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Math Expert V
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Is xy < 0? (1) |x − y| > |x| − |y| (2) x > y  [#permalink]

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13 00:00

Difficulty:   95% (hard)

Question Stats: 34% (02:07) correct 66% (01:45) wrong based on 321 sessions

HideShow timer Statistics Is xy < 0?

(1) |x − y| > |x| − |y|
(2) x > y

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GMAT 1: 640 Q48 V28 Re: Is xy < 0? (1) |x − y| > |x| − |y| (2) x > y  [#permalink]

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IMHO

1) |x − y| > |x| − |y| --> is true if one of the variables is positive and the other is negative. Suff.
2) x > y --> not suff.
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Re: Is xy < 0? (1) |x − y| > |x| − |y| (2) x > y  [#permalink]

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1
[quote="LevanKhukhunashvili"]IMHO

1) |x − y| > |x| − |y| --> is true if one of the variables is positive and the other is negative. Suff.
2) x > y --> not suff.[/quote]

What about |2-5|>|2|-|5| ? 2 and 5 are both positive. Answer (C)

[size=80][b][i]Posted from my mobile device[/i][/b][/size]
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GMAT 1: 640 Q48 V28 Re: Is xy < 0? (1) |x − y| > |x| − |y| (2) x > y  [#permalink]

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Iamnowjust True. Catch Kudos
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Re: Is xy < 0? (1) |x − y| > |x| − |y| (2) x > y  [#permalink]

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2
Bunuel wrote:
Is xy < 0?

(1) |x − y| > |x| − |y|
(2) x > y

(1) we can try with plugging in values which satisfy this statement. Lets take x=4, y=3 (both +ve and x >y). Here LHS = 1 and RHS = 1. Not true
Now lets take x=3, y=4 (both +ve, x<y). Here LHS = 1, RHS = -1. True, and in this case x*y is positive
Now lets take x=3, y=-3 (one +ve, one -ve). Here LHS = 6, RHS = 0. True, and in this case x*y is negative.
So we cannot determine with surety whether x*y is positive or negative. Not sufficient.

(2) Not sufficient obviously.

Combining, x has to be greater than y. So in this case x-y will always be positive but there could be various cases:
If x is positive and y is 0, then statement 1 will not be true.
If x is positive and y is negative, then statement 1 will be true.
If x is 0 and y is negative, then again statement 1 will be true.

So both statement 1 and 2 are coming true to be in two cases: one where x is positive, y is negative (here x*y < 0) OR second where x is zero, y is negative (here x*y = 0). So we cant be sure whether x*y will be 0 or less than 0. Not sufficient.

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Re: Is xy < 0? (1) |x − y| > |x| − |y| (2) x > y  [#permalink]

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Iamnowjust wrote:
LevanKhukhunashvili wrote:
IMHO

1) |x − y| > |x| − |y| --> is true if one of the variables is positive and the other is negative. Suff.
2) x > y --> not suff.

What about |2-5|>|2|-|5| ? 2 and 5 are both positive. Answer (C)

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I think u missed one case what if both are negative and x>y then...
for ex x = -20 and y = -30

in the case above also both statement satisfies but xy > 0

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Is xy < 0? (1) |x − y| > |x| − |y| (2) x > y  [#permalink]

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amanvermagmat wrote:
Bunuel wrote:
Is xy < 0?

(1) |x − y| > |x| − |y|
(2) x > y

(1) we can try with plugging in values which satisfy this statement. Lets take x=4, y=3 (both +ve and x >y). Here LHS = 1 and RHS = 1. Not true
Now lets take x=3, y=4 (both +ve, x<y). Here LHS = 1, RHS = -1. True, and in this case x*y is positive
Now lets take x=3, y=-3 (one +ve, one -ve). Here LHS = 6, RHS = 0. True, and in this case x*y is negative.
So we cannot determine with surety whether x*y is positive or negative. Not sufficient.

(2) Not sufficient obviously.

