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23 Jun 2016, 15:39
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In the equation x^2-7x+n=0, n is a constant and x is a variable. Is (x-6) a factor of x^2-7x+n=0?
(1) n=6
(2) (x-1) is a factor of x2-7x+n=0.
But for 1) if we put n=6 into the equation wouldn't that yield 2 different values for x? namely x=6 or x=1? So why's this statement sufficient?
This line of logic is consistent with a a similar question,
If x^2-k·x+24=0, is x=-6?
(1) (x+6) is a factor of x2-k·x+24, where k is a constant, and x is a variable.
(2) (x+4) is a factor of x2-k·x+24, where k is a constant, and x is a variable.
because Stat.(1) means either e or f are 6, so the other must be 4 (e·f=24). The roots therefore are x1=-6 x2=-4, which means you cannot determine whether x is -6. Hence, Stat.(1)->Maybe->IS->BCE.
Stat.(2) means either e or f are 4, so the other must be 6 (e·f=24). The roots therefore are x1=-4 x2=-6, which means you cannot determine whether x is -6. Hence, Stat.(2)->Maybe->IS->CE.
Stat.(1+2) mean the factored form is (x+4)(x+6), so either e or f is 4, and the other is 6. The roots therefore are x1=-4 x2=-6, which means you cannot determine whether x is -6. Hence, Stat.(1+2)->Maybe->IS->E.
Thank you!
(1) n=6
(2) (x-1) is a factor of x2-7x+n=0.
Ans:
D
D
This line of logic is consistent with a a similar question,
If x^2-k·x+24=0, is x=-6?
(1) (x+6) is a factor of x2-k·x+24, where k is a constant, and x is a variable.
(2) (x+4) is a factor of x2-k·x+24, where k is a constant, and x is a variable.
Ans=E
Stat.(2) means either e or f are 4, so the other must be 6 (e·f=24). The roots therefore are x1=-4 x2=-6, which means you cannot determine whether x is -6. Hence, Stat.(2)->Maybe->IS->CE.
Stat.(1+2) mean the factored form is (x+4)(x+6), so either e or f is 4, and the other is 6. The roots therefore are x1=-4 x2=-6, which means you cannot determine whether x is -6. Hence, Stat.(1+2)->Maybe->IS->E.
Thank you!
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23 Jun 2016, 16:13
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ha15
Dear ha15,
I'm happy to respond.
I'm not sure, but I think you might be confusing different meanings of the word "factor." It means one thing to say one number is a factor of another (e.g. 3 is a factor of 36), but it means something slightly different to talk about algebraic factors---for example, (x - 3) is a factor of x^2 - 8x + 15.
In the first question, for statement #1, if we get the value n = 6, then the we get the quadratic x^2-7x+6. Technically, this is a poorly written question, because it makes sense to talk about the factor of a quadratic, such as x^2-7x+6, but it is pure nonsense to ask for the factor of an equation, as this question does: the equation is x^2-7x+6 = 0. Equations don't have factors, but the quadratic expression that appears in the equation can be factored. That's a very sloppy mistake on the part of the question writer.
You said: "if we put n=6 into the equation wouldn't that yield 2 different values for x? namely x=6 or x=1? So why's this statement sufficient?"
Notice, my friend, we are NOT asked for the value of x. You are answering a question that was not asked. The question is whether the binomial variable expression (x-6) is a factor of the quadratic variable expression x^2-7x+6. It's true, we often use factoring to solve for the value of x in quadratics, but no one is asking for the value of x here: the focus is on the factoring itself.
I will admit that part of your confusion is caused by the mistake on the part of the question author. It was 100% incorrect for the author to include the "=0" and this mistake encouraged your confusion.
Your analysis of the second question is perfect. Notice that this question was asking something quite different: it was asking for the value of x.
Does all this make sense?
Mike
24 Jun 2016, 14:52
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The two DS problems are asking subtly different questions. "Is x-6 a factor?" isn't quite the same question as "is x = 6?"
For instance, imagine that a DS question included the information that f(x) = 0, but didn't tell you what f(x) was. Then, one of the statements tells you that f(x) = x^2 - 5x - 6.
If the question asked was "is x = 6", you can't give a definite answer, even though you know what f(x) is. That's because x could be either 6 or -1.
If the question asked was "is (x-6) a factor of f(x)", you can give a definite answer. The answer is "yes".
For instance, imagine that a DS question included the information that f(x) = 0, but didn't tell you what f(x) was. Then, one of the statements tells you that f(x) = x^2 - 5x - 6.
If the question asked was "is x = 6", you can't give a definite answer, even though you know what f(x) is. That's because x could be either 6 or -1.
If the question asked was "is (x-6) a factor of f(x)", you can give a definite answer. The answer is "yes".
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
