Is sqrt((x-3)^2) = 3 - x
1) x is not equal to 3
2) -x(abs val of x) > 0
Ans is B, but why doesn't the first statement give us enough info? The way I see it, the question is really asking us whether x-3 = 3-x. What option for x is there (other than 3) that satisfies the first statement?
And statement 2 only tells us that x is positive, but how is that enough to answer the question?
Thanks.
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Statement give Sqrt((x-3)^2)
i.e positive root of (x-3)^2.
Now statement 1 tells us that X is not 3.
So X can be anything except 3. If X = 2 then the main statement holds true, i.e
Sqrt (2-3)^2 = 1 = 3-2
When X = 4, this doesn't hold good.
Sqrt (4-3)^2 = 1 not equal to 3-4
So statement 1 is insufficient.
From statement two, we get X is negative value. Then only -x * (abs value of x) can be > 0.
for eq, let x = -2 then
Sqrt (-2-3)^2 = 5
3 - (-2) = 5.
This will hold true for any negative value of X.
Hence B is sufficient.
i.e positive root of (x-3)^2.
Now statement 1 tells us that X is not 3.
So X can be anything except 3. If X = 2 then the main statement holds true, i.e
Sqrt (2-3)^2 = 1 = 3-2
When X = 4, this doesn't hold good.
Sqrt (4-3)^2 = 1 not equal to 3-4
So statement 1 is insufficient.
From statement two, we get X is negative value. Then only -x * (abs value of x) can be > 0.
for eq, let x = -2 then
Sqrt (-2-3)^2 = 5
3 - (-2) = 5.
This will hold true for any negative value of X.
Hence B is sufficient.
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- Senior | Next Rank: 100 Posts
- Posts: 73
- Joined: Wed Jan 28, 2009 9:00 am
- Thanked: 6 times
- GMAT Score:680
Anand,
I am not sure whether this is the correct reason, but just trying.
The question Is sqrt((x-3)^2) = 3 - x ? So before starting we are not sure, whether the equality stands good, so how can we square it and proceed?
Suppose we are asked Is -5 = 5? If we square this we get 25 = 25 and we say the equation satisfies, but that is not the actual case right? -5 is not equal to 5 at the first place.
In the way i have solved, i found the values of the two sides of the equation separately and then tried to equate it.
Hope this makes sense.
I am not sure whether this is the correct reason, but just trying.
The question Is sqrt((x-3)^2) = 3 - x ? So before starting we are not sure, whether the equality stands good, so how can we square it and proceed?
Suppose we are asked Is -5 = 5? If we square this we get 25 = 25 and we say the equation satisfies, but that is not the actual case right? -5 is not equal to 5 at the first place.
In the way i have solved, i found the values of the two sides of the equation separately and then tried to equate it.
Hope this makes sense.