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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

If A, B & C can build a wall in 4 hours,working together, [#permalink]

Show Tags

02 Sep 2013, 12:39

3

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

38% (02:28) correct
62% (01:50) wrong based on 267 sessions

HideShow timer Statistics

If A, B & C can build a wall in 4 hours, working together, at their respective rates. If their working rates remain the same, who among the three can build the same wall in shortest amount of time working independently?

(1) Working alone B can build the same wall in more than eight but less than eleven days. (2) Working together B and C can build the same wall in five days.

If A, B & C can build a wall in 4 hours,working together, at their respective rates. :- Let's Assume that A is building the wall in x days. So in one day he will build 100/x% of wall AND in one hour he will build \(\frac{100}{24x} %\) of wall

A is building the wall in y days. So in one day he will build 100/y% of wall AND in one hour he will build \(\frac{100}{24y} %\) of wall

A is building the wall in z days. So in one day he will build 100/z% of wall AND in one hour he will build \(\frac{100}{24z} %\) of wall

A, B & C can build a wall in 4 hours :- That means in 4 hours A, B, C working together are building \(\frac{100}{4} = 25%\) wall

If their working rates remain the same ,who among the three can build the same wall in shortest amount of time working independently? :- Which among the \(\frac{100}{24x}, \frac{100}{24y}, \frac{100}{24z}\) least ???

1) Working alone B can build the same wall in more than eight but less than eleven days. :- \(\frac{100}{24*8} < %--completion--by--B--in--one--hour < \frac{100}{24*11}\) -----------------------------> 0.52% < % completion by B in one hour < 0.38% No mention of Rates of A or C. Hence Insufficient.

2) Working together B and C can build the same wall in five days. ------> B and C, working together, can build \(\frac{100}{5} = 20%\) wall in one day OR \(\frac{20}{24} = 0.833%\) wall in one hour.

Recall the Highlighted Part. A,B,C together are building 25% wall in one hour AND B and C together are building 0.833% wall, So A must be completing 25 - 8.33 = 24.16% wall in one hour. That Means A's Rate is greatest. Thus we only have to determine individual rates of B and C in order to decide whose rate is least. This choice does not give us individual rates of B and C. Hence Insufficient.

1 + 2) :- 0.52% < % completion by B in one hour < 0.38% AND 0.833% = % completion by B and C Together.

B's Minimum rate can be 0.39% in that case C's rate will be (0.833 - 0.39) = 0.44%, B's rate is least B's Maximum rate can be 0.51% in that case C's rate will be (0.833 - 0.51) = 0.32%, C's rate is least

Two different answer. Hence Insufficient. Choice E _________________

Re: If A, B & C can build a wall in 4 hours,working together, [#permalink]

Show Tags

17 Sep 2013, 04:00

2

This post received KUDOS

To my understanding, the question is asking "who among the three can build the same wall in shortest amount of time working independently", or who has the fastest rate. Hence, I chose (B), since A must have the fastest rate (as shown in the answer above).

Re: If A, B & C can build a wall in 4 hours,working together, [#permalink]

Show Tags

17 Sep 2013, 05:30

If A, B & C can build a wall in 4 hours, working together, at their respective rates. If their working rates remain the same, who among the three can build the same wall in shortest amount of time working independently?

(1) Working alone B can build the same wall in more than eight but less than eleven days. (2) Working together B and C can build the same wall in five days.

Let a be the rate at which A builds a wall, B be the rate for B and C be the rate of work for C

A+B+C = 1/4

if A=B=C : each = 1/12 (i.e. each can build the wall in 12 hours) 1) says B can build wall at max in 8 days therefore max (B) = 1/(24*8) = 1/192 therefore A + C = 1/4 - 1/92 cant conclude anything !!

2) B + C can build wall in 5 days - 5*24 = 120 hours Therefore B + C = 1/120 A + B + C = 1/4 therefore A = 1/4-1/120 = 29/120 which is individually more than B+C. Now since neither B nor C can do negative work, A does the work fastest.

Re: If A, B & C can build a wall in 4 hours,working together, [#permalink]

Show Tags

18 Sep 2013, 01:58

innocous wrote:

If A, B & C can build a wall in 4 hours, working together, at their respective rates. If their working rates remain the same, who among the three can build the same wall in shortest amount of time working independently?

