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

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Let f(x)= (x-p)(x-q). If f(11)=f(20)=0, then f(10)=? [#permalink]

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[GMAT math practice question]

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

A. \(1\)
B. \(-1\)
C. \(5\)
D. \(-5\)
E. \(10\)
[Reveal] Spoiler: OA

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Let f(x)= (x-p)(x-q). If f(11)=f(20)=0, then f(10)=? [#permalink]

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New post 12 Jan 2018, 00:52
Option E

f(11)=f(20)=0
(11-p)(11-q)= (20-p)(20-q)=0

121-11(p+q)+pq=400-20(p+q)+pq=0
p+q=31
now consider single case,

(11-p)(11-q)=0
121-11(p+q)+pq=0
121-11*31+pq=0

pq=220

Hence f(10) = 100-10*31+220 = 10


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Re: Let f(x)= (x-p)(x-q). If f(11)=f(20)=0, then f(10)=? [#permalink]

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New post 12 Jan 2018, 05:34
Q=11 or 20 nd P is vice versa

So after substitution

F(10)= -1 * -10 =10

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Re: Let f(x)= (x-p)(x-q). If f(11)=f(20)=0, then f(10)=? [#permalink]

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New post 14 Jan 2018, 17:33
=>

Since \(11\) and \(20\) are roots of \(f(x) = 0\), we must have \(f(x) = (x-11)(x-20)\).
Thus, \(f(10) = (10-11)(10-20) = (-1)(-10) = 10.\)

Therefore, the answer is E.
Answer : E
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Re: Let f(x)= (x-p)(x-q). If f(11)=f(20)=0, then f(10)=? [#permalink]

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New post 14 Jan 2018, 18:29
MathRevolution wrote:
[GMAT math practice question]

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

A. \(1\)
B. \(-1\)
C. \(5\)
D. \(-5\)
E. \(10\)


\(f(11) = f(20) = 0\).

\(f(11) = (11-p) (11-q)\), either \(p = 11\) or \(q = 11\).
\(f(20) = (20-p) (20-q)\), either \(p = 20\), or \(q = 20\).

Case 1: Let \(p = 11, q = 20\).
\(f(10) = (10-11) (10-20) = 10\).

Case 2: Let \(p = 20, q = 11\).
\(f(10) = (10-20) (10-11) = 10\).

Ans - E.
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Re: Let f(x)= (x-p)(x-q). If f(11)=f(20)=0, then f(10)=? [#permalink]

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New post 22 Jan 2018, 13:24
Am I the one who spent over 5 mins for this? :O
Re: Let f(x)= (x-p)(x-q). If f(11)=f(20)=0, then f(10)=?   [#permalink] 22 Jan 2018, 13:24
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