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# X and Y are two positive numbers. Is X > Y ? (1) (X+Y)/2 > Y (2)

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DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1343
Location: India
X and Y are two positive numbers. Is X > Y ? (1) (X+Y)/2 > Y (2)  [#permalink]

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13 Aug 2018, 22:54
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Difficulty:

45% (medium)

Question Stats:

68% (01:32) correct 32% (01:36) wrong based on 57 sessions

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X and Y are two positive numbers. Is X > Y ?

(1) (X+Y)/2 > Y

(2) X is Z% less than the sum (X+Y), where Z is a positive number and Z < 40.
Manager
Joined: 09 Oct 2015
Posts: 222
X and Y are two positive numbers. Is X > Y ? (1) (X+Y)/2 > Y (2)  [#permalink]

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14 Aug 2018, 00:08
option a straight away gives the ans

but for option b, on simplifying, we get that x/y>1.5
so yes

ans is d
Manager
Joined: 06 Nov 2016
Posts: 60
Location: Viet Nam
GPA: 3.54
Re: X and Y are two positive numbers. Is X > Y ? (1) (X+Y)/2 > Y (2)  [#permalink]

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25 Aug 2018, 19:01
amanvermagmat wrote:
X and Y are two positive numbers. Is X > Y ?

(1) (X+Y)/2 > Y

(2) X is Z% less than the sum (X+Y), where Z is a positive number and Z < 40.

If $$X=Y$$ then $$X=Y=\frac{(X+Y)}{2}=(X+Y)∗(1−\frac{50}{100})$$
(1) $$\frac{(X+Y)}{2}>Y$$ --> X < Y -> Sufficient.
(2) $$X= (X+Y)*(1-\frac{Z}{100})$$.
Since $$Z<40$$, $$(X+Y)*(1-\frac{Z}{100}) > (X+Y)∗(1−\frac{50}{100})$$ --> $$X>(X+Y)∗(1−\frac{50}{100})$$, thus X > Y -> Sufficient.
_________________
Re: X and Y are two positive numbers. Is X > Y ? (1) (X+Y)/2 > Y (2) &nbs [#permalink] 25 Aug 2018, 19:01
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