If x and y are positive, is x < 10 < y ?
1. x<y and xy =100
2. x^2 < 100 < y^2
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OG16 - DS 66
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amina.shaikh309
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Dario@VinciaPrep
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Hi!
Let's consider STATEMENT 1. If x and y could be the same, they would be both 10, as 10^2=100. As they are different, one of them must be more than 10, and that's going to be y, and the other one must be less than 10, and that's going to be x. So 10 will be between x and y. Thus STATEMENT 1 ALONE IS SUFFICIENT.
Let's consider STATEMENT 2. If all of the numbers are positive (it is stated in the question that x and y are positive), we can extract the square root of all of the three terms of this double inequality...and that leads to the same answer as statement 1: 10 will be between x and y. Thus STATEMENT 2 ALONE IS SUFFICIENT.
The answer is D.
Let's consider STATEMENT 1. If x and y could be the same, they would be both 10, as 10^2=100. As they are different, one of them must be more than 10, and that's going to be y, and the other one must be less than 10, and that's going to be x. So 10 will be between x and y. Thus STATEMENT 1 ALONE IS SUFFICIENT.
Let's consider STATEMENT 2. If all of the numbers are positive (it is stated in the question that x and y are positive), we can extract the square root of all of the three terms of this double inequality...and that leads to the same answer as statement 1: 10 will be between x and y. Thus STATEMENT 2 ALONE IS SUFFICIENT.
The answer is D.
