Let X = X's rate, Y = Y's rate, and Z = Z's rate.Robots X, Y, and Z each assemble components at
their respective constant rates. If rx is the ratio of
Robot X's constant rate to Robot Z's constant rate and
xy 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)rx < ry
(2)ry < l
When they say ry is less than why cant we take it as negative
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.
On the GMAT, the term ratio refers only to POSITIVE values.
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.
SUFFICIENT.
The correct answer is C.
