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# Is x < y?

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Senior Manager
Joined: 29 Jan 2011
Posts: 367
Followers: 0

Kudos [?]: 166 [0], given: 87

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22 Sep 2011, 23:32
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Difficulty:

45% (medium)

Question Stats:

67% (02:17) correct 33% (01:12) wrong based on 15 sessions

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Is x < y?

(1) 1/x < 1/y
(2) x/y < 0
[Reveal] Spoiler: OA
Senior Manager
Joined: 29 Jan 2011
Posts: 367
Followers: 0

Kudos [?]: 166 [0], given: 87

Re: Is x < y? [#permalink]

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22 Sep 2011, 23:41
siddhans wrote:
Tried searching for this but couldnt find it...

is x<y?
(1) 1/x < 1/y
(2) x/y < 0

St1) 1/x < 1/y

x and y can have sign or different signs

Case a: If x and y have same signs

1/x < 1/y

[highlight]can we cross multiply ?[/highlight]
y>x

Case b: if x and y have different signs

x has to be negative and y has to be positive in this case

thus , y> x

[highlight]example : -(1/3) < -(1/2)

on cross multiplying -2 > -3
[/highlight]

Thus 1 can be sufficient...

St2)
x/y < 0

Thus x and y have different signs....

Hence insufficient

Manager
Joined: 20 Aug 2011
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Re: Is x < y? [#permalink]

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23 Sep 2011, 00:05
Question-

Is x<y?

Statement 1
1/x<1/y

We don't whether x &/or y are positive or negative.
inequalities-review-69016.html

Statement 2
Insufficient.

1+2

From 2,
Either x or y is negative

2+1,
We can see that x is -ve

Hence, C
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Manager
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Re: Is x < y? [#permalink]

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23 Sep 2011, 00:21
1
KUDOS
is x<y?
(1) 1/x < 1/y
(2) x/y < 0

statement 1 . 1/x < 1/y.

let 1/x = 1/3 and 1/y =1/2 so 1/x < 1/Y as 1/3 is less than 1/2, but when we flip the reciprocal we see x =3 and y= 2, which means x > y

now let 1/x =-1/2 and 1/y =1/3 , so again 1/x < 1/y as -1/2 (-0.5) is less than 1/3 (0.33), but flip the reciprocal, we see x =-2 and y =+3, which means y>x, so two different values, hence this statement is insuffiecient.

statement 2, x/y < 0. this only tells that one of these 2 variable is negative and one of these 2 variable is positive, but we don't know which.

combining statements we see, only x could be negative , because if we put x as positive and y is negative, the first statement does not holds true. for example if 1/x = 1/2 and y = -1/3 first statement will become meaningless. as positive number can never be less than negative number.

Re: Is x < y?   [#permalink] 23 Sep 2011, 00:21
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