Hello,

I saw this question on GMAT Prep Test 1, and was a little lost..

Q. Is sq.root((x - 3)^2) = 3 - x

1) x not equal to 3
2) -x|x| > 0

Reasoning:
1. is sufficient, as the answer is "NO" ?. I solved sq. root((x - 3)^2) to be (x - 3)., and if
x is not equal to 3, then its never equal. (I think I am making a mistake here, but
just want to confirm)
2. is sufficient too. -x|x| > 0 is a lengthy of writing x is a negative number ? Is that
correct? and the equation is true for negative numbers.

So my answer was D, but the real answer is B (statement 2 is sufficent).

Can someone help?. I feel solving the equation within the question was wrong
on my part, but I cannot figure out why.

thanks,
tarak

Taking a the square root of anything is really expressing it to the one-half power. In this example, it's tempting to take (x-3)^2(1/2) and translate the question into: Is x - 3 = 3 - x? However, since the original x-3 in the question stem was squared, it's really asking: Is the absolute value of x - 3 = 3 - x?

From statement 1 we know x isnt 3, but if x is 2 we get a "yes" to the question but if x any multitude of other numbers we get a "no", so its insufficient.

You were correct in stating that statement 2 does tell us x is negative. This is important because when we look back at the translated stem (with absolute values), we can see that the equation will ALWAYS be equal if X is negative (i think you meant to flip the inequality sign in your previous post). Subtracting from a negative is akin to adding to a positive when the number is less than 0.

Hope that helps. I actually haven't seen this question so if my reasoning is off feel free to correct me....... [/u]

there have been a lot of threads on this problem, but admittedly it's a tough one to search (there's pretty much a total lack of viable search terms). here is one of them.

gmat7/18, you are correct about the absolute value. but you can go one step further: just make the realization that |x - 3| = (x - 3) if (x - 3) is positive or 0, and |x - 3| = (3 - x), the opposite, if (x - 3) is negative or 0. notice that i've made two statements in the case that x - 3 = 0, but both of them happen to be true and consistent (because positive 0 and negative 0 are the same number).
therefore, the question prompt can be rephrased as, is (x - 3) negative or 0?
which can then be rephrased again, to, is x < 3?

once you have that rephrase, the statements are a lot easier to handle. it becomes clear that (2) is sufficient: if x is negative, then it's definitely less than 3.

nb: this is the case with a great many data sufficiency problems. if a question prompt has a difficult rephrase, then the statements will always be easy to handle once you've found that rephrase. therefore, although you may feel skeevy about spending lots of time rephrasing a problem, it's worth it if you succeed.