ajit257 wrote:
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) \(r_y<1\)
We are given that rx = 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 = rx
We are also given that ry = 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 = ry
We need to determine whether C is greater than both A and B.
Statement One Alone:
rx < ry
Statement one tells us that A/C < B/C. We can multiply both sides by C and obtain:
A < B
Thus, the 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.
Statement Two Alone:
ry < 1
Since ry < 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.
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
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