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Is x > 0 ? (1) xy > 0 (2) x + y > 0

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Is x > 0 ? (1) xy > 0 (2) x + y > 0  [#permalink]

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New post 10 Aug 2010, 14:58
1
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

73% (00:55) correct 27% (00:56) wrong based on 71 sessions

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Is x > 0 ?

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

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New post 10 Aug 2010, 15:04
Bull78 wrote:
Is \(X > 0\) ?

1) \(xy>0\)

2) \(x+y>0\)


From Statement 1, x and y have the same sign. Not sufficient, since both could be negative.

From Statement 2, x and y could certainly both be positive, but it might be that x = -1 and y = 2, say. Not sufficient.

Taken together, we know from statement 1 that x and y share the same sign. Could they both be negative? No, because if they were, x+y would need to be negative, and that's not the case, as we learn from statement 2. So both x and y need to be positive, and the answer is C.
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Re: Is x > 0 ? (1) xy > 0 (2) x + y > 0  [#permalink]

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New post 11 Aug 2010, 19:10
Bull78 wrote:
Is \(X > 0\) ?

1) \(xy>0\)

2) \(x+y>0\)


Statement A:

xy > 0

(x, y) could be (-ve, -ve) or (+ve, +ve). Since there are two scenarios, we can't say whether x is +ve.

Insufficient.

Statement B:

x + y > 0

(x,y) can be (3, 4) or (7, -6) or (-8, 25). Hence cannot say x is +ve.

Insufficient.

Combining Statement A & B, xy > 0 & x+y > 0.
(x, y) could be (+ve, +ve) and not (-ve, -ve).
(x,y) can be (3, 4) and not (7, -6) or (-8, 25).


Hence statement A and B can be used together and not alone to answer this question.

Answer : C.
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Re: Is x > 0 ? (1) xy > 0 (2) x + y > 0  [#permalink]

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New post 12 Jan 2016, 02:18
is there an algebraic solution to this problem? thanks
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Re: Is x > 0 ? (1) xy > 0 (2) x + y > 0  [#permalink]

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New post 29 Nov 2019, 05:48
Anyone could give more explaination? Why not E?
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Re: Is x > 0 ? (1) xy > 0 (2) x + y > 0  [#permalink]

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New post 29 Nov 2019, 05:59
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Mamsi wrote:
Anyone could give more explaination? Why not E?



1 stm just tels us that x and y have the same +- nature and none of them is 0
2 stm tells us that x>-y

From the both statements we have got
If x is positive y is positive and satisfy the second statement x>-y
If x is negative then y is negative too, with this we cant satisfy the second statement negative number cant be more than any positive number

So only option one (when x and y are positive) is left

Hope it's clear
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Re: Is x > 0 ? (1) xy > 0 (2) x + y > 0  [#permalink]

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New post 29 Nov 2019, 06:03
LevanKhukhunashvili wrote:
Mamsi wrote:
Anyone could give more explaination? Why not E?



1 stm just tels us that x and y have the same +- nature and none of them is 0
2 stm tells us that x>-y

From the both statements we have got
If x is positive y is positive and satisfy the second statement x>-y
If x is negative then y is negative too, with this we cant satisfy the second statement negative number cant be more than any positive number

So only option one (when x and y are positive) is left

Hope it's clear



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Re: Is x > 0 ? (1) xy > 0 (2) x + y > 0   [#permalink] 29 Nov 2019, 06:03
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