Two machines, Y and Z, work at constant

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NandishSS: Master | Next Rank: 500 Posts; Posts: 366; Joined: Fri Jun 05, 2015 3:35 amFollowed by: 2 members; Thanked: 3 times

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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Source: Beat The GMAT — Problem Solving | Tue Aug 23, 2016 6:23 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

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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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

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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