Is sqrt [(x-3)^2] = 3-x
1) x is not equal to 3
2) -x*lxl > 0
not sure of the OA B
Thanks
sqrt [(x-3)^2] = 3-x ?
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From the question we know that 3 -x can't be negative since we can't take a sqrt of a negative number, so x has to be less than or equal to 3 for the equation to work.vittalgmat wrote:Is sqrt [(x-3)^2] = 3-x
1) x is not equal to 3
2) -x*lxl > 0
not sure of the OA B
Thanks
1) x is not equal to 3
x = 4
doesn't work since we can't take the sqrt of a negative value
x = -4
will work
INSUFFICIENT
2) -x*lxl > 0
this tells us that -x*positive > 0
so - x must be positive, and x must be negative
if x is negative, then any value will make the original equation true.
SUFFICIENT B)
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Rule: sqrtx^2 = lxlvittalgmat wrote:Is sqrt [(x-3)^2] = 3-x
1) x is not equal to 3
2) -x*lxl > 0
not sure of the OA B
Thanks
sqrt [(x-3)^2] = 3-x
lx-3l = 3-x
to satisfy above equation x can be any negative value, 0,1,2 & 3.
Statement I
1) x is not equal to 3
x could 6,7,8 or any negative value. We can have both yes & no. Insufficient.
Statement II
2) -x*lxl > 0
for this equation to hold true x has to be negative, therefore any negative value will give us the answer yes. Sufficient.
Hence B.
Hope this helps.
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Guys. I still don't get it. The absolute method |x-3| works but lets plug in a number and see. Statement B only tells us that x is negative for sure.
Let x = -7
So equation becomes
Sqrt (-7-1)^2 = 3 - (-7)
so sqrt (100) = 10
Now sqrt (100) can have two values, 10 and -10 .. The other side is clearly 10.
So how is B the correct answer ?
Let x = -7
So equation becomes
Sqrt (-7-1)^2 = 3 - (-7)
so sqrt (100) = 10
Now sqrt (100) can have two values, 10 and -10 .. The other side is clearly 10.
So how is B the correct answer ?
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Square root of a number x^2 is defined as below(You can Wiki or Google if you still doubt this)
f(x) = Square root(x^2) = x if x >= 0 and -x if x <0. In other words, f(x) = Square root(x^2) = |x|(always positive).
Square root(100) can be 10 and never -10.
sqrt [(x-3)^2] = 3-x = -(x-3), only if x-3 is negative. The question can now be rephrased to
Answer B
let me know if you think you need further help!
f(x) = Square root(x^2) = x if x >= 0 and -x if x <0. In other words, f(x) = Square root(x^2) = |x|(always positive).
Square root(100) can be 10 and never -10.
sqrt [(x-3)^2] = 3-x = -(x-3), only if x-3 is negative. The question can now be rephrased to
Is (x-3)<0 ?
The value of x can be greater than 3(x-3 >0) or less than 3 (x-3<0). Hence Insufficient!1) x is not equal to 3
-x*|x| > 0 Implies -x * Positive number = Positive number. So -x should be a positive number and therefore x a negative number.If x is a negative number, x-3 is also a negative number(-ve + -ve = -ve).So, we can answer the question, Is (x-3)<0 ? with a YES! Hence sufficient!2) -x*|x| > 0
Answer B
let me know if you think you need further help!
Anil Gandham
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Be definition:vittalgmat wrote:Is sqrt [(x-3)^2] = 3-x
1) x is not equal to 3
2) -x*|x| > 0
not sure of the OA B
√(x²) = |x|.
|x-y| is the DISTANCE between x and y.
The DISTANCE between two numbers must be greater than or equal to 0.
The question stem above, rephrased: Is |x-3| = 3-x?
In words:
Is the DISTANCE between x and 3 equal to the DIFFERENCE of 3 and x?
The answer will be YES if the DIFFERENCE of 3 and x is greater than or equal to 0:
3-x≥0
x≤3.
The question stem rephrased: Is x≤3?
Statement 1: x is not equal to 3.
It is possible that x<3 or that x>3.
INSUFFICIENT.
Statement 2: -x*|x| > 0 .
Thus, the left-hand side must be positive*positive or negative*negative.
Since |x| cannot be negative, both factors on the left-hand side must be positive.
Thus:
-x>0
x<0.
Since x<0, we know that x≤3.
SUFFICIENT.
The correct answer is B.
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