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# GMAT: Data sufficiency 24

103-106, pg. 287. Created by Sal Khan.

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• I did not get the explanation of question 105.. It was to be proved that |x| = y-z ... From statement 1 we get |x| = -x & statement 2 we get x<0. How does these two statements together solve the question? • Sal's explanation was like this:
In order to prove that |x| = y-z from statement 1, |x| has to be -x, which means that x has to be 0 or a negative number, but we weren't told so, until the second statement said that x is less than 0. So we need both statements to prove the given equation.

Let me explain it this way:

Statement 1)
x+y = z --> x = z-y = -(y-z) --> -x = y-z
If x is 0 or a positive number, |x| = x = -(y-z)
If x is 0 or a negative number, |x| = -x = y-z
But we don't know what x is.

Statement 2)
x is a negative number.

From both statements, |x| = y-z
• question 105 around in; i saw the explanation below but im still unclear on how it works. if |x| = -x doesnt this tell us that the value of x is negative? since |x| = positive, the only way -x is positive is if x itself is negative (a (-)(-#) situation, giving a +#. whereas if x is positive than -x is negatvie and cannot be = |x|.
(1 vote) 