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# Jane can make a handcrafted drum in 4 weeks. Zane can make a similar

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Math Expert
Joined: 02 Sep 2009
Posts: 60627
Jane can make a handcrafted drum in 4 weeks. Zane can make a similar  [#permalink]

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27 Feb 2015, 06:02
00:00

Difficulty:

5% (low)

Question Stats:

96% (01:11) correct 4% (01:25) wrong based on 163 sessions

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Jane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks. If they both work together, how many weeks will it take for them to produce 15 handcrafted drums?

A. 30
B. 36
C. 70
D. 80
E. 150

Kudos for a correct solution.

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Re: Jane can make a handcrafted drum in 4 weeks. Zane can make a similar  [#permalink]

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27 Feb 2015, 07:28
1
Ans : (B).
J = 4 weeks per item = 1/28 of an item / day
Z = 6 weeks per item = 1/42 item / day
Combined = 1/42 + 1/28 = 5/84 of an item per day.
Let them take x weeks to complete 1 item => x/7 per day => 15x/7 = 5/84 => 36.

Is this correct? Or is there a faster solution?
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Posts: 91
Jane can make a handcrafted drum in 4 weeks. Zane can make a similar  [#permalink]

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Updated on: 28 Feb 2015, 10:30
1
Rate of Jane = 1/4 drum per week

Rate of Zane = 1/6 drum per week

Rate of Jane + Rate of Zane = 1/4 + 1/6 = 5/12

Next step: set up an equation.

5/12 = 15/x

*its important to understand the equation. 5/12 states that in order to make 5 drums, it will take 12 hours. This allows you to set up the opposite equation to solve for x (as seen above).

Alternatively, you can interpret 5/12 as the amount of time it takes to make one drum. So you could also divide 15 by 5/12 and this will also give you the answer, 36, however it's a much more cumbersome way to solve the problem.

x = 36. (B)

Posted from my mobile device

Originally posted by ak1802 on 27 Feb 2015, 13:00.
Last edited by ak1802 on 28 Feb 2015, 10:30, edited 1 time in total.
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Re: Jane can make a handcrafted drum in 4 weeks. Zane can make a similar  [#permalink]

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27 Feb 2015, 13:54
3
Hi All,

This question is presented as a Work Formula question, which means that you can do the math in a couple of different ways. You can do "per unit" math or use the Work Formula. In this prompt though, there's ANOTHER way to get to the correct answer, but you have to notice how the numbers 'intersect' with one another....

Jane can make a drum in 4 weeks
Zane can make a drum in 6 weeks

It's interesting that those numbers are both even integers. Since the least common multiple of 4 and 6 is 12, we can figure out a quick calculation....

Jane can make 3 drums in 12 weeks
Zane can make 2 drums in 12 weeks

So, in 12 weeks, they make a total of 5 drums. I bring this up because the question asks how long it takes the two of them to make 15 drums....

12 weeks/5 drums =
36 weeks/15 drums

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Re: Jane can make a handcrafted drum in 4 weeks. Zane can make a similar  [#permalink]

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27 Feb 2015, 15:42
1
IMO its B

i would do something like this in exam:
small mental note ( A do x work in q days ; B do same x work in Y days.. then together = (q+y)/(q*y) and then reciprocal of it.)

(6+4)/(6*4)= 10/24
(24/10)*15= 36

would really appreciate if there is something quicker can be done.

Kudos please if it happened to be a quick way somehow.
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Re: Jane can make a handcrafted drum in 4 weeks. Zane can make a similar  [#permalink]

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27 Feb 2015, 19:11
Celestial09 wrote:
IMO its B

i would do something like this in exam:
small mental note ( A do x work in q days ; B do same x work in Y days.. then together = (q+y)/(q*y) and then reciprocal of it.)

(6+4)/(6*4)= 10/24
(24/10)*15= 36

would really appreciate if there is something quicker can be done.

Kudos please if it happened to be a quick way somehow.

How fast are you looking to solve the problem?

The biggest hurdle any test-taker faces is recognizing the problem, and formulating a plan of attack.

You should be familiar with work/rate problems, and your plan of attack should be straightforward.

