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Absolute values
Source: Beat The GMAT — Data Sufficiency |
IMO B
lxl=lyl?
1) x-y=6
x=3 y=-3 yes condition satifies 1 and the answer is yes but
if x=9 y=3 No hence insuffient
2)x+y=0
x=-y
so Yes Suffienct
lxl=lyl?
1) x-y=6
x=3 y=-3 yes condition satifies 1 and the answer is yes but
if x=9 y=3 No hence insuffient
2)x+y=0
x=-y
so Yes Suffienct
I think it diff way and i just want to know whether my way is correct or not. I think for proving mod x = mod y
we need to prove, if we take out mode... x = y ( if both are > 0) and -x = -y ( if <0)
coz by def of mode , mod x = x if x >0
mod x = -x if x<0
So, do we need to prove both condition in the ques below..or not.
Going by my method.
1.x-y =6
....>>> Not Suff
2. x+y=0, x=-y
utting back...mod(-y) = mod(y ) ....
... y = y ( If Y >00
-y = y( if y<0 )...not true. ....so B Insuff
taking together
x-y=6
x+y=0
x =3,y =-3
Here again comes my ques.
Do we have to put values and consider mode by >0 and <0
Pls f any1 can explain
we need to prove, if we take out mode... x = y ( if both are > 0) and -x = -y ( if <0)
coz by def of mode , mod x = x if x >0
mod x = -x if x<0
So, do we need to prove both condition in the ques below..or not.
Going by my method.
1.x-y =6
....>>> Not Suff
2. x+y=0, x=-y
utting back...mod(-y) = mod(y ) ....
... y = y ( If Y >00
-y = y( if y<0 )...not true. ....so B Insuff
taking together
x-y=6
x+y=0
x =3,y =-3
Here again comes my ques.
Do we have to put values and consider mode by >0 and <0
Pls f any1 can explain
GMAT/MBA Expert
-
Ian Stewart
- GMAT Instructor
- Posts: 2623
- Location: Montreal
- Thanked: 1090 times
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vivek, I don't really follow your logic, but if:
|x| = |y|
then either x = y, or x = -y.
|x| is just the distance between 0 and x on the number line. If |x| = |y|, then x and y are both the same distance from zero. They're either both on the same side of zero, in which case they're equal, or they're on opposite sides of zero, in which case one is the negative of the other.
|x| = |y|
then either x = y, or x = -y.
|x| is just the distance between 0 and x on the number line. If |x| = |y|, then x and y are both the same distance from zero. They're either both on the same side of zero, in which case they're equal, or they're on opposite sides of zero, in which case one is the negative of the other.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
ianstewartgmat.com
ianstewartgmat.com
GMAT/MBA Expert
-
Ian Stewart
- GMAT Instructor
- Posts: 2623
- Location: Montreal
- Thanked: 1090 times
- GMAT Score:780
No, not quite. If |x| = |y|, there are four possibilities (you do not seem to be considering the last two below):vivek.kapoor83 wrote:but i just wanted to know..do we need to prove both the equations.
x, y both positive --> x = y
x, y both negative --> x = y
x positive, y negative --> x = -y
x negative, y positive --> x = -y
Which is why I said above that |x| = |y| is true if x = y or x = -y. Note that -x = -y is exactly the same equation as x=y (just multiply both sides by -1), so there is no need to consider it separately.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
ianstewartgmat.com
ianstewartgmat.com
