Data Sufficiency

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.....

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.