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
Answer: D
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If x and y are positive, is x < 10 < y ?
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jjjinapinch
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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
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
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
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
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Scott@TargetTestPrep
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We are given that x and y are positive and we must determine whether x < 10 < y.jjjinapinch wrote:If x and y are positive, is x < 10 < y ?
(1) x < y and xy = 100
(2) x^2 < 100 < y^2
Statement One Alone:
x < y and xy = 100
From statement one we know that y is greater than x and xy = 100. We can isolate x in the equation xy = 100 and obtain:
x = 100/y
We now can substitute 100/y for x in the inequality x < y and then isolate y.
100/y < y
100 <y^2
√100<√(y^2)
10 < |y|
Since we are told that y is positive, |y| > 10 means y > 10. Since xy = 100 and y is greater than 10, then x must be less than 10. Thus, x < 10 < y. Statement one alone is sufficient to answer the question.
Statement Two Alone:
x^2 < 100 < y^2
Taking the square root gives us:
√(x^2) < √100 < √(y^2)
|x| < 10 < |y|
Since x and y are both positive, x < 10 < y. Statement two alone is also sufficient to answer the question.
Answer: D
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