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

 It is currently 24 May 2019, 23:08 ### 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
Your Progress

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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # D01-29

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 55271
D01-29  [#permalink]

### Show Tags

28 00:00

Difficulty:   95% (hard)

Question Stats: 50% (02:28) correct 50% (02:24) wrong based on 149 sessions

### HideShow timer Statistics

Mac can finish a job in $$M$$ days and Jack can finish the same job in $$J$$ days. After working together for $$T$$ days, Mac left and Jack alone worked to complete the remaining work in $$R$$ days. If Mac and Jack completed an equal amount of work, how many days would have it taken Jack to complete the entire job working alone?

(1) $$M = 20$$ days

(2) $$R = 10$$ days

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 55271
Re D01-29  [#permalink]

### Show Tags

4
5
Official Solution:

Mac can finish the job in $$M$$ days: the rate of Mac is $$\frac{1}{M}$$ job/day;

Jack can finish the job in $$J$$ days: the rate of Jack is $$\frac{1}{J}$$ job/day;

After working together for $$T$$ days, Mac left and Jack alone worked to complete the remaining work in $$R$$ days, hence Mac worked for $$T$$ days only and did $$\frac{T}{M}$$ part of the job while Jack worked for $$T+R$$ days and did $$\frac{T+R}{J}$$ part of the job;

Since Mac and Jack completed an equal amount of work (so half of the job each) then $$\frac{T}{M}=\frac{1}{2}$$ and $$\frac{T+R}{J}=\frac{1}{2}$$. So, $$T=\frac{M}{2}$$ and $$T=\frac{J}{2}-R$$, therefore $$\frac{M}{2}=\frac{J}{2}-R$$, which gives $$J=M+2R$$.

(1) $$M = 20$$ days. Not sufficient, we still need the value of $$R$$.

(2) $$R = 10$$ days. Not sufficient, we still need the value of $$M$$.

(1)+(2) $$J=M+2R=20+2*10=40$$. Sufficient.

Answer: C
_________________
Intern  Joined: 12 Aug 2015
Posts: 3
Schools: Wharton '18 (A)
GMAT 1: 710 Q50 V36 Re: D01-29  [#permalink]

### Show Tags

Hi Bunuel -

What was your thought process in not setting T/M = 1/2 and T+R/J = 1/2 equal to each other? That is, T/M = T+R/J? I was stuck after I did such (algebraic mess, and leads you to the wrong conclusion). Would be great to learn your thought process.
Intern  Joined: 12 Nov 2015
Posts: 44
Re: D01-29  [#permalink]

### Show Tags

One option is to go by options and see check with the values.

It gives an idea that both values are required to find out the value of J.
Senior Manager  G
Joined: 19 Oct 2012
Posts: 306
Location: India
Concentration: General Management, Operations
GMAT 1: 660 Q47 V35 GMAT 2: 710 Q50 V38 GPA: 3.81
WE: Information Technology (Computer Software)
Re: D01-29  [#permalink]

### Show Tags

mystseen wrote:
Hi Bunuel -

What was your thought process in not setting T/M = 1/2 and T+R/J = 1/2 equal to each other? That is, T/M = T+R/J? I was stuck after I did such (algebraic mess, and leads you to the wrong conclusion). Would be great to learn your thought process.

Here the idea is to find the value of 'J'. Therefore, the focus should be to eliminate the extra variables where ever you can. I was also stuck with the same bit as you did, but i realized that one can eliminate the variable 'T' by substituting the variable 'T' in the other equation (Jack's equation) which kinda did the trick as I was left with an equation with only M, R and J.
Hope this helps a little bit.
_________________
Citius, Altius, Fortius
Intern  Joined: 23 Jul 2015
Posts: 1
GMAT 1: 680 Q50 V32 GPA: 3.6
Re D01-29  [#permalink]

### Show Tags

I think this is a high-quality question and I agree with explanation.
Intern  Joined: 19 Jun 2014
Posts: 8
Re D01-29  [#permalink]

### Show Tags

I think this is a high-quality question and I agree with explanation.
Intern  Joined: 12 Feb 2016
Posts: 8
Re: D01-29  [#permalink]

### Show Tags

This is definitely a high quality question. I solve it using a number of variable approach and i want to ask to some math expert whether it is correct.

===R================T===========W
*==(1/m)+(1/t)=========t==========(t/m)+(t/j) => in time = t M&J working together complete $$(t/m)+(t/j)$$

**==1/j===========((mj/m+j-t)====== 1-((t/m)+(t/j)) J works at his constant rate $$1/j$$ for the remaining time which is equal to $$((1/m)+(1/j))- t$$

We are asked to find j:
from ** we can multiply R*T=W and find a single equation in 3 unknowns therefore we need stat 1 and stat 2 which gives us 2 unknown to find the third one.
Is the process correct ?
Senior Manager  Joined: 31 Mar 2016
Posts: 376
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34 GPA: 3.8
WE: Operations (Commercial Banking)
Re D01-29  [#permalink]

### Show Tags

I think this is a high-quality question and I agree with explanation.
Current Student B
Joined: 11 Feb 2015
Posts: 77
Location: United States
Concentration: Strategy, General Management
Schools: Duke '20 (A)
GMAT 1: 760 Q50 V42 GPA: 3.7
WE: Engineering (Energy and Utilities)
Re D01-29  [#permalink]

### Show Tags

I think this is a high-quality question and I agree with explanation.
Current Student B
Joined: 23 Nov 2016
Posts: 72
Location: United States (MN)
GMAT 1: 760 Q50 V42 GPA: 3.51
D01-29  [#permalink]

### Show Tags

Maybe I don't understand this completely. I understand that T/M = (R+T)/J. If W is the total work done, then both of these equal W/2. Thus, it's clear that T/M=(R+T)/J=W/2.

