GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Oct 2019, 07:42

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Jane can paint the wall in J hours, and Bill can paint the

Author Message
TAGS:

Hide Tags

Intern
Joined: 29 Oct 2013
Posts: 2
Re: Jane can paint the wall in J hours, and Bill can paint the  [#permalink]

Show Tags

03 Dec 2016, 09:56
Looking at the first statement:

Ra = 1/a=1/(2k)
Rb=1/b=1/(2n)
convert 4:48 to hours: 4 + 48/60 = 4 + ⅘ = 20/5 + ⅘ = 24/5
24/5 (1/2k + 1/2n) = 1
24/5 (1/2) (1/k + 1/n) = 1
12/5 (k+n)/(kn) = 1
(k+n)/(kn) = 5/12
k+n=5
kn=12

However, there are no such positive integers k and n. Is the problem ill-defined or I miss something?
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15271
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Jane can paint the wall in J hours, and Bill can paint the  [#permalink]

Show Tags

03 Dec 2016, 12:36
Hi lexxus,

This DS question is a bit more 'layered' than most DS questions. From the prompt, we know that J and B are both EVEN INTEGERS. We're asked if J and B are equal. This is a YES/NO question.

Fact 1 tells us that it takes the two people 4 4/5 hours to paint the wall together. There are only 2 possible pairs of even integers that will lead to THAT result:

6 and 24
8 and 12

In both situations, the answer to the question is NO, so Fact 1 is SUFFICIENT.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Intern
Joined: 11 Jul 2017
Posts: 18
Re: Jane can paint the wall in J hours, and Bill can paint the  [#permalink]

Show Tags

09 Feb 2018, 00:33
Is noon always = 12pm?
Retired Moderator
Joined: 22 Aug 2013
Posts: 1428
Location: India
Re: Jane can paint the wall in J hours, and Bill can paint the  [#permalink]

Show Tags

09 Feb 2018, 05:49
sucal000 wrote:
Is noon always = 12pm?

Yes, what else could it be
Intern
Joined: 06 Dec 2016
Posts: 25
Location: India
Concentration: Technology, Sustainability
WE: Engineering (Energy and Utilities)
Re: Jane can paint the wall in J hours, and Bill can paint the  [#permalink]

Show Tags

28 Aug 2018, 04:50
Bunuel wrote:
Nice solutions atish and sriharimurthy, +1 to both of you.

Though it can be done easier.

Jane and Bill working together will paint the wall in $$T=\frac{JB}{J+B}$$ hours. Now suppose that $$J=B$$ --> $$T=\frac{J^2}{2J}=\frac{J}{2}$$, as $$J$$ and $$B$$ are even $$J=2n$$ --> $$T=\frac{2n}{2}=n$$, as $$n$$ is an integer, working together Jane and Bill will paint the wall in whole number of hours, meaning that in any case $$T$$ must be an integer.

(1) They finish painting in 4 hours and 48 minutes, $$T$$ is not an integer, --> $$J$$ and $$B$$ are not equal. Sufficient.

(2) $$J+B=20$$, we can even not consider this one, clearly insufficient. $$J$$ and $$B$$ can be $$10$$ and $$10$$ or $$12$$ and $$8$$.

Hi Bunuel,

Correct me if I am wrong.

Before jumping into the individual statements, it has been found that "T" must be an integer.
Now in statement 2: 1st case :10 and 10 gives me T as an integer but 2nd case: 12 and 8 {(1/12+1/8)*T =1} does not give T as an integer. So is it not that J and B have to be 10 and 10. Please give your suggestion.

Thank you.
_________________
War with the clock!
Math Expert
Joined: 02 Sep 2009
Posts: 58453
Re: Jane can paint the wall in J hours, and Bill can paint the  [#permalink]

Show Tags

28 Aug 2018, 04:57
Rishovnits wrote:
Bunuel wrote:
Nice solutions atish and sriharimurthy, +1 to both of you.

Though it can be done easier.

Jane and Bill working together will paint the wall in $$T=\frac{JB}{J+B}$$ hours. Now suppose that $$J=B$$--> $$T=\frac{J^2}{2J}=\frac{J}{2}$$, as $$J$$ and $$B$$ are even $$J=2n$$ --> $$T=\frac{2n}{2}=n$$, as $$n$$ is an integer, working together Jane and Bill will paint the wall in whole number of hours, meaning that in any case $$T$$ must be an integer.

(1) They finish painting in 4 hours and 48 minutes, $$T$$ is not an integer, --> $$J$$ and $$B$$ are not equal. Sufficient.

(2) $$J+B=20$$, we can even not consider this one, clearly insufficient. $$J$$ and $$B$$ can be $$10$$ and $$10$$ or $$12$$ and $$8$$.

Hi Bunuel,

Correct me if I am wrong.

Before jumping into the individual statements, it has been found that "T" must be an integer.
Now in statement 2: 1st case :10 and 10 gives me T as an integer but 2nd case: 12 and 8 {(1/12+1/8)*T =1} does not give T as an integer. So is it not that J and B have to be 10 and 10. Please give your suggestion.

Thank you.

From the stem we got that T is an integer IF J = B, not that T is an integer in all cases.
_________________
Intern
Joined: 06 Dec 2016
Posts: 25
Location: India
Concentration: Technology, Sustainability
WE: Engineering (Energy and Utilities)
Jane can paint the wall in J hours, and Bill can paint the  [#permalink]

Show Tags

28 Aug 2018, 05:28
Bunuel wrote:
Rishovnits wrote:
Bunuel wrote:
Nice solutions atish and sriharimurthy, +1 to both of you.

Though it can be done easier.

Jane and Bill working together will paint the wall in $$T=\frac{JB}{J+B}$$ hours. Now suppose that $$J=B$$--> $$T=\frac{J^2}{2J}=\frac{J}{2}$$, as $$J$$ and $$B$$ are even $$J=2n$$ --> $$T=\frac{2n}{2}=n$$, as $$n$$ is an integer, working together Jane and Bill will paint the wall in whole number of hours, meaning that in any case $$T$$ must be an integer.

(1) They finish painting in 4 hours and 48 minutes, $$T$$ is not an integer, --> $$J$$ and $$B$$ are not equal. Sufficient.

(2) $$J+B=20$$, we can even not consider this one, clearly insufficient. $$J$$ and $$B$$ can be $$10$$ and $$10$$ or $$12$$ and $$8$$.

Hi Bunuel,

Correct me if I am wrong.

Before jumping into the individual statements, it has been found that "T" must be an integer.
Now in statement 2: 1st case :10 and 10 gives me T as an integer but 2nd case: 12 and 8 {(1/12+1/8)*T =1} does not give T as an integer. So is it not that J and B have to be 10 and 10. Please give your suggestion.

Thank you.

From the stem we got that T is an integer IF J = B, not that T is an integer in all cases.

Okay. I missed it. Thanks
_________________
War with the clock!
Non-Human User
Joined: 09 Sep 2013
Posts: 13258
Re: Jane can paint the wall in J hours, and Bill can paint the  [#permalink]

Show Tags

31 Aug 2019, 13:16
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Jane can paint the wall in J hours, and Bill can paint the   [#permalink] 31 Aug 2019, 13:16

Go to page   Previous    1   2   [ 28 posts ]

Display posts from previous: Sort by