Question

Robots X, Y, and Z each assemble components at their respective constant rates. If $r_x$ is the ratio of Robot X's constant rate to Robot Z's constant rate and $r_y$ is the ratio of Robot Y's constant rate to Robot Z's constant rate, is Robot Z's constant rate the greatest of the three?
(1) $r_x<r_y$
(2) $r_y<1$

• 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 C Both statements together are sufficient, but neither statement alone is sufficient.

Let X, Y, and Z represent the constant rates of Robots X, Y, and Z, respectively. Then, and, We have to determine if Z is the greatest of X, Y, and Z.

• Since then and X < Y. However, no information is given about the value of Z in relation to the values of X and Y. Thus, statement 1 is insufficient. Since , then and Y < Z. However, no information is given about the value of X in relation to the values of Y and Z. Thus, statement 2 is insufficient.
• Taking (1) and (2) together, X < Y from (1) and Y < Z from (2) so, X < Z. Thus, Z is greater than both X and Y and is the greatest of the three.