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a real number

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a real number

by JJJooe » Wed Aug 26, 2009 3:59 am
p(x)and q(x)are two quadratic functions, for each real number x, the function, p(x)/q(x), is also a real number?

(1) p (2)=0, p(3)=0

(2) q (0)=0, q(1)=0

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what's the definition of real numbers? how to know whether a number is a real number or not?

Can someone help with it?thanks!!
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Source: — Data Sufficiency |
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by pradeepsarathy » Wed Aug 26, 2009 9:51 am
If my understanding is correct, then the question asks whether the function p(x)/q(x) is a real number, for all real numbers 'x'.

Stmt 1 -

We know only the values of the expression p(x) for x = 2 and x = 3.Hence insufficient

Stmt2 -

We know only the values of expression q(x) for x = 0 and x = 1.Hence insufficinet

Stmt 1 and Stmt 2 taken together -

The values of the expression p(x) and q(x) are known only for x = 2 , x = 3 and x = 0 , x = 1 respectively.
These values alone are not sufficient.

Hence IMO E
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by JJJooe » Wed Aug 26, 2009 2:44 pm
Stmt2 -

We know that the values of expression q(x) for x = 0 and x = 1 are zero.in other words, q(x) can be 0 as the denominator of p(x)/q(x) when this fraction doesnot exist...

so sufficient.

choose B？
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by pradeepsarathy » Wed Aug 26, 2009 2:51 pm
But q(x) can hold a valid value for other values of 'x', say x = 2, 3, 4 ...
I believe the question asks for 'each real number x' and not a specific real number.
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by JJJooe » Wed Aug 26, 2009 3:02 pm
as q(x) cannot hold a valid value for each value of 'x', we can say that the function p(x)/q(x), is not a real number for each real number x but rather for some real numbers(at least when x=0 or 1, q(x) makes the function p(x)/q(x) invalid)
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by pradeepsarathy » Wed Aug 26, 2009 6:26 pm
hmm...interesting argument....
can we have the OA pls?
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by JJJooe » Wed Aug 26, 2009 7:44 pm
==
i've no idea the OA...so i posted it here
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