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04 Jun 2018, 11:05
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
61% (01:29) correct
39%
(01:52)
wrong
based on 269
sessions
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If \((x - 6)(x - m) = x^2 + rx + k\). What is the value of m?
(1) \(k = 18\)
(2) \(r = -9\)
(1) \(k = 18\)
(2) \(r = -9\)
04 Jun 2018, 11:16
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Bunuel
If \((x - 6)(x - m) = x^2 + rx + k\), what is the value of m?
(1) \(k = 18\)
(2) \(r = -9\)
(1) \(k = 18\)
(2) \(r = -9\)
Sweet question, Bunuel!!
Target question: What is the value of m?
Given: (x - 6)(x - m) = x² + rx + k
Use F.O.I.L. to expand left side: x² - mx - 6x + 6m = x² + rx + k
Rewrite left side as follows: x² + (-m - 6)x + 6m = x² + rx + k
This tells us two things:
-m - 6 = r
6m = k
Now onto the statements!!
Statement 1: k = 18
We already know that 6m = k
This means: 6m = 18
So, m = 3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: r = -9
We already know that -m - 6 = r
This means: -m - 6 = -9
Solve to get: m = 3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
General Discussion
04 Jun 2018, 22:14
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Bunuel
If \((x - 6)(x - m) = x^2 + rx + k\). What is the value of m?
(1) \(k = 18\)
(2) \(r = -9\)
(1) \(k = 18\)
(2) \(r = -9\)
Statement(1):-
Let's put the value of k in the given quadratic equation, we have
\(x^2\)-(6+m)x+6m= \(x^2\)+rx+18
Now equating the constant terms in both the sides of quadratic equation we have,
6m=18 or m=3.
Therefore, Statement(1) is sufficient.
Statement(2):-
Let's put the value of r in the given quadratic equation, we have
\(x^2\)-(6+m)x+6m= \(x^2\)+(-9)x+k
Now equating the co-efficient x in both the sides of quadratic equation we have,
-(6+m)=-9
or, m=3
Therefore, Statement(2) is sufficient.
Hence, answer option(D)
