OG Question 105

hi
|x|=x or |x|=-x

the above is simply stating that x could be positive in the first case, or x could have a negative value in the second case where the absolute value would be equal to minus x since x is negative

now the questions asks
Is |x|=y-z?

Remember this is a Yes or No question
Firstly statement two by itself (x<0) is Insufficient...
looking at the first statement
(1) x+y=z
this can be rewritten as
-x= y-z
if x is positive, the y-z has a negative value and the answer is NO since an absolute value cant equal a negative number, on the other hand if x is negative in equation (1) then -x = |x| = y-z since all these values are positive with the same numberical value and the asnwer is YES...since answer could be yes or no, then (1) insufficient

equation 2 tells us that x is negative or x<0 so the two statements together are sufficient

2. States that x<0. and 1. states that x+y = z.
x = z-y => -x = y-z.

So its suff.

take these nos. -2, 4, 2 or 2,2,4 and try. |x| = y-z.

Raj Peddisetty.

2. States that x<0. and 1. states that x+y = z.
x = z-y => -x = y-z.

So its suff.

take these nos. -2, 4, 2 or 2,2,4 and try. |x| = y-z.

Raj Peddisetty.