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Two machines, Y and Z, work at constant

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by NandishSS » Tue Aug 23, 2016 6:23 am
Two machines, Y and Z, work at constant rates producing identical items. Machine Y produces 3 items in the same time Machine Z produces 2 items. If machine Y takes 9 minutes to produce a batch of items, how many minutes does it take for machine Z to produce the same number of items?

A. 6
B. 9
C. 9(1/2)
D. 12
E. 13(1/2)

Source:GMATPrep EP 2

OA:E
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by Brent@GMATPrepNow » Tue Aug 23, 2016 6:39 am
NandishSS wrote:Two machines, Y and Z, work at constant rates producing identical items. Machine Y produces 3 items in the same time Machine Z produces 2 items. If machine Y takes 9 minutes to produce a batch of items, how many minutes does it take for machine Z to produce the same number of items?

A. 6
B. 9
C. 9(1/2)
D. 12
E. 13(1/2)
Let's assign a NICE VALUE to the number of items in a batch and go from there.

Machine Y produces 3 items in the same time Machine Z produces 2 items
Let's say there are 3 items in a batch.

Machine Y takes 9 minutes to produce a batch of items
So, machine Y takes 9 minutes to produce 3 items
From the other information, we can conclude that machine Z takes 9 minutes to produce 2 items.
In other words, machine Z produces 1 item every 4.5 minutes.
So, if a batch is 3 items, then the time it takes machine Z to produce a batch = (3)(4.5) = 13.5 minutes


Answer: E

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by DavidG@VeritasPrep » Tue Aug 23, 2016 7:12 am
NandishSS wrote:Two machines, Y and Z, work at constant rates producing identical items. Machine Y produces 3 items in the same time Machine Z produces 2 items. If machine Y takes 9 minutes to produce a batch of items, how many minutes does it take for machine Z to produce the same number of items?

A. 6
B. 9
C. 9(1/2)
D. 12
E. 13(1/2)

Source:GMATPrep EP 2

OA:E
Note, also that rate and time have a reciprocal relationship. If I'm running at 2 times your speed, I'll cover the same distance in 1/2 the time. Similarly,
If one machine (Y) is working at 3/2 the rate of another machine (Z), it will take 2/3 as much time as the other machine. Y completes the task in 9 minutes. If 9 = (2/3)T, then T = 13.5, or E
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by GMATGuruNY » Tue Aug 23, 2016 7:21 am
NandishSS wrote:Two machines, Y and Z, work at constant rates producing identical items. Machine Y produces 3 items in the same time Machine Z produces 2 items. If machine Y takes 9 minutes to produce a batch of items, how many minutes does it take for machine Z to produce the same number of items?

A. 6
B. 9
C. 9(1/2)
D. 12
E. 13(1/2)
Machine Y produces 3 items in the same time Machine Z produces 2 items.
Implication:
(Y's rate)/(Z's rate) = 3/2.

Rate and time are RECIPROCALS.
Thus:
(Y's time)/(Z's time) = 2/3.

Rephrasing this time ratio, we get:
(Z's time) = (3/2)(Y's time).

Since Y takes 9 minutes to produce a batch, the time for Z to produce a batch = (3/2)(9) = 13.5 minutes.

The correct answer is E.
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by Matt@VeritasPrep » Thu Sep 01, 2016 6:12 pm
Let's say that each machine produces x items. We know that

Work = Rate * Time, so

x = 3 * (Y's time)

x = 2 * (Z's time)

and

3 * (Y's time) = 2 * (Z's time)

so (Z's time) = (3/2) * (Y's time), and from there it's a snap :)
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