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# M14-07

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Math Expert
Joined: 02 Sep 2009
Posts: 44656

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16 Sep 2014, 00:51
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Difficulty:

15% (low)

Question Stats:

77% (00:50) correct 23% (00:46) wrong based on 113 sessions

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If working together, brothers Tom and Jack can paint a wall in 4 hours, how much time would it take Jack to paint the wall alone?

(1) Jack is painting twice as fast as Tom.

(2) If Tom painted twice as fast as he actually does, the brothers would finish the work in 3 hours.
[Reveal] Spoiler: OA

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16 Sep 2014, 00:51
Official Solution:

Statement (1) by itself is sufficient. S1 reduces to equation $$\frac{1}{J} + \frac{1}{2J} = \frac{1}{4}$$, where $$J$$ denotes the time it takes Jack to paint the wall alone. From this equation, $$J = 6$$.

Statement (2) by itself is sufficient. S2 reduces to equation $$\frac{1}{J} + 2*(\frac{1}{4} - \frac{1}{J}) = \frac{1}{3}$$, where $$\frac{1}{4} - \frac{1}{J}$$ is Tom's actual painting speed. From this equation, $$J = 6$$.

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09 Dec 2014, 12:08
Bunuel wrote:
Official Solution:

Statement (1) by itself is sufficient. S1 reduces to equation $$\frac{1}{J} + \frac{1}{2J} = \frac{1}{4}$$, where $$J$$ denotes the time it takes Jack to paint the wall alone. From this equation, $$J = 6$$.

Statement (2) by itself is sufficient. S2 reduces to equation $$\frac{1}{J} + 2*(\frac{1}{4} - \frac{1}{J}) = \frac{1}{3}$$. $$\frac{1}{4} - \frac{1}{J}$$ is Tom's actual painting speed. From this equation, $$J = 6$$.

For statement 2, I think the correct equation is 1/J + 2(1/4 - 1/J) = 1/3

That would yield J = 6.. what am I doing wrong here? Substituting equation for Tom into the given statement and solving..
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Joined: 02 Sep 2009
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09 Dec 2014, 12:30
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codeblue wrote:
Bunuel wrote:
Official Solution:

Statement (1) by itself is sufficient. S1 reduces to equation $$\frac{1}{J} + \frac{1}{2J} = \frac{1}{4}$$, where $$J$$ denotes the time it takes Jack to paint the wall alone. From this equation, $$J = 6$$.

Statement (2) by itself is sufficient. S2 reduces to equation $$\frac{1}{J} + 2*(\frac{1}{4} - \frac{1}{J}) = \frac{1}{3}$$, where $$\frac{1}{4} - \frac{1}{J}$$ is Tom's actual painting speed. From this equation, $$J = 6$$.

For statement 2, I think the correct equation is 1/J + 2(1/4 - 1/J) = 1/3

That would yield J = 6.. what am I doing wrong here? Substituting equation for Tom into the given statement and solving..

You have the same equation as above.

Alternative explanation:
If working together, brothers Tom and Jack can paint a wall in 4 hours, how much time would it take Jack to paint the wall alone?

Say the rates of Tom and Jack are T job/hour and J job/hour, respectively. Their combined rate is T+J job/hour, and we are told that it equals to 1/4 job/hour.

Thus given that T+J=1/4 job/hour.

(1) Jack is painting twice as fast as Tom --> J=2T --> T+2T=1/4 --> T=1/12 --> J=2/12=1/6 --> (time)=(reciprocal of rate)=6 hours. Sufficient.

(2) If Tom painted twice as fast as he actually does, the brothers would finish the work in 3 hours. This statement implies that if the rate of Tom were 2T instead of T, the brothers combined rate would be 1/3 job/hour, thus 2T+J=1/3. Solving T+J=1/4 and 2T+J=1/3 gives J=1/6. Sufficient.

Hope it helps.
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02 Oct 2015, 06:05
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. The solution of statement 2 seems to be misguiding in the test analysis (but not in the forum post). Perhaps a 'comma' is required after 1/3 in the explanation of the second statement.
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Vishwa

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02 Oct 2015, 08:54
Vishwa25 wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. The solution of statement 2 seems to be misguiding in the test analysis (but not in the forum post). Perhaps a 'comma' is required after 1/3 in the explanation of the second statement.

Check alternative explanation here: m14-184001.html#p1453535
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29 Feb 2016, 04:59
Bunuel wrote:
codeblue wrote:
Bunuel wrote:
Official Solution:

Statement (1) by itself is sufficient. S1 reduces to equation $$\frac{1}{J} + \frac{1}{2J} = \frac{1}{4}$$, where $$J$$ denotes the time it takes Jack to paint the wall alone. From this equation, $$J = 6$$.

Statement (2) by itself is sufficient. S2 reduces to equation $$\frac{1}{J} + 2*(\frac{1}{4} - \frac{1}{J}) = \frac{1}{3}$$, where $$\frac{1}{4} - \frac{1}{J}$$ is Tom's actual painting speed. From this equation, $$J = 6$$.

