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Machines P, Q, and R produce aluminum cans at their respective 31 Dec 2023, 05:16
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C
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70% (01:53) correct 30% (01:46) wrong based on 641 sessions

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Machines P, Q, and R produce aluminum cans at their respective constant rates. Is machine P's rate greater than machine Q's rate?

(1) Machine P's rate is greater than machine R's rate.

(2) Machines P and R, working simultaneously, produce a total of 1,000 aluminum cans in half the time that it takes machine Q, working alone, to produce 1,000 aluminum cans.


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C
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Bunuel
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Machines P, Q, and R produce aluminum cans at their respective 03 Sep 2024, 09:18
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rishika_agarwal11

chetan2u
Machines P, Q, and R produce aluminum cans at their respective constant rates. Is machine P's rate greater than machine Q's rate?

(1) Machine P's rate is greater than machine R's rate.
Nothing about Q.

(2) Machines P and R, working simultaneously, produce a total of 1,000 aluminum cans in half the time that it takes machine Q, working alone, to produce 1,000 aluminum cans.
Two cases
a) P and R have same rate, which will be then equal to Q.
b) P and R have different rates, then one will be greater and other lesser.


Combined.
We know P>R, so surely P>Q>R
Sufficient


C
Hi, I did not understand how did we conclude that P>Q>R.

Please explain.­
Show more
­
Machines P, Q, and R produce aluminum cans at their respective constant rates. Is machine P's rate greater than machine Q's rate?

Assuming the rates of machines P, Q, and R are p, q, and r, respectively, the question asks whether q < p.

(1) Machine P's rate is greater than machine R's rate.

This tells us r < p, but doesn't provide information about q. Not sufficient.

(2) Machines P and R, working simultaneously, produce a total of 1,000 aluminum cans in half the time that it takes machine Q, working alone, to produce 1,000 aluminum cans.

This statement implies that the combined rate of machines P and R is twice that of the rate of machine Q, which translates to p + r = 2q, or q = (p + r)/2. This, in turn, implies that the value of q must be between the values of p and r (q cannot be less than both p and r or more than both p and r because in this case p + r = 2q won't hold, so we must have either p < q < r, p = q = r, or r < q < p). Not sufficient.

(1)+(2) Since from (1) r < p and from (2) we know that q must be between the values of p and r, then we have r < q < p. Sufficient.

Answer: C.­
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GMAT Focus 1: 735 Q90 V89 DI81
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Machines P, Q, and R produce aluminum cans at their respective 31 Dec 2023, 06:20
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Machines P, Q, and R produce aluminum cans at their respective constant rates. Is machine P's rate greater than machine Q's rate?

(1) Machine P's rate is greater than machine R's rate.
Nothing about Q.

(2) Machines P and R, working simultaneously, produce a total of 1,000 aluminum cans in half the time that it takes machine Q, working alone, to produce 1,000 aluminum cans.
Two cases
a) P and R have same rate, which will be then equal to Q.
b) P and R have different rates, then one will be greater and other lesser.


Combined.
We know P>R, so surely P>Q>R
Sufficient


C
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rishika_agarwal11
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Machines P, Q, and R produce aluminum cans at their respective 02 Sep 2024, 04:41
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chetan2u
Machines P, Q, and R produce aluminum cans at their respective constant rates. Is machine P's rate greater than machine Q's rate?

(1) Machine P's rate is greater than machine R's rate.
Nothing about Q.

(2) Machines P and R, working simultaneously, produce a total of 1,000 aluminum cans in half the time that it takes machine Q, working alone, to produce 1,000 aluminum cans.
Two cases
a) P and R have same rate, which will be then equal to Q.
b) P and R have different rates, then one will be greater and other lesser.


Combined.
We know P>R, so surely P>Q>R
Sufficient


C
Show more
Hi, I did not understand how did we conclude that P>Q>R.

Please explain.­
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rishika_agarwal11
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Machines P, Q, and R produce aluminum cans at their respective 03 Sep 2024, 09:33
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Bunuel

rishika_agarwal11

chetan2u
Machines P, Q, and R produce aluminum cans at their respective constant rates. Is machine P's rate greater than machine Q's rate?

(1) Machine P's rate is greater than machine R's rate.
Nothing about Q.

(2) Machines P and R, working simultaneously, produce a total of 1,000 aluminum cans in half the time that it takes machine Q, working alone, to produce 1,000 aluminum cans.
Two cases
a) P and R have same rate, which will be then equal to Q.
b) P and R have different rates, then one will be greater and other lesser.


Combined.
We know P>R, so surely P>Q>R
Sufficient


C
Hi, I did not understand how did we conclude that P>Q>R.

Please explain.­
­
Machines P, Q, and R produce aluminum cans at their respective constant rates. Is machine P's rate greater than machine Q's rate?

Assuming the rates of machines P, Q, and R are p, q, and r, respectively, the question asks whether q < p.

(1) Machine P's rate is greater than machine R's rate.

This tells us r < p, but doesn't provide information about q. Not sufficient.

(2) Machines P and R, working simultaneously, produce a total of 1,000 aluminum cans in half the time that it takes machine Q, working alone, to produce 1,000 aluminum cans.

This statement implies that the combined rate of machines P and R is twice that of the rate of machine Q, which translates to p + r = 2q, or q = (p + r)/2. This, in turn, implies that the value of q must be between the values of p and r (q cannot be less than both p and r or more than both p and r because in this case p + r = 2q won't hold, so we must have either p < q < r, p = q = r, or r < q < p). Not sufficient.

(1)+(2) Since from (1) r < p and from (2) we know that q must be between the values of p and r, then we have r < q < p. Sufficient.

Answer: C.­
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­Thanks, I understood now..
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Machines P, Q, and R produce aluminum cans at their respective 22 Sep 2025, 16:11
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