Data Sufficiency

Hello BTG

Would appreciate a little help on the following question:



Thanks in advance

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.
SUFFICIENT.

The correct answer is C.

lucas211 wrote:Hello BTG

Would appreciate a little help on the following question:

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
ry 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

Thanks in advance

Assume the individual rates be X, Y and Z respectively for the robots.
Given: X/Z = rx and Y/Z = ry
Required: Is Z the greatest?

Statement 1: rx < ry
Hence X/Z < Y/Z
Or, X < Y - (i)
We do not have any information about Z.
INSUFFICIENT

Statement 2: ry < l
Or Y/Z < 1
Hence Y < Z - (ii)
We do not know anything about X.
INSUFFICIENT

Combining both statements:
From (i) and (ii), we know that
X < Y and Y < Z
Hence X < Y < Z

SUFFICIENT

Correct Option: C