Ds - 1000Q

Question

Is sqrt((x-3)^2)=3-x 1) x not equal to 3 2) -xlxl>0 Show the evidence please

ggarr · Answer

A 

1) (x-3)^2 = 3-x
2) x^2 - 6x + 9 = 3-x
3) x^2 + 9 = 3 + 5x
4) x^2 + 6 = 5x
5) x^2 - 5x + 6 = 0
6) x=2 and 3

Statement 1 says x doesn't equal 3. That leaves 2.

Statement 2 tells us that x is positive. That could be 2 or 3.

Is this right?

SimaQ · Answer

Nope.

You forgot to raise (3-x)^2.....

dwivedys · Answer

Going with B - stmt 2 alone is sufficient but 1 is not. since -x|x| >0 ==> x < 0. This means x - 3 < 0 and therefore we know that x - 3 is a negative number that is being squared. when you take the sqr root of the square of a negative number we should consider the negative root as the result. sqrt(-3^2) = -3 Thus sqrt((x-3)^2) = - (x - 3) = 3-x What do you think??

Googlore · Answer

My answer is D. From the stem we get: 

(x-3)^2=(3-x)^2

Plug in any values for x and they are equal. It seems that you can solve this from the info. in the stem, is that right?

ggarr · Answer

Don't the 2 equations equal one another? If so, wouldn't the answer be D?

MBAlad · Answer

I'm puzzled by this one - as mentioned, the stem gives an equivalent equation

uphillclimb · Answer

Maybe I'm really far off on this one, but...
the square root of (x-3)^2...isn't that just (x-3)? So isn't the question asking, is x-3 = 3-x? And if you solve the equation, then the stem is just, is x = 3? If that's the case, then only A is correct...
What is OA?

Ahamdevam · Answer

From-1 : we get (x-3) or 3-x
From-2 : x < 0 means x-3 must be negative which when sqared.
on sqare-rooting it should give us 3 - x. 

so Stmt-2 alone is sufficient.. 

B

ywilfred · Answer

St1:

x = 2, sqrt((x-3)^2) = 1, 3-x = 1 --> LHS = RHS
x = 7, sqrt((x-3)^2) = 4, 3-7 = -4 --> LSH != RHS

Insufficient.

St2:

|x| is alway positive, so x must be negative for -x|x| to be positive.

x = -1, sqrt((x-3)^2) = 4, 3-x = 4 --> LHS = RHS
x = -2, sqrt((x-3)^2) = 5, 3-x = 5 --> LHS = RHS
x = -7, sqrt((x-3)^2) = 10, 3-x = 10 --> LHS = RHS
x = -1/2, sqrt((x-3)^2) = 3.5, x-x = 3.5 --> LHS = RHS

I'll take B.

trivikram · Answer

Straight B....

-x|x| > 0 if x is -ve.

|x| is always positive

for -x|x| > 0 then x has to be -ve.

1) Isnt needed 

\So B

SimaQ · Answer

OA is B.

I needed the clearence on -xlxl>0 part....

Googlore · Answer

I think I'm mixed up with simplifying. Can somebody explain why 
sqrt((x-3)^2)=3-x isn't the same as (x-3)^2=(3-x)^2 ?

dwivedys · Answer

(x-3)^2=(3-x)^2 are equal. But the if squares of two numbers are equal doesn't mean that the numbers too are equal. They could be opposite in sign and still their squares would be the same.

Ds - 1000Q

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards