.87

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20 Jun 2018, 04:23
Hi Bunuel ,

f(x)=(x−p)(x−q)

f(11)=f(20)

If I take p and q as 15.5 then also f(11) = F(20) , I was not given that p & Q are root .(x−p)(x−q)

F(11)=(11-15.5)(11.15.5) = F(20) = (20-11.5)(20-11.5)

Please correct me , I am confused .
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6815
GMAT 1: 760 Q51 V42
GPA: 3.82

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05 Aug 2018, 22:09
baru wrote:
Hi Bunuel ,

f(x)=(x−p)(x−q)

f(11)=f(20)

If I take p and q as 15.5 then also f(11) = F(20) , I was not given that p & Q are root .(x−p)(x−q)

F(11)=(11-15.5)(11.15.5) = F(20) = (20-11.5)(20-11.5)

Please correct me , I am confused .

You didn't consider f(11) = 0 and f(20) = 0.
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Intern
Joined: 06 Feb 2018
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21 Dec 2018, 01:51
I think this the explanation isn't clear enough, please elaborate. I thought 11 and 20 will replace x in the F(x) and I got answer 1. I equated f(11) to f(20) to get values in terms of p+q and pq and then substituted in answer
Re M61-03 &nbs [#permalink] 21 Dec 2018, 01:51
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# M61-03

Moderators: chetan2u, Bunuel

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