Recognition + plan of attack should be about 20 seconds, if not less. This leaves you an entire 1 minute and 40 seconds to solve the problem.
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Re: Jane can make a handcrafted drum in 4 weeks. Zane can make a similar  [#permalink]

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27 Feb 2015, 21:53
Bunuel wrote:
Jane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks. If they both work together, how many weeks will it take for them to produce 15 handcrafted drums?

A. 30
B. 36
C. 70
D. 80
E. 150

Kudos for a correct solution.

Jane takes 4 week to make a drum.
So, task done by Jane in 1 week = 1/4

Zane takes 6 week to make a drum.
So, task done by Zane in 1 week = 1/6

Total task in 1 week = 1/4 + 1/6
= 5/12
So, 5/12 drums are produced in 1 week.
So, 15 drums are produced in (15 * 1) / (5/12)
= (15*12)/5
= 36
Hence option B.

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Re: Jane can make a handcrafted drum in 4 weeks. Zane can make a similar  [#permalink]

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28 Feb 2015, 12:05

Firstly, lets find the time needed to make ONE handcrafted when BOTH guys working : jane's rate is 4 weeks and zane's is 6 : so, (1/4 +1/6) *t = 1

Or : (10/24) *t = 1 and 10 *t =24 or t = 24/10 or 2.4 weeks ( the time needed to make ONE handcrafted ) so , easily the time need to make 15 handcrafted is : 15 *2.4 = 36

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Posts: 60627
Re: Jane can make a handcrafted drum in 4 weeks. Zane can make a similar  [#permalink]

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02 Mar 2015, 06:45
Bunuel wrote:
Jane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks. If they both work together, how many weeks will it take for them to produce 15 handcrafted drums?

A. 30
B. 36
C. 70
D. 80
E. 150

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

Method I: the rates solution

“Jane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks.” Jane’s rate is (1 drum)/(4 weeks) = 1/4. Zane’s rate is (1 drum)/(6 weeks) = 1/6. The combined rate of Jane + Zane is
R = 1/4 + 1/6 = 3/12 + 2/12 = 5/12

That’s the combined rate. We need to make 15 drums — we have a rate and we have an amount, so use the “art” equation to solve for time:
T = A/R = 15/(5/12) = 15*(12/5) = (15/5)*12 = 3*12 = 36

BTW, notice in the penultimate step, the universal fraction strategy: cancel before you multiply (Tip #3: http://magoosh.com/gmat/2012/can-i-use- ... -the-gmat/. Jane and Zane need 36 weeks to make 15 drums.

Method II: the proportion solution

“Jane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks.” Let’s find the LCM of 4 and 6 — that’s 12 weeks. In a 12 week period, Jane, making a drum every 4 weeks, makes three drums. In a 12 week period, Zane, making a drum every 6 weeks, makes two drums. Therefore, in a 12 weeks period, they produce 5 drums between the two of them. If they make 5 drums in 12 weeks, they need triple that time, 36 weeks, to make 15 drums. Therefore, Jane and Zane need 36 weeks to make 15 drums.

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Jane can make a handcrafted drum in 4 weeks. Zane can make a similar  [#permalink]

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26 Jan 2017, 09:54
Simple work formula
two individuals Jane , Zane make 1 handcraft drum in 4 and 6 weeks respectively
Together how much time for 15 handcrafts
$$\frac{(4)(6)}{(4+6)}$$
$$\frac{24}{10}$$
2.4 weeks for 1 handcraft
For 15 handcrafts ----- 2.4x15 = 36 weeks
B
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Re: Jane can make a handcrafted drum in 4 weeks. Zane can make a similar  [#permalink]

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07 Dec 2019, 12:22
Rate of Jane: rj= 1/4
Rate of Zane: rz=1/6
then ... we use W = r t
substituting ...

15 = (rj + rz)*t

= (1/4 + 1/6)

15 = (5/12)* t

15 * 12
5

3 * 12 = t
Re: Jane can make a handcrafted drum in 4 weeks. Zane can make a similar   [#permalink] 07 Dec 2019, 12:22
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