Absolute Coordinates-GMAT CAT 5

[stutis]

Hi

My question is regarding Q14 (in my case) of CAT 5. The problem goes like this:

In which quadrant of the coordinate plane does the point (x, y) lie?

(1) |xy| + x|y| + |x|y + xy > 0
(2) -x < -y < |y|

My doubt is in the solution of the first stem. This is the explanation given by MGMAT

1) SUFFICIENT: The key to evaluating this statement is to see which values of x and y actually satisfy it ("crack the code"). To do so, consider all possibilities for the signs of x and y.
- x > 0, y > 0: The left side becomes xy + xy + xy + xy = 4xy, which is a positive number; the statement is satisfied.
- x < 0, y > 0: The left side becomes xy - xy + xy - xy = 0, so the statement is not satisfied.
- x > 0, y < 0: The left side becomes xy + xy - xy - xy = 0, so the statement is not satisfied.
- x < 0, y < 0: The left side becomes xy - xy - xy + xy = 0, so the statement is not satisfied.
- Either x or y (or both) is 0: The left side becomes 0 + 0 + 0 + 0 = 0, so the statement is not satisfied.
Therefore, statement (1) can be rephrased simply as "Both x and y are positive." The point (x, y) is thus in the first quadrant.

My question is regarding sign of IxyI (first term in first stem)

MGMAT notes clearly state that when evaluating Ix-yI:
if x-y>0 or x>y, then Ix-yI = x-y
if x-y<0 or x<y, then Ix-yI = y-x

Applying same rule to IxyI (first term of the stem 1),
if xy>0 then IxyI should open up as xy
if xy<0 then IxyI should open up as -xy

However, in the solution given above, IxyI is assumed throughout to be positive and open up as "xy".

Can you please clarify, since the solution to stem 1 changes based on this query?

Many Thanks
Stuti

[nitin_prakash_khanna]

I dont know whether its a nice catch or its just written without really considering the order of terms.

lets just take one case.
x<0, y>0
for conevnience lets plug in x= -5 & y=5, so our reference x*y = -25 for this case.

|xy|= |-5*5| = 25 = -xy (exactly what you observed)
x|y|= -5*|5| = -25 = xy (now if you look the explanation the second term is written as -xy, though its equal to xy)
|x|y= 5*5= 25 = -xy (once again the explanation has written it as xy)
xy = xy (we dont need to change anything but its written as -xy)

so if you add up, it will add up to zero.
So either all the terms are written incorrectly or someone first calculated all the terms and re-arranged them in a certain order for simlification.

In any case its a sum zero game :>

Instructors, what say?

[vishalsahdev03]

The second statement tells:
y is less than its absolute value, i.e.
y is negative and x is less than y, Hence x is negative, therefore, both x and y are negative.

(x,y) lie in fourth qaurd.
Hence, statement 2 is sufficient.

Hi

Applying same rule to IxyI (first term of the stem 1),
if xy>0 then IxyI should open up as xy
if xy<0 then IxyI should open up as -xy

However, in the solution given above, IxyI is assumed throughout to be positive and open up as "xy".

Can you please clarify, since the solution to stem 1 changes based on this query?

Many Thanks
Stuti

Thats the same point I got struck on !!

Please explain the concept !!

Thanks in advance !!

[nitin_prakash_khanna]

"Vishalsahdev03"

You are correct that St.2 is SUFFICIENT , but (x,y) doesnt lie in 4th quadrant, becuase then the two statements will contradict.

if you look St.2 says
-x < -y < |y|

if y<0 then -y=|y| its not less than |y|
if y>0 , its only then -y <|y|

so y>0

And -x<-y
or x>y
and since y>0 , x>0 also. So (x,y) lies in 1st Quadrant not 4th.

HTH

[vishalsahdev03]

"Vishalsahdev03"

You are correct that St.2 is SUFFICIENT , but (x,y) doesnt lie in 4th quadrant, becuase then the two statements will contradict.

if you look St.2 says
-x < -y < |y|

if y<0 then -y=|y| its not less than |y|
if y>0 , its only then -y <|y|

so y>0

And -x<-y
or x>y
and since y>0 , x>0 also. So (x,y) lies in 1st Quadrant not 4th.

HTH

I think thats a correction, you are correct its in First Quadrant !!

Thanks !

[RonPurewal]

Hi

My question is regarding Q14 (in my case) of CAT 5. The problem goes like this:

In which quadrant of the coordinate plane does the point (x, y) lie?

(1) |xy| + x|y| + |x|y + xy > 0
(2) -x < -y < |y|

My doubt is in the solution of the first stem. This is the explanation given by MGMAT

1) SUFFICIENT: The key to evaluating this statement is to see which values of x and y actually satisfy it ("crack the code"). To do so, consider all possibilities for the signs of x and y.
- x > 0, y > 0: The left side becomes xy + xy + xy + xy = 4xy, which is a positive number; the statement is satisfied.
- x < 0, y > 0: The left side becomes xy - xy + xy - xy = 0, so the statement is not satisfied.
- x > 0, y < 0: The left side becomes xy + xy - xy - xy = 0, so the statement is not satisfied.
- x < 0, y < 0: The left side becomes xy - xy - xy + xy = 0, so the statement is not satisfied.
- Either x or y (or both) is 0: The left side becomes 0 + 0 + 0 + 0 = 0, so the statement is not satisfied.
Therefore, statement (1) can be rephrased simply as "Both x and y are positive." The point (x, y) is thus in the first quadrant.

My question is regarding sign of IxyI (first term in first stem)

MGMAT notes clearly state that when evaluating Ix-yI:
if x-y>0 or x>y, then Ix-yI = x-y
if x-y<0 or x<y, then Ix-yI = y-x

Applying same rule to IxyI (first term of the stem 1),
if xy>0 then IxyI should open up as xy
if xy<0 then IxyI should open up as -xy

However, in the solution given above, IxyI is assumed throughout to be positive and open up as "xy".

Can you please clarify, since the solution to stem 1 changes based on this query?

Many Thanks
Stuti

ah, yeah, ok. i see what they're doing.

these statements are definitely incorrect. BUT, what they are trying to do here is indicate the SIGN (+/-) of EACH of the terms.

for instance, note the second part:
"- x < 0, y > 0: The left side becomes xy - xy + xy - xy = 0, so the statement is not satisfied."
actually, ALL FOUR of these terms are wrong. if x is negative and y is positive, then |xy| is actually -xy, x|y| is actually +xy, |x|y is actually -xy, and xy is xy (of course).
...but what they're trying to say here is that the terms are, in order, positive, negative, positive, and negative.

what the answer key should say, for this instance, is
the four terms are positive + negative + positive + negative, and all of them have the same magnitude. therefore, their sum is 0.

same for the other parts.

...but yeah, we'll have to fix this.