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Let function f(x)=(x-a)(x-b). If f(10)=f(20)=0, f(30)=?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6517
GMAT 1: 760 Q51 V42
GPA: 3.82
Let function f(x)=(x-a)(x-b). If f(10)=f(20)=0, f(30)=?  [#permalink]

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25 Oct 2017, 01:21
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35% (medium)

Question Stats:

67% (01:39) correct 33% (02:40) wrong based on 78 sessions

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[GMAT math practice question]

Let function f(x)=(x-a)(x-b). If f(10)=f(20)=0, f(30)=?

A. 50
B. 100
C. 150
D. 200
E. 250

_________________

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" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 17 Oct 2016 Posts: 321 Location: India Concentration: Operations, Strategy GPA: 3.73 WE: Design (Real Estate) Re: Let function f(x)=(x-a)(x-b). If f(10)=f(20)=0, f(30)=? [#permalink] Show Tags 25 Oct 2017, 01:30 Option D f(10) gives a=10 or b=10. Similarly f(20) gives a=20 or b=20. Substituting for f(30) we get 200 Sent from my iPhone using GMAT Club Forum _________________ Help with kudos if u found the post useful. Thanks PS Forum Moderator Joined: 25 Feb 2013 Posts: 1217 Location: India GPA: 3.82 Let function f(x)=(x-a)(x-b). If f(10)=f(20)=0, f(30)=? [#permalink] Show Tags 25 Oct 2017, 01:41 $$f(10)=f(20) =>(10-a)(10-b)=(20-a)(20-b)$$ solve this to get $$a+b=30$$ but $$(10-a)(10-b)=0$$, so if $$a=10$$, then $$b=20$$ and if $$b=10$$ then $$a=20$$ again $$(20-a)(20-b)=0$$ so if $$a=20$$, $$b=10$$ and if $$b=20$$ then $$a=10$$ $$f(30)=(30-a)(30-b)$$ so if $$a=10$$ then $$b=20$$ and $$f(30)=(30-10)(30-20)=200$$ and if $$a=20$$, then $$b=10$$ and $$f(30)=(30-20)(30-10)=200$$ Option D Intern Joined: 12 Oct 2017 Posts: 40 Re: Let function f(x)=(x-a)(x-b). If f(10)=f(20)=0, f(30)=? [#permalink] Show Tags 25 Oct 2017, 02:26 1 We have: +. f(10) = (10-a)(10-b) = 0 => a = 10 or b = 10 +. f(20) = (20-a)(20-b) = 0 => a = 20 or b = 20 +. f(10) = f(20) = 0 => (a=10; b=20) or (a=20, b=10). Since a,b plays same role in the equation => we just have to select 1 pair of (a,b) = (10,20) => f(30) = (30 - 10)*(30-20) = 200. Hence, the answer is D ---- Kindly press +1 kudos if the explanation is clear Thank you! Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6517 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Let function f(x)=(x-a)(x-b). If f(10)=f(20)=0, f(30)=? [#permalink] Show Tags 27 Oct 2017, 00:31 1 => Since f(10) = f(20) = 0, f(x) = (x-10)(x-20). f(30) = (30-10)(30-20) = 20*10 = 200. Therefore, the answer is D. Answer: D _________________ 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: Let function f(x)=(x-a)(x-b). If f(10)=f(20)=0, f(30)=? &nbs [#permalink] 27 Oct 2017, 00:31
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