GMAT Prep Math zy < xy < 0 |x-z| + |x| = |z|

[TheChakra]

I cannot find the GMAT Prep Math folder, so I am posting the question here.

If zy < xy < 0, is |x-z| + |x| = |z|?

1. z < x
2. y < 0

Knowing the answer, I can try values and confirm the answer. But, would like to know if anyone was able to rephrase the questions to be a little more helpful?

The answer is D

[TheChakra]

I cannot find the GMAT Prep Math folder, so I am posting the question here.

If zy < xy < 0, is |x-z| + |x| = |z|?

1. z < x
2. y < 0

Knowing the answer, I can try values and confirm the answer. But, would like to know if anyone was able to rephrase the questions to be a little more helpful?

The answer is D

BTw, This is the best I could come up with ..

Multiply |y| across so the question then is is |xy-zy| = |zy| - |xy|

There are multiple scenarios here (xy - zy < 0 and > 0), but the only scenario that doesn't break xy<xy<0 is

xy - zy > 0, zy < 0, xy < 0

--> xy > zy , zy < 0, xy < 0

The only way you can satisfy all of the above is when z < x or y < 0 , which is the answer

[y]

Given solution looks good. But it is very hard to think like that. I did not find a standard route to achieve the solution like this.

[Guest83]

I may be way off here, let me know what you guys think.

Firstly, since both ZY and XY are both less than 0, this implies that Z and X are both negative or positive (depending on value of y)

if Y is negative:
Z and X are both positive. Since ZY < XY, this means X<Z.

if Y is positive:
Z and X are both negative. Since ZY < ZX, this means X>Z.


Now, statement 1 says that Z<X. This means that Y is positive.

|X-Z| + |X| = |Z| -> Z-X + X = Z -> YES


Statement 2:
Y < 0. This implies that X<Z.


|X-Z| + |X| = |Z| -> X-Z + X = Z -> NO


Therefore, both statements are sufficient.

Does this make sense?

[TheChakra]

I may be way off here, let me know what you guys think.

Firstly, since both ZY and XY are both less than 0, this implies that Z and X are both negative or positive (depending on value of y)

if Y is negative:
Z and X are both positive. Since ZY < XY, this means X<Z.

if Y is positive:
Z and X are both negative. Since ZY < ZX, this means X>Z.


Now, statement 1 says that Z<X. This means that Y is positive.

|X-Z| + |X| = |Z| -> Z-X + X = Z -> YES


Statement 2:
Y < 0. This implies that X<Z.


|X-Z| + |X| = |Z| -> X-Z + X = Z -> NO


Therefore, both statements are sufficient.

Does this make sense?

this is good.

[Guest]

Hi can someone tell me the best way to tackle absolute value problems for data sufficiency.I know we should solve for X>0 and X<0.Is there an example someone could provide or an approach which is beneficial

Thanks

[RonPurewal]

Hi can someone tell me the best way to tackle absolute value problems for data sufficiency.I know we should solve for X>0 and X<0.Is there an example someone could provide or an approach which is beneficial

Thanks

well, there are different breeds of absolute value problems, so (as usual) there's no one neat, solid answer to a question like that. however:
* if a problem contains the symbols "> 0" or "< 0" at any point, you can rest assured that the crux of the problem involves the signs of quantities. (the problem in this thread is a perfect example.)
if you encounter such a problem, you should immediately devote all of your energy to rephrasing the question prompt and/or statements to equivalent formulations involving 'positive'/'negative'.

for instance, if you see
zy < xy < 0
you should think:
* z and x have the same sign
* y must have the opposite of whatever sign those two have
* therefore, (x y z) is either (+ - +) or (- + -)

that sort of reasoning will be an excellent start. from there, there's no telling which way the wind will blow - just study your number properties, and you should be able to figure out the rest.

oh yeah, you should avoid 'solving' if at all possible: you should try to think in the abstract about the signs of the numbers, and about the situation resulting from each possible combination of signs. if that sort of reasoning gets you nowhere, then try plugging in numbers and solving as plan b.

[DLALL2001]

Hi MG, i am new on this forum. i have taken 2 of the practice tests till now and scored 540 in the first one and 630 in the second (42Q and 32V). i feel i could have done much better as i believe i didnt pace my self well during the test. i have taken all the manhattan books and they have been very helpful in clearing the concepts.
i will be taking my gmat the next month. Can you pls advice me what should be my startegy this month to increase my score to 650+. Also would it also be possible for you to kindly access my tests and advice on the areas i need to concentrate on. Since i am working i am only able to study at night for 2-3 hrs. In Verbal i just not able to score on CR. Especially the BOLD question types. Can anyone pls advice on how to attempt these type of questions.

thanks
deepti

[StaceyKoprince]

Hi, Deepti, welcome! I responded to your question in the general questions thread. Please take a moment to look at the forum guidelines and other "read me" posts at the tops of the folders. Those should give you a good orientation on how to use the forums.

[guest11]

I may be way off here, let me know what you guys think.

Firstly, since both ZY and XY are both less than 0, this implies that Z and X are both negative or positive (depending on value of y)

if Y is negative:
Z and X are both positive. Since ZY < XY, this means X<Z.

if Y is positive:
Z and X are both negative. Since ZY < ZX, this means X>Z.


