if x is positive, is x > 3?

a. (x-1)^2 > 4
b. (x-2)^2 > 9

Lets look at item A first. If we make x = 2 then 2-1^4 = 1. So it doesn't satisfy statement A. Lets try x = 4 which then means 4-1^2 = 9. We can't plug in any fractions because they would just get smaller when raised to a power, so based on our test of x = 4, (which is the lowest we can go) statement A is satisfied.

Lets try the same for statement B. Let's make x = 6. 6-2^2 = 16 and it is greater than 9. What about if we make x = 5? 5-2^2 = 9 So 5 is the lowest we can go with statement B.

Both statements individually satisfy the question so the answer IMO is D.

OMG............. I forgot about if x is positive ((((((((((

1. (x-1)^2 > 4
can also be written as:
(x-1) > +-2 (square rooting both sides)

x-1 >2 and x-1>-2
x>3 and x>-1

x is positive so x>-1 is not valid (implies x != 0)

x>3 (sufficient)

2. (x-2)^2 > 9

x-2 > +-3

x-2>3 and x-2>-3
x>5 and x>-1

again...x has to be positive so x>-1 is not valid.

x>5 or x!>3 (sufficient)

Guys, what do you think:

Do this answers x>3 and x>5 contradict here each other?

I think yes because they are different. But still answer is D

4meonly wrote:Guys, what do you think:

Do this answers x>3 and x>5 contradict here each other?

I think yes because they are different. But still answer is D

Good thinking man.

But remember the question asks whether x is greater than 3. And both statement proves that.

you are looking for a common solution for both statements which is X > 5

But I like the way you think.

4meonly wrote:Guys, what do you think:

Do this answers x>3 and x>5 contradict here each other?

I think yes because they are different. But still answer is D

No they do not.

If you need to combine both, solution would be intersection of two.
ie
x>5

but our Qn is answered with A and B separately so ans is D

May be this is not a good e.g. of contradiction.
Yes, we definetly can aswer the main question, but
from 1 we get x>3 and from 2 we get x>5
So, from 1) x=4 satisfies but from 2) does not
Contradiction? I think Yes.
I agree with answer D here, but I ask general question about contradiction.


Please look through this topic
https://www.beatthegmat.com/pls-chk-if-a ... html#93080

I absolutely believe GMAT Expert Stacey Koprince, but still I have some doubts... I think that answers can contradict.

Anyway, contradiction rarely affects the final answer.