For statement 2, I think the correct equation is 1/J + 2(1/4 - 1/J) = 1/3

That would yield J = 6.. what am I doing wrong here? Substituting equation for Tom into the given statement and solving..

You have the same equation as above.

Alternative explanation:
If working together, brothers Tom and Jack can paint a wall in 4 hours, how much time would it take Jack to paint the wall alone?

Say the rates of Tom and Jack are T job/hour and J job/hour, respectively. Their combined rate is T+J job/hour, and we are told that it equals to 1/4 job/hour.

Thus given that T+J=1/4 job/hour.

(1) Jack is painting twice as fast as Tom --> J=2T --> T+2T=1/4 --> T=1/12 --> J=2/12=1/6 --> (time)=(reciprocal of rate)=6 hours. Sufficient.

(2) If Tom painted twice as fast as he actually does, the brothers would finish the work in 3 hours. This statement implies that if the rate of Tom were 2T instead of T, the brothers combined rate would be 1/3 job/hour, thus 2T+J=1/3. Solving T+J=1/4 and 2T+J=1/3 gives J=1/6. Sufficient.

Hope it helps.

Hi Bunuel,

could you explain how you come to J=2/12? I think I am looking at it the wrong way, since I would come to the following calculation:
J=2T --> 1/T+1/(2T)=1/4 --> 3/2T=1/4 --> 2T=12 T=6.

I am trying to turn my calculation around but still always get the same wrong answer.

Thank you.
Math Expert
Joined: 02 Aug 2009
Posts: 5777

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29 Feb 2016, 05:51
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Expert's post
Erina89 wrote:
Bunuel wrote:
For statement 2, I think the correct equation is 1/J + 2(1/4 - 1/J) = 1/3

That would yield J = 6.. what am I doing wrong here? Substituting equation for Tom into the given statement and solving..

You have the same equation as above.

Alternative explanation:
If working together, brothers Tom and Jack can paint a wall in 4 hours, how much time would it take Jack to paint the wall alone?

Say the rates of Tom and Jack are T job/hour and J job/hour, respectively. Their combined rate is T+J job/hour, and we are told that it equals to 1/4 job/hour.

Thus given that T+J=1/4 job/hour.

(1) Jack is painting twice as fast as Tom --> J=2T --> T+2T=1/4 --> T=1/12 --> J=2/12=1/6 --> (time)=(reciprocal of rate)=6 hours. Sufficient.

(2) If Tom painted twice as fast as he actually does, the brothers would finish the work in 3 hours. This statement implies that if the rate of Tom were 2T instead of T, the brothers combined rate would be 1/3 job/hour, thus 2T+J=1/3. Solving T+J=1/4 and 2T+J=1/3 gives J=1/6. Sufficient.

Hope it helps.

Quote:
Hi Bunuel,

could you explain how you come to J=2/12? I think I am looking at it the wrong way, since I would come to the following calculation:
J=2T --> 1/T+1/(2T)=1/4 --> 3/2T=1/4 --> 2T=12 T=6.

I am trying to turn my calculation around but still always get the same wrong answer.

Thank you.

Hi,
before Bunuel puts in his bit, let me tell you where are you going wrong..
its not J=2T, but T=2J..

(1) Jack is painting twice as fast as Tom -->
if you are talking of time taken as J and T then T=2J, as speed of J is twice that of T..
If you are taking J and T as speed, then J=2T..

since you are talking of the Equation
1/T+1/(2T).. you are taking T and J as the time taken, then T=2J.

so eq will be
1/J + 1/2J..
Redo and you will get the answer

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29 Feb 2016, 07:28
Thank you. I knew I somehow looked at it the wrong way...
Study Buddy Forum Moderator
Joined: 04 Sep 2016
Posts: 902
Location: India
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03 Dec 2017, 15:21
chetan2u wrote:
Erina89 wrote:
Bunuel wrote:
For statement 2, I think the correct equation is 1/J + 2(1/4 - 1/J) = 1/3

That would yield J = 6.. what am I doing wrong here? Substituting equation for Tom into the given statement and solving..

You have the same equation as above.

Alternative explanation:
If working together, brothers Tom and Jack can paint a wall in 4 hours, how much time would it take Jack to paint the wall alone?

Say the rates of Tom and Jack are T job/hour and J job/hour, respectively. Their combined rate is T+J job/hour, and we are told that it equals to 1/4 job/hour.

Quote:
[b]Hi,
before Bunuel puts in his bit, let me tell you where are you going wrong..
its not J=2T, but T=2J..

chetan2u

But in the alternate explanation given by Bunuel above he mentions J = 2T
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Re: M14-07   [#permalink] 03 Dec 2017, 15:21
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# M14-07

Moderators: chetan2u, Bunuel

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