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# Is xy = x^2 ? (1) x + y < 0 (2) xy < 0

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Math Expert
Joined: 02 Sep 2009
Posts: 47037
Is xy = x^2 ? (1) x + y < 0 (2) xy < 0 [#permalink]

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24 Sep 2017, 23:53
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Difficulty:

35% (medium)

Question Stats:

55% (00:50) correct 45% (00:42) wrong based on 40 sessions

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Is xy = x^2 ?

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

_________________
Senior Manager
Joined: 02 Jul 2017
Posts: 294
GMAT 1: 730 Q50 V38
Re: Is xy = x^2 ? (1) x + y < 0 (2) xy < 0 [#permalink]

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25 Sep 2017, 00:51
1
Is xy = x^2 ?
so find if x = y. and x can be -ve or +ve

so let x= -5 , if y =-5 => xy =x^2
or if x = 5 and y =5 => xy = x^2

(1) x + y < 0
5+5<0 false
(-5)+(-5) <0 true
Insufficient

(2) xy < 0
this implies x and y have opposte sign .. if x= +ve than y = -ve => xy <0 or else if x = -ve than y = +ve so xy <0
=> This implies x can never be equal to y with sign .
Even if magnitude of x and y are same = 2 => x=2 and y need to be -2 => xy = -4 < 0
=> xy can never be equal to x^2
Sufficient

Intern
Joined: 04 Jun 2015
Posts: 6
Re: Is xy = x^2 ? (1) x + y < 0 (2) xy < 0 [#permalink]

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25 Sep 2017, 01:07
Bunuel wrote:
Is xy = x^2 ?

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

I think the answer is E.

1) states that x<y- doesn't say if they are equal or not
2)xy<0 - it can be x=-6 and y =1 or vice a versa.

c) not sufficient from 1) and 2)
Senior Manager
Joined: 02 Jul 2017
Posts: 294
GMAT 1: 730 Q50 V38
Is xy = x^2 ? (1) x + y < 0 (2) xy < 0 [#permalink]

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25 Sep 2017, 01:18
ankitavijay wrote:
Bunuel wrote:
Is xy = x^2 ?

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

I think the answer is E.

1) states that x<y- doesn't say if they are equal or not
2)xy<0 - it can be x=-6 and y =1 or vice a versa.

c) not sufficient from 1) and 2)

2)xy<0 - it can be x=-6 and y =1 or vice a versa.
By this sentence we get the information that xy can never be equal to x^2
This is sufficient to answer the question as yes or no.

if x=-6 and y =1 than xy is not equal to x^2.
That's why option B is sufficient to give definite answer for question.
Intern
Joined: 04 Jun 2015
Posts: 6
Re: Is xy = x^2 ? (1) x + y < 0 (2) xy < 0 [#permalink]

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25 Sep 2017, 01:24
Nikkb wrote:
ankitavijay wrote:
Bunuel wrote:
Is xy = x^2 ?

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

I think the answer is E.

1) states that x<y- doesn't say if they are equal or not
2)xy<0 - it can be x=-6 and y =1 or vice a versa.

c) not sufficient from 1) and 2)

2)xy<0 - it can be x=-6 and y =1 or vice a versa.
By this sentence we get the information that xy can never be equal to x^2
This is sufficient to answer the question as yes or no.

if x=-6 and y =1 than xy is not equal to x^2.
That's why option B is sufficient to give definite answer for question.

I think you missed to consider the following: x=1, y=-1. In this case E should be the answer
Senior Manager
Joined: 02 Jul 2017
Posts: 294
GMAT 1: 730 Q50 V38
Is xy = x^2 ? (1) x + y < 0 (2) xy < 0 [#permalink]

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25 Sep 2017, 01:37
ankitavijay wrote:
Nikkb wrote:
ankitavijay wrote:

I think the answer is E.

1) states that x<y- doesn't say if they are equal or not
2)xy<0 - it can be x=-6 and y =1 or vice a versa.

c) not sufficient from 1) and 2)

2)xy<0 - it can be x=-6 and y =1 or vice a versa.
By this sentence we get the information that xy can never be equal to x^2
This is sufficient to answer the question as yes or no.

if x=-6 and y =1 than xy is not equal to x^2.
That's why option B is sufficient to give definite answer for question.

I think you missed to consider the following: x=1, y=-1. In this case E should be the answer

so if x = 1 and y = -1

xy = 1 * (-1) = -1
and x^2 = (1)^2 = 1

still xy is not equal to x^2.
So answer will always be NO, for all the values of x and y

as multiplication of x and y will always be -ve it can not be equal to square of a number which will always be +ve

So for all values of x and y satisfying equation given by statement 2 , we will get answer "False" for the question.

Hence statement 2 is sufficient to give a definite answer.
Manager
Joined: 14 Sep 2016
Posts: 149
Re: Is xy = x^2 ? (1) x + y < 0 (2) xy < 0 [#permalink]

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25 Sep 2017, 02:57
What if we reduce the question to xy = x^2 to y = x ?
hence the question asks is y=x ?

from option B we can make out that x and y are of opposite sign. Hence, Option B is Sufficient.

Correct me if i am wrong here.

Thank you
Re: Is xy = x^2 ? (1) x + y < 0 (2) xy < 0   [#permalink] 25 Sep 2017, 02:57
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