Last Updated on May 9, 2023
GMAT OFFICIAL GUIDE DS
Solution:
We are given that x and y are positive and we must determine whether x < 10 < y.
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. We can eliminate answer choices B, C and E.
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
