Question

If x and y are positive, is $x<10<y$?
(1) $x<y$ and $xy=100$
(2) $x^2<100<y^2$

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is D Each statement alone is sufficient.

• Given that $x<y$, multiply both sides by x, which is positive, to get . Then, since $xy=100$, it follows that Similarly, multiply both sides of $x<y$ by y, which is positive, to get . Again, since $xy=100$, it follows that . Combining, and gives from which it follows that $x<10<y$, since x and y are both positive. Thus, statement 1 is sufficient.
  
• Given that , it follows that $x<10<y$ as explained above. Thus, statement 2 is also sufficient.