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If x and y are positive, is x < 10 < y

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Source: — Data Sufficiency |

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by Anurag@Gurome » Thu Feb 28, 2013 3:39 am
neerajeai wrote:If x and y are positive, is x < 10 < y ?
(1) x < y and xy = 100
(2) x² < 100 < y²
Point to note : x and y are positive. hence, we can multiply or divide any inequality with either x or y without bothering about the inequality sign.

Statement 1: x < y ---> x² < xy ---> x² < 100 ---> x < 10
Similarly, y > x ---> y² > xy ---> y² > 100 ---> y > 10
hence, x < 10 < y

Sufficient

Statement 2: As x² < 100 ---> x < 10
And as y² > 100 ---> y > 10
hence, x < 10 < y

Sufficient

The correct answer is D.
Last edited by Anurag@Gurome on Thu Feb 28, 2013 3:44 am, edited 1 time in total.
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by neerajeai » Thu Feb 28, 2013 3:40 am
Lets look at Option 1:
If x<y and xy=100, and given that these numbers are positive, following combinations could be true;
x=1 y=100 or x=2 y=50 or x=4 y=25 x=5 y=20
all the above cases prove that x<10<y
So rule out B,C, E. Possible answers A, D

Lets now look at option 2:
it says, x^2<100,
therefore, x<10 or x>-10
similarly as y^2>100
therefore, y>10 or y<-10
So we can say that x <10 but cannot say y>10 (because it could be that y<-10)

So Answer =A

However OG has answer as D. Can someone explain how?
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by neerajeai » Thu Feb 28, 2013 3:43 am
neerajeai wrote:Lets look at Option 1:
If x<y and xy=100, and given that these numbers are positive, following combinations could be true;
x=1 y=100 or x=2 y=50 or x=4 y=25 x=5 y=20
all the above cases prove that x<10<y
So rule out B,C, E. Possible answers A, D

Lets now look at option 2:
it says, x^2<100,
therefore, x<10 or x>-10
similarly as y^2>100
therefore, y>10 or y<-10
So we can say that x <10 but cannot say y>10 (because it could be that y<-10)

So Answer =A

However OG has answer as D. Can someone explain how?
Thanks Anurag. The catch is in the premise.
numbers are positive :)
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by Anurag@Gurome » Thu Feb 28, 2013 3:43 am
neerajeai wrote:Lets look at Option 1:
If x<y and xy=100, and given that these numbers are positive, following
...

So we can say that x <10 but cannot say y>10 (because it could be that y<-10)

...
However OG has answer as D. Can someone explain how?
Hope that helps.
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