Now, statement 1 says that Z<X. This means that Y is positive.

|X-Z| + |X| = |Z| -> Z-X + X = Z -> YES


Statement 2:
Y < 0. This implies that X<Z.


|X-Z| + |X| = |Z| -> X-Z + X = Z -> NO


Therefore, both statements are sufficient.

Does this make sense?

Close.

From the question:
zy < xy < 0



Implies:
1. Since zy and xy are < 0 , then if y > 0, z < 0 and x < 0, and if y < 0, then x > 0 and z > 0.
2. If y > 0
-- divide by y, no change in sign, so z < x
3. If y < 0
-- divide by y, change the sign, so y > x

Statement 1: z < x
From #2 above, we know that y > 0. Also we know that x < 0 and z < 0.
So,
|x-z| + |x| = x-z + (-x) = -z
Since z < 0, then -z > 0 and -z = |z| SUFFICIENT

Statement 2: y > 0
From #2 we know that z < x and same answer as statement 1.

[Guest]

I may be way off here, let me know what you guys think.

Firstly, since both ZY and XY are both less than 0, this implies that Z and X are both negative or positive (depending on value of y)

if Y is negative:
Z and X are both positive. Since ZY < XY, this means X<Z.

if Y is positive:
Z and X are both negative. Since ZY < ZX, this means X>Z.


Now, statement 1 says that Z<X. This means that Y is positive.

|X-Z| + |X| = |Z| -> Z-X + X = Z -> YES


Statement 2:
Y < 0. This implies that X<Z.


|X-Z| + |X| = |Z| -> X-Z + X = Z -> NO


Therefore, both statements are sufficient.

Does this make sense?

Close.

From the question:
zy < xy < 0



Implies:
1. Since zy and xy are < 0 , then if y > 0, z < 0 and x < 0, and if y < 0, then x > 0 and z > 0.
2. If y > 0
-- divide by y, no change in sign, so z < x
3. If y < 0
-- divide by y, change the sign, so y > x

Statement 1: z < x
From #2 above, we know that y > 0. Also we know that x < 0 and z < 0.
So,
|x-z| + |x| = x-z + (-x) = -z
Since z < 0, then -z > 0 and -z = |z| SUFFICIENT

Statement 2: y > 0
From #2 we know that z < x and same answer as statement 1.

SORRY MADE A TYPO, RIGHT ANSWER BELOW:

Close.

From the question:
zy < xy < 0

Implies:
1. Since zy and xy are < 0 , then if y > 0, z < 0 and x < 0, and if y < 0, then x > 0 and z > 0.
2. If y > 0
-- divide by y, no change in sign, so z < x
3. If y < 0
-- divide by y, change the sign, so z > x (typo fixed)

Statement 1: z < x
From #2 above, we know that y > 0. Also we know that x < 0 and z < 0.
So,
|x-z| + |x| = x-z + (-x) = -z
Since z < 0, then -z > 0 and -z = |z| SUFFICIENT
Addendum: Take an example s.t. x,z<0 and and z<x. Say z=-10 and x=-5. Clearly -10<-5. Furthere more, x-z=-5-(-10)=-5+10=5. Since 5>0 we know that |x-z| = x-z.

Statement 2: y > 0
From #2 we know that z < x and same answer as statement 1.[code][/code]

[rfernandez]

[alysekilleen]

I am struggling with the logic of this problem. Can't you answer the question with the inequality given in the question stem alone?

I understand that the gmat would not provide a DS question that could be answered without the statement prompts, but I must be misunderstanding how to compute (or conceptualize) the problem because zy < xy < 0 seems sufficient to answer the question.

Can someone please help me out?

Thank you!

[trang.kieu.phung]

I cannot find the GMAT Prep Math folder, so I am posting the question here.

If zy < xy < 0, is |x-z| + |x| = |z|?

1. z < x
2. y < 0

Knowing the answer, I can try values and confirm the answer. But, would like to know if anyone was able to rephrase the questions to be a little more helpful?

The answer is D

From zy < xy < 0, we have: zy < xy <--> y(x - z) > 0 (*)
From (*), there are 2 cases:
A. y > 0 AND x > z
B. y < 0 AND x < z

So the question can be rephrased as A and B
To tackle this problem, we will use the question stem and the statements to identify the sign of the absolute value.

From statement (1): z < x ---> A is true ---> y > 0
Also, we have: zy < 0, so z < 0
We have: xy < 0 ---> x < 0

Hence, we can identify the signs of the absolute values:
(x - z) + (-x) = -z ---> this is true

So (1) is suff

From Statement (2): y < 0 ---> B is true ---> x < z
Bcuz y < 0 ---> z > 0 and x > 0

Then we get:
-(x - z) + x = z ---> true

So (2) is suff
And answer is D

Hope this helped.

[RonPurewal]

I am struggling with the logic of this problem. Can't you answer the question with the inequality given in the question stem alone?

heh. yep.
read all about it:
post30742.html#p30742

incidentally, this is the only question i've seen like this (i.e., the only question i've seen on which the prompt itself -- without either of the numbered statements -- is actually enough information to solve the problem).

still, if you see a problem like this, the answer is quite unambiguous: it's definitely possible to solve the problem with each of the numbered statements alone (since it's already possible to solve it without either of them!). therefore, given the actual definitions of the answer choices, it's still clear that the answer to the problem, overall, is (d): "each statement alone is sufficient".

but, yes, i'm troubled by this problem. they were pretty clearly asleep when they wrote this one.