Problem Solving

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

ry=y's rate/ z's rate

rate is a positive factor so the ratio will be positive.

solution:

let rx=X/Z

ry=Y/Z

(1) X/Z < Y/Z

so X<Y

no info about Z

so insufficient

(2) Y/Z<1

so Y<Z

no info about X

so insufficient

TOGETHER X<Y<Z

SO ANSWER IS C

[email protected] wrote: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

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.
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
Thus, Z is the greatest of the 3 rates.
SUFFICIENT.

The correct answer is C.

[email protected] wrote:
When they say ry is less than why cant we take it as negative

I dont think there is such a thing call a negative rate.
All rate should be positive or 0.

faraz_jeddah wrote:

[email protected] wrote:
When they say ry is less than why cant we take it as negative

I dont think there is such a thing call a negative rate.
All rate should be positive or 0.

That is correct, at least on a typical math problem. I suppose, in theory, that a negative rate would be the rate at which you "undo" a project and move away from a goal or some sort of countervailing force inhibiting one's progress (like a current in a river acting against the motion of a boat). Even then, though, that rate is only "negative" in the sense that it reduces another rate.