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

This topic has 1 expert reply and 0 member replies
jjjinapinch Senior | Next Rank: 100 Posts
Joined
24 Jul 2017
Posted:
83 messages

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

Mon Aug 07, 2017 8:52 am
If x and y are positive, is x < 10 < y ?
(1) x < y and xy = 100
(2) x^2 < 100 < y^2

Official Guide question

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
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Mon Aug 07, 2017 4:11 pm
Hi jjjinapinch,

We're told that X and Y are POSITIVE. We're asked if X < 10 < Y. This is a YES/NO question. We can solve it with a mix of TESTing VALUES and Number Properties.

1) X < Y and (X)(Y) = 100

With the information in Fact 1, we know that X and Y cannot be the same value (X < Y). IF they were the same value, then we would have (10)(10) = 100. Since that's NOT possible though - and both variables are POSITIVE - the only option is for X to DECREASE from 10 and Y to INCREASE from 10. Thus, the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

2) X^2 < 100 < Y^2

Since both variables are POSITIVE, we know that X MUST be less than 10 and that Y MUST be greater than 10. Thus, the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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