M14-07

Question

Tom and Jack, working together, can paint a wall in 4 hours. How long would it take Jack to paint the wall alone?

(1) Jack paints the wall twice as fast as Tom.
 
(2) If Tom could paint twice as fast as he currently does, he and Jack could paint the wall in 3 hours.

Bunuel · Accepted Answer

Official Solution:

Tom and Jack, working together, can paint a wall in 4 hours. How long would it take Jack to paint the wall alone? 
 
Let the  rate  of Tom be T walls per hour and the rate of Jack be J walls per hour. Together, their combined rate is T + J walls per hour, and we know that it equals 1/4 wall per hour:  T + J = \frac{1}{4} 
 
(1) Jack paints the wall twice as fast as Tom.
 
We can express this relationship as  J = 2T . Substituting this into the equation above gives us  T+2T= \frac{1}{4} , which simplifies to  T=\frac{1}{12} . Thus,  J=\frac{2}{12}=\frac{1}{6} . Since time is the reciprocal of rate, we can determine that it would take Jack 6 hours to paint the wall alone. Sufficient.
 
(2) If Tom could paint twice as fast as he currently does, he and Jack could paint the wall in 3 hours.
 
This statement implies that if Tom's rate were 2T instead of T, then their combined rate would be  2T+J=\frac{1}{3} . Subtracting the original equation from this equation gives us  2T+J-(T+J)=\frac{1}{3} -\frac{1}{4} , which simplifies to  T=\frac{1}{12} . Substituting this into either equation gives us  J=\frac{1}{6} . Thus, it would take Jack 6 hours to paint the wall alone. This answer is also sufficient.

Answer: D

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

BottomJee · Answer

I think this is a  high-quality  question and I agree with explanation.

jshimchi · Answer

Where are the choices?

Posted from my mobile device

Bunuel · Answer

Hi,

This is a data sufficiency question. Options for DS questions are always the same and usually omitted on the site.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following post  ALL YOU NEED FOR QUANT .

Hope this helps.

sssdd1234 · Answer

I think this is a  high-quality  question and I agree with explanation.

shaliny · Answer

hii Bunuel, 
i have done this as, assume tom doing that work in T hrs and Jack is doing the same work in J hrs so combined efficiency = 1/T+ 1/J= 1/4
statement 1- J=2T, put in 1/T+ 1/J= 1/4 and get T= 6 hrs, what is wrong in this?? where am i making mistake?

Bunuel · Answer

Your mistake is in how you set up the equation.

You wrote 1/T + 1/J = 1/4, but that assumes T and J are the  times  to paint the wall, not the rates. In the official solution, T and J represent  rates  (walls per hour), so the combined rate is T + J = 1/4.

If instead you treat T and J as times, then Tom’s rate is 1/T and Jack’s rate is 1/J, so the combined rate is 1/T + 1/J. That should equal  1 wall in 4 hours , i.e. 1/4, but then you also must carefully apply the condition “Jack is twice as fast as Tom.” That means Jack’s time J is half of Tom’s time T (J = T/2), not J = 2T.

That’s where your setup went wrong: you flipped the relationship between their times.

shaliny · Answer

got it, Thankuu:)

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