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If the average (arithmetic mean) of x and y is positive, is x positive

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If the average (arithmetic mean) of x and y is positive, is x positive [#permalink]

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New post 10 Jan 2018, 05:36
1
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

48% (00:49) correct 52% (01:05) wrong based on 57 sessions

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Concentration: Technology, Healthcare
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Re: If the average (arithmetic mean) of x and y is positive, is x positive [#permalink]

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New post 10 Jan 2018, 08:23
Qstn says average of (x+y)/2 is positive. So either both x and y are positive or one is positive and one negative. Both x and y cannot be negative. Statement 1 says xy>0 so both is positive. Both negative does not apply. So statement 1 is enough. Statement 2 says x - y >0. so X is greater than Y. If both are positive x >y. Both can also be negative with x<y which also gives x-y>0. So statement 2 is true for both x as positive and x as negative. So statement 2 not sufficient. So answer is A

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Re: If the average (arithmetic mean) of x and y is positive, is x positive [#permalink]

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New post 10 Jan 2018, 08:53
statement 1: xy>0
x>0,y>0 : mean x+y/2>0
x<0 ,y<0:mean x+y/2 is negative
so x>0 y>0;statement 1 is sufficient
statement2: x-y>0 ; x>y . Mean can be positive or negative.
statement 2 is not sufficient.
Answer :A
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Re: If the average (arithmetic mean) of x and y is positive, is x positive [#permalink]

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New post 10 Jan 2018, 09:24
From the question statement we get (x+y)/2 >0 or x+y>0

Statement 1 xy>0 so either both x and y are positive or both CA and y are negative . Since x+y>0 so both x and y shall be positive. So this statement is sufficient

Statement 2
x-y>0 adding x+y>0 gives x>0. So this statement is also sufficient.

Let me know if I am overlooking something

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Re: If the average (arithmetic mean) of x and y is positive, is x positive   [#permalink] 10 Jan 2018, 09:24
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If the average (arithmetic mean) of x and y is positive, is x positive

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