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Quant - Linear equations with parameters [#permalink]

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01 Aug 2012, 08:16

1

This post received KUDOS

Relevant to an old question (was M03-Q23): m23-74149.html

Consider the the equation \(Ax=B\), where \(A\) and \(B\) are given real numbers, and \(x\) is to be found. There are three possible scenarios:

1) \(A\neq0\). In this case, the given equation has a unique solution given by \(\frac{B}{A}\). Doesn't matter who is \(B\), it can be also 0, as 0 divided by a non-zero number is 0. 2) \(A = 0\) and \(B = 0\). In this case, the given equation has infinitely many solutions, as for any number \(x\), \(0 * x = 0\). 3) If \(A = 0\), but \(B\neq0\), then the given equation has no solution, because \(Ax = 0 * x = 0 \neq{B}\).

I hope the above can help when discussing any linear equation with one unknown and parameters (letters instead of numbers as coefficients).
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

If A, B, and C are known, then as long as C>B, A and y could only be one number. the trick is that A,B, and C are all known, if A was unknown then the answer would be infinite. For Example, 4y + 2 = 3, A=4 y=1/4 B=2 C=3, A B and C are known and C>B, so y is an easy calculation.

unless I am misinterpreting it, A is already known, so its value being more than one shouldnt matter.

"How many different numbers y" requires a definite answer in GMAT. It should be for instance 2,3 or any other number. It cannot be "can be determined" vs "cannot be determined"

All the explanations above make sense, but this question seems to me as non-standard as far as GMAT is concerned
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from statement 1 ; C>B , it doesn't make any sense , as it doesn't affect the value of y.

statement 2; A>0, this condition should exist since A can't be zero.

so, we can answer this question using statement 2. the Ans is B.

but this question asks about the different values of y. and, by using both these statement together or alone we cant say how many values does y have. hence, if we look from this perspective, the answer will be E.

plz tell the OA and source of question.
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kudos me if you like my post.

Attitude determine everything. all the best and God bless you.

If A, B and C are known the only case where y will have an unknown number of values is when A = 0 because there will be infinite possibilities. So, B correctly pinpoints that aspect.

I agree that B give answer, but question is asking for a specific number of Y values right? with Statement 2 we can say that we can find the value of y. but here we get multiples with different values of A B and C right????

Please correct me if if am wrong....
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S1 is not sufficient. Consider \(A = 0\) (the answer is 0) and \(A = 1\) (the answer is 1).

S2 is sufficient. Because \(A \gt 1\) , \(A \gt 0\) and the only \(y\) that satisfies the condition is \(\frac{C - B}{A}\) . The correct answer is B.

Is the explanation for statement 2 correct? Why couldn't y = 0 and some other number as well?

IMO both statement 1 and 2 are insufficient becasue question ask about how many diffrent number. using both statement 1 and 2 still we can get infinite numbers of solution, hence answer should be E

S1 is not sufficient. Consider \(A = 0\) (the answer is 0) and \(A = 1\) (the answer is 1).

S2 is sufficient. Because \(A \gt 1\) , \(A \gt 0\) and the only \(y\) that satisfies the condition is \(\frac{C - B}{A}\) . The correct answer is B.

Is the explanation for statement 2 correct? Why couldn't y = 0 and some other number as well?

S1 says C>B, and the question says Ay + B = C, doesn't this mean A cannot be equal to 0, because if it was, then B = C (from Ay + B = C) and thus contradicting Statement 1.