How can you say that T/M=1/2, when you don't know how much work was done? Which part of this question allows us to say that W=1, thus T/M=(R+T)/J=1/2?? Ie, which part of the prompt restrict the variables such that we know W=1?
Math Expert V
Joined: 02 Sep 2009
Posts: 55271
Re: D01-29  [#permalink]

### Show Tags

brooklyndude wrote:
Maybe I don't understand this completely. I understand that T/M = (R+T)/J. If W is the total work done, then both of these equal W/2. Thus, it's clear that T/M=(R+T)/J=W/2.

How can you say that T/M=1/2, when you don't know how much work was done? Which part of this question allows us to say that W=1, thus T/M=(R+T)/J=1/2?? Ie, which part of the prompt restrict the variables such that we know W=1?

We consider the whole work to be done as 1 unit of work or as 100% of the work. So, T/M=1/2 means that Mac completed half (50%) of the work whatever this work is.
_________________
Intern  B
Joined: 21 Oct 2015
Posts: 8
Re: D01-29  [#permalink]

### Show Tags

I think this is a high quality question and l agree with the explanation
Intern  B
Joined: 02 Apr 2018
Posts: 15
Re: D01-29  [#permalink]

### Show Tags

Basic question regarding ratios since my ratios grip is weak

If instead of saying that work was equal, the question had said, Mac did 30% of the work that Jack did,

this would mean Mac work/ Jack work = 3/ 10

In case of above ratio, it would be correct to say that Mac did 3/ 13 and Jack did 10/13 work right?

Hence T/M = 3/ 13 right?

Just want to solidify my grip on ratios, that is why asking
Math Expert V
Joined: 02 Sep 2009
Posts: 55271
Re: D01-29  [#permalink]

### Show Tags

RahulS90 wrote:
Basic question regarding ratios since my ratios grip is weak

If instead of saying that work was equal, the question had said, Mac did 30% of the work that Jack did,

this would mean Mac work/ Jack work = 3/ 10

In case of above ratio, it would be correct to say that Mac did 3/ 13 and Jack did 10/13 work right?

Hence T/M = 3/ 13 right?
Just want to solidify my grip on ratios, that is why asking

Yes, that's correct. What do you denote by T and M in highlighted part?
_________________
Intern  B
Joined: 17 Jul 2018
Posts: 16
Re: D01-29  [#permalink]

### Show Tags

When you say "T/M" part of the job...why are we putting time over rate? W=RT...so I don't understand why we are putting the number of days, T (time), over the rate (M).

Same thing for the other equation.

Thank you
Math Expert V
Joined: 02 Sep 2009
Posts: 55271
Re: D01-29  [#permalink]

### Show Tags

leonsandcastle332 wrote:
When you say "T/M" part of the job...why are we putting time over rate? W=RT...so I don't understand why we are putting the number of days, T (time), over the rate (M).

Same thing for the other equation.

Thank you

Both M and T denote time:
Mac can finish the job in M days (the rate is 1/M, so job over time);
Mac worked for T days.

In T days Mac does T/M part of the job.

Consider this: say Mac needs 2 days to do the job. In 1 day he does 1/2 part of the job.

Hope it's clear.
_________________
Intern  B
Joined: 17 Jul 2018
Posts: 16
Re: D01-29  [#permalink]

### Show Tags

I think I'm almost there, but not quite there.

We are setting Time to a value...so we're not really using the W=RT formula with this problem?
Math Expert V
Joined: 02 Sep 2009
Posts: 55271
Re: D01-29  [#permalink]

### Show Tags

leonsandcastle332 wrote:
I think I'm almost there, but not quite there.

We are setting Time to a value...so we're not really using the W=RT formula with this problem?

We are solving using ratios of work done.
_________________
Intern  B
Joined: 17 Jul 2018
Posts: 16
Re: D01-29  [#permalink]

### Show Tags

Bunuel wrote:
leonsandcastle332 wrote:
I think I'm almost there, but not quite there.

We are setting Time to a value...so we're not really using the W=RT formula with this problem?

We are solving using ratios of work done.

Don't we need a variable for rate in this ratio? Re: D01-29   [#permalink] 15 Aug 2018, 18:38

Go to page    1   2    Next  [ 30 posts ]

Display posts from previous: Sort by

# D01-29

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

Moderators: chetan2u, Bunuel Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.

#### MBA Resources  