28-Q5 在线等

nicboy

    

Q5:

    

Is ½x½< 1?

    

(1)   ½x + 1½ = 2½x - 1½

    

(2)
            ½x - 3½
        ≠ 0

    

                  

    

A. Statement (1) ALONE is
sufficient, but statement (2) alone is not sufficient.

    

B. Statement (2) ALONE is
sufficient, but statement (1) alone is not sufficient.

    

C. BOTH statements TOGETHER
are sufficient, but NEITHER statement ALONE is sufficient.

    

D. EACH statement ALONE is
sufficient.

    

E. Statements (1) and (2) TOGETHER
are NOT sufficient.

    

                                                                                                  Answer:
A ( C)

bth

I think in case of absolute value of numbers we should approach by using the number line concept.

|x|<1 means whether x is within the range of -1 and 1.

Stem1:

|x+1|=2|x-1|

=> |x-(-1)| =2|x-1|

Meaning, the distance between -1 and x is twice the distance between x and 1.

Now, take a number line.

                                                         x                                                       x

...............|................|....i......i.......|.....i.......i......|..................|......................|..................|

                                -1               0                  1                 2                     3                 4

See the number line we find two positions of x. x=1/3 or x=3. NOT SUFF.

Stem2:

|x-3| not equal to 0. Then what ? NOT SUFF.

1+2:

From 1 we get two value of x. In 2 it has been said that x is not equal to 3. So, x=1/3. SUFF.

Answer is C.

nicboy

Thx a lot

gnaixwh

from condition 1, we know that (x+1)=2(x-1) or (x+1)=-2(x-1), which means x is either 3 or 1/3, not sufficient.

from condition 2, we know that x is not equal to +/-3, not sufficient.

but combine both we can derive that x = 1/3.

nicboy

I understand bth's graph, but I don't understand by only math calculation, how to get x=1/3, I can only get x=3, thanks