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

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Math Expert
Joined: 02 Sep 2009
Posts: 58445
If the average (arithmetic mean) of x and y is positive, is x positive  [#permalink]

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05 Jan 2018, 01:11
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Difficulty:

25% (medium)

Question Stats:

80% (01:10) correct 20% (01:23) wrong based on 37 sessions

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

(1) The average (arithmetic mean) of x and y is 8.
(2) 2x > 2y

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

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05 Jan 2018, 08:38
If the average (arithmetic mean) of x and y is positive, this means the sum of x and y is positive.

(1) The average (arithmetic mean) of x and y is 8, this gives x+y =16. but we can have (x,y) = (10,6) or (-2,18). Hence x can be negative or positive, So, it is insufficient.
(2) 2x > 2y . this gives x>y or x-y >0
and also from question stem, x+y = positive .
this gives x +y>0

Adding x-y >0 & x +y>0 , we get x>0. It is sufficient.
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Re: If the average (arithmetic mean) of x and y is positive, is x positive   [#permalink] 05 Jan 2018, 08:38
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