Combining, x has to be greater than y. So in this case x-y will always be positive but there could be various cases:
If x is positive and y is 0, then statement 1 will not be true.
If x is positive and y is negative, then statement 1 will be true.
If x is 0 and y is negative, then again statement 1 will be true.

So both statement 1 and 2 are coming true to be in two cases: one where x is positive, y is negative (here x*y < 0) OR second where x is zero, y is negative (here x*y = 0). So we cant be sure whether x*y will be 0 or less than 0. Not sufficient.

No, if x or y equal to 0 then it can't fulfill the statement 1, because |x − y| = |x| − |y|, not |x − y| > |x| − |y|, so exclude this situation.
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Re: Is xy < 0? (1) |x − y| > |x| − |y| (2) x > y  [#permalink]

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1
colinlin1 wrote:
amanvermagmat wrote:
Bunuel wrote:
Is xy < 0?

(1) |x − y| > |x| − |y|
(2) x > y

(1) we can try with plugging in values which satisfy this statement. Lets take x=4, y=3 (both +ve and x >y). Here LHS = 1 and RHS = 1. Not true
Now lets take x=3, y=4 (both +ve, x<y). Here LHS = 1, RHS = -1. True, and in this case x*y is positive
Now lets take x=3, y=-3 (one +ve, one -ve). Here LHS = 6, RHS = 0. True, and in this case x*y is negative.
So we cannot determine with surety whether x*y is positive or negative. Not sufficient.

(2) Not sufficient obviously.

Combining, x has to be greater than y. So in this case x-y will always be positive but there could be various cases:
If x is positive and y is 0, then statement 1 will not be true.
If x is positive and y is negative, then statement 1 will be true.
If x is 0 and y is negative, then again statement 1 will be true.

So both statement 1 and 2 are coming true to be in two cases: one where x is positive, y is negative (here x*y < 0) OR second where x is zero, y is negative (here x*y = 0). So we cant be sure whether x*y will be 0 or less than 0. Not sufficient.

No, if x or y equal to 0 then it can't fulfill the statement 1, because |x − y| = |x| − |y|, not |x − y| > |x| − |y|, so exclude this situation.

Hello Colinlin

Lets take x=0 and y = -2. Then LHS = |x - y| = |0 - (-2)| = 2 while RHS = |0| - |-2| = 0 - 2 = -2. Here LHS and RHS are NOT equal and LHS > RHS.
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Re: Is xy < 0? (1) |x − y| > |x| − |y| (2) x > y  [#permalink]

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I) |x-y|>|x|-|y|
Above equation is satisfied when
x=-3 y=-4 xy>0
X=-4 y=3 xy<0
X=2 y=-3 xy<0
Insufficient

II)x>y
Y can be positive or negative and same for x
Eg 3>2 or 3>-2
So xy can be +ve or -ve
Insufficient

Combining both
x>y can result in xy > 0 or xy<0
So insufficient

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Re: Is xy < 0? (1) |x − y| > |x| − |y| (2) x > y  [#permalink]

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Consider X=-2 and Y=-3, we get |-2+3|>|-2|-|-3|
ie., 1 > -1 . But since -2*-3 is not less than 0 it is insufficient.
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Is xy < 0? (1) |x − y| > |x| − |y| (2) x > y  [#permalink]

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Bunuel wrote:
Is xy < 0?

(1) |x − y| > |x| − |y|
(2) x > y

Dear chetan2u,
Is there a way to solve this without plugging in numbers?
Thanks a lot, always.
Math Expert V
Joined: 02 Aug 2009
Posts: 7763
Re: Is xy < 0? (1) |x − y| > |x| − |y| (2) x > y  [#permalink]

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1
jayantbakshi wrote:
Bunuel wrote:
Is xy < 0?

(1) |x − y| > |x| − |y|
(2) x > y

Dear chetan2u,
Is there a way to solve this without plugging in numbers?
Thanks a lot, always.

Hi Jayant,

If you can imagine these numbers on a number line it will help you..

