# Robots X, Y, and Z each assemble component…

## Solution:

We are given that r_x = the ratio of robot X’s constant rate to robot Z’s constant rate. If we let A = the rate of robot X and C = the rate of robot Z, we can say:

A/C = r_x

We are also given that r_y = the ratio of robot Y’s constant rate to robot Z’s constant rate. If we let B = the rate of robot Y, we can say:

B/C = r_y

We need to determine whether C is greater than both A and B.

Statement One Alone:

r_x < r_y

Statement one tells us that A/C < B/C. We can multiply both sides by C and obtain:

A < B

Thus rate of robot X is less than the rate of robot Y. However, we still do not know whether the rate of robot Z is greater than the rate of either robot X or robot Y. Statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

r_y < 1

Since r_y < 1, B/C < 1 or B < C.

Thus, the rate of robot Z is greater than the rate of robot Y. However, we still do not know whether the rate of robot Z is greater than the rate of robot X. Statement two is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

From statements one and two we know that the rate of robot X is less than the rate of robot Y and that the rate of robot Z is greater than the rate of robot Y. Thus, if the rate of robot Y is less than the rate of robot Z, then the rate of robot X must also be less than the rate of robot Z. Therefore, the rate of robot Z must be the greatest.

Answer: C