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Robots X, Y, and Z each assembled components at their

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Robots X, Y, and Z each assembled components at their

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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) \(r_y < 1\)

OA C

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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) \(r_y < 1\)
Let X = X's rate, Y = Y's rate, and Z = Z's rate.
r(x) = the ratio of X's rate to Z's rate = X/Z.
r(y) = the ratio of Y's rate to Z's rate = Y/Z.
Note:
X, Y and Z all represent rates and thus must be POSITIVE.

Statement 1: r(x) < r(y)
In other words:
X/Z < Y/Z.
Since Z>0, we can multiply each side by Z:
(X/Z) * Z < (Y/Z) * Z
X < Y.
No way to determine whether Z is the greatest of the 3 rates.
INSUFFICIENT.

Statement 2: r(y) < 1

In other words:
Y/Z < 1.
Since Z>0, we can multiply each side by Z:
(Y/Z) * Z < 1 * Z
Y < Z.
No way to determine whether Z is the greatest of the 3 rates.
INSUFFICIENT.

Statements combined:

Since X < Y and Y < Z, we get:
X < Y < Z
Thus, Z is the greatest of the 3 rates.
SUFFICIENT.

The correct answer is C.

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