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

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

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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

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Re: Let function f(x)=(x-a)(x-b). If f(10)=f(20)=0, f(30)=? [#permalink]

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New post 25 Oct 2017, 02:30
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


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

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New post 25 Oct 2017, 02:41
\(f(10)=f(20) =>(10-a)(10-b)=(20-a)(20-b)\)

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
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Re: Let function f(x)=(x-a)(x-b). If f(10)=f(20)=0, f(30)=? [#permalink]

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New post 25 Oct 2017, 03:26
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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
----

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Re: Let function f(x)=(x-a)(x-b). If f(10)=f(20)=0, f(30)=? [#permalink]

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New post 27 Oct 2017, 01:31
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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
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Re: Let function f(x)=(x-a)(x-b). If f(10)=f(20)=0, f(30)=?   [#permalink] 27 Oct 2017, 01:31
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