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 < 1
Answer: C
** My questions are below to avoid spoiling the answer for those that want to attempt the problem.
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bml1105
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Can ry not be less than 0 because we are talking about constant rates of assembling components?
In the answer, it mentions that because ry < 1, then y must be less than z. Technically, y or z could be a negative improper fraction and still be less than 1. I just want to make sure I'm supposed to be assuming that the reason they say y < z is because of the scenario and not a concept I'm missing.
In the answer, it mentions that because ry < 1, then y must be less than z. Technically, y or z could be a negative improper fraction and still be less than 1. I just want to make sure I'm supposed to be assuming that the reason they say y < z is because of the scenario and not a concept I'm missing.
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Uva@90
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Hi Bml1105,bml1105 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 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 < 1
** My questions are below to avoid spoiling the answer for those that want to attempt the problem.
Is Answer C ?
Given:
X/Z =rx =>Z =X/rx
Y/Z =ry =>Z =Y/ry
To Find: Z>(X and Y) or not.
Statement 1: rx < ry
since,
X/rx = Y/ry and rx < ry
So, Y > X
nothing about Z, Hence Insufficient.
Statement 2: ry < 1
Z =Y/ry and ry < 1
Hence Z > Y.
Hence Insufficient.
Combine 1 and 2
z>y>x
Hence Sufficient.
Answer is C
Regards,
Uva.
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GMATGuruNY
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On the GMAT, the term ratio will always refer to POSITIVE values.bml1105 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 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 < 1
Answer: C
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Jeff@TargetTestPrep
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We are given that rx = the ratio of robot X's constant rate to robot Z's constant rate.bml1105 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 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 < 1
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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