1) |X|-|y| will never be greater than |x-y|
2) whenever |y|>|X|, LHS, |x-y|, will be POSITIVE while RHS, |X|-|y| will be negative..
So when both X and y are positive and y>X,
Or both negative and x>y
3) whenever the signs are different, again statement I will be true..

Knowing above points, you would know that statement I is true for both cases- one when both are same sign and second when both are different...
but we are looking for both X and y of different sign..

Combined..
Even if x>0....
Both can be negative
Or both can be of different sign..
So insufficient..

Even rules for |X+y|<|X|+|y| can be learnt
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Re: Is xy < 0? (1) |x − y| > |x| − |y| (2) x > y  [#permalink]

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Bunuel wrote:
Is xy < 0?

(1) |x − y| > |x| − |y|
(2) x > y

Statement (1) says distance between x and y is greater than the difference between distance of x and y from origin. This holds true only when x and y are of opposite sign.
so xy<0.....sufficient
statement(2) is insufficient clearly.

Ans A
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Re: Is xy < 0? (1) |x − y| > |x| − |y| (2) x > y  [#permalink]

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chetan2u wrote:
jayantbakshi wrote:
Bunuel wrote:
Is xy < 0?

(1) |x − y| > |x| − |y|
(2) x > y

Dear chetan2u,
Is there a way to solve this without plugging in numbers?
Thanks a lot, always.

Hi Jayant,

If you can imagine these numbers on a number line it will help you..

1) |X|-|y| will never be greater than |x-y|
2) whenever |y|>|X|, LHS, |x-y|, will be POSITIVE while RHS, |X|-|y| will be negative..
So when both X and y are positive and y>X,
Or both negative and x>y
3) whenever the signs are different, again statement I will be true..

Knowing above points, you would know that statement I is true for both cases- one when both are same sign and second when both are different...
but we are looking for both X and y of different sign..

Combined..
Even if x>0....
Both can be negative
Or both can be of different sign..
So insufficient..

Even rules for |X+y|<|X|+|y| can be learnt

|x-y| has to be greater then |x| - |y|. whenever signs of x and y are same both sides become equal. so X and Y has to be of different sign
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Re: Is xy < 0? (1) |x − y| > |x| − |y| (2) x > y  [#permalink]

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Bunuel wrote:
Is xy < 0?

(1) |x − y| > |x| − |y|
(2) x > y

Question: is xy < 0 ?

Statement 1: |x − y| > |x| − |y|

for x = 0, y = -1, we get 1 > -1....hence xy = 0...therefore NO
for x = 1, y = -1, we get 2 > 0....hence xy < 0...therefore YES

Statement 1 is not sufficient.

Statement 2: x > y

for x = 0, y = -1, we get 0 > -1...hence xy = 0....therefore NO
for x = 1, y = -1, we get 1 > -1...hence xy < 0....therefore YES

Statement 2 is not sufficient.

Combining, we can use
x = 0, y = -1, to satisfy both statements & we get xy = 0...NO
x = 1, y = -1, to satisfy both statements & we get xy < 0...YES

Combining is not Sufficient.

Thanks,
GyM
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Re: Is xy < 0? (1) |x − y| > |x| − |y| (2) x > y  [#permalink]

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Hi Bunuel could you please explain how this question is different from the one below

Is |x - y| > |x| - |y|?

(1) y < x
(2) xy < 0

( A GMATPREP question)

because in this question, XY < 0, is sufficient. Im not sure why it does not work other way around.

Thank you.
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Posts: 55801
Re: Is xy < 0? (1) |x − y| > |x| − |y| (2) x > y  [#permalink]

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NWSL wrote:
Hi Bunuel could you please explain how this question is different from the one below

Is |x - y| > |x| - |y|?

(1) y < x
(2) xy < 0

( A GMATPREP question)

because in this question, XY < 0, is sufficient. Im not sure why it does not work other way around.

Thank you.

That question is discussed here: https://gmatclub.com/forum/is-x-y-x-y-1 ... 23108.html Hope it helps.
_________________ Re: Is xy < 0? (1) |x − y| > |x| − |y| (2) x > y   [#permalink] 04 Feb 2019, 02:38
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