On referring to your explanation for problem in the link attached below.
https://www.beatthegmat.com/a-data-from- ... tml#359007
Is A positive?
1. x^2 - 2*x + A is positive for all x
2. A*x^2 + 1 is positive for all x
For the above problem. On referring to your explanation as below::::
It's key to understand exactly what a statement is telling you.
(1) x^2 - 2*x + A is positive for all x
To satisfy this statement, we have to have an A that makes the expression positive for EVERY POSSIBLE value of x.
Well, if x=0, then the expression simply equals A. So, in order for the statement to be positive when x=0, A must be positive. Therefore, to guarantee that the expression is ALWAYS positive, regardless of the value of x, we have to have a positive A: sufficient, eliminate B, C and E.
My Doubt:
How come you arrived at A as answer by testing for x=0 alone.
for example take
x=2 , then statement 1(x^2 - 2*x + A is positive for all x
) gives 4-4+ A = A and since statement is +ve A must be positive (Good or x=0,2)
x=3 , then the statement 1 gives 9-6+A= 3+ A so, inorder for this (3+A) to be positive A can be -1 , -2 or any positive number?
In this case we cannot say A is +ve , then A is wrong answer ....Am i right????
Please correct me if iam wrong here.....
Stuart Kovinsky --- did i get your solution wrong??
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I'm not sure why you posted this in a separate thread. In any case, I posted a solution to this question here:
https://www.beatthegmat.com/a-t67877.html
My second reply in that thread addresses your question specifically.
https://www.beatthegmat.com/a-t67877.html
My second reply in that thread addresses your question specifically.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
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Hi,
as Ian notes, if you have a question about a post in an existing thread, it's much more efficient to just reply to that thread rather than start a new one.
In any case, Ian answers your specific question in the thread he linked (thread hijacker!) and I believe his answer is the same as on the one in my original post - since we need a value of A that makes the statement true for ALL values of x, and since a positive value for A is required by some values of x, only a positive value of A guarantees that the statement will be true.
So, while for some specific values of x A doesn't need to be positive, a positive A will still make those cases true.
as Ian notes, if you have a question about a post in an existing thread, it's much more efficient to just reply to that thread rather than start a new one.
In any case, Ian answers your specific question in the thread he linked (thread hijacker!) and I believe his answer is the same as on the one in my original post - since we need a value of A that makes the statement true for ALL values of x, and since a positive value for A is required by some values of x, only a positive value of A guarantees that the statement will be true.
So, while for some specific values of x A doesn't need to be positive, a positive A will still make those cases true.
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
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