(1) Working alone B can build the same wall in more than eight but less than eleven days. (2) Working together B and C can build the same wall in five days.

Hi, Let A,B and C be the independent rates so we have from Q stem that

ABC/ (BC+AB+AC) = 4

From St 1 we have 8<B<11 and thus B can take any value in this range but we donot know anything about A and B hence St 1 alone is not sufficient So A and D ruled out

from St 2 we have BC/(B+C)= 5

again in this information we can have many possible combinations so not sufficent

Together we get that

ABC/ (BC+AB+AC) = 4 8<B<11 BC/(B+C)= 5

Now lets take B=9 we can find the value of C as 45/4 days (~11.something) so B is less than C Substituting in ABC/ (BC+AB+AC) = 4 we get A =396/19 so A is around ~ 20 days

So B has least time

Now lets take B =10 then value of C is also 10 and value of A will be A=20

But now B and C will have least days

Since 2 answers are possible

Ans is E

Another Possible Option to this Q will be (On Combining all statement)

We know that

1/A +1/B+1/C = 1/4

Now 1/B+1/C= 1/5 SO We get A= 20 days

Also taking value of B in the given range

1/ 9+1/C= 1/5------C =45/4 (So B is least) but 1/10+1/C= 1/5 -------> C =10 (So both B and C are least ) _________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Re: If A, B & C can build a wall in 4 hours,working together, [#permalink]

Show Tags

30 Sep 2013, 04:49

innocous wrote:

If A, B & C can build a wall in 4 hours, working together, at their respective rates. If their working rates remain the same, who among the three can build the same wall in shortest amount of time working independently?

(1) Working alone B can build the same wall in more than eight but less than eleven days. (2) Working together B and C can build the same wall in five days.

Not Gmat type, tedious calculation 1) clearly insufficient

statement 2 : using this we can calculate the rate of A or the number of days A will take to make the wall assuming 24 hours make 1 day , together they make the wall in 1/6 day ( 4/24)

using this we get A takes 5/29 days to make the wall

now we still have no idea of individual time taken by B and C , so this is insufficient

1+2

A takes 5/29 days , lets assume B takes 8 days ( from statement 1), then C takes 40/3 days or approx 13 days here A takes the least amount of time

using statement 1 if we assume B takes 11 days , we know A takes 5/29 days then we get C takes 55/6, approx 9 days here also A takes the least amount if time

hence for both the limits of B,both B and C are more than A.

there is no way I can make A take more then 9 days to build the whole wall alone, A takes hours well as individually both B and C take days. So A takes the least amount of time.

So it seems 1+2 is sufficient to answer the question. _________________

Re: If A, B & C can build a wall in 4 hours,working together, [#permalink]

Show Tags

12 Oct 2013, 23:39

1

This post received KUDOS

GIVEN in the question:-

Together A,B and Cs' rate of work is \(\frac{1}{4}\)

TO FIND:- Who among A,B and C can build the wall in the shortest amount of time

STATEMENT 1 The time range of B is \(8<t<11\) days so the rate range would be \(\frac{1}{11}<R<\frac{1}{8}\). But we are not given any info about A and C. INSUFFICIENT

STATEMENT 2 Working Together B and C build the wall in 5 days, thus their \(Rate=\frac{1}{5}\) From here and the GIVEN we can deduce that A's \(Rate=\frac{1}{20}\) But still don't know anything about B and Cs' rate. INSUFFICIENT

STATEMENT 1 and 2 together A,B and Cs' rate of work is \(\frac{1}{4}\) B's Rate range: \(\frac{1}{11}<R<\frac{1}{8}\) A's Rate= \(Rate=\frac{1}{20}\) So C's Rate comes out to be = \(\frac{1}{4}-\frac{1}{A}-\frac{1}{B}\) = \(\frac{1}{5}-\frac{1}{9} = \frac{4}{45}= \frac{45}{4} days\) OR =\(\frac{1}{5}-\frac{1}{10}= \frac{1}{10}= 10days\) But B also can build the wall in 10 days as evident from the range \(8<t<11\) days Thus INSUFFICIENT

Re: If A, B & C can build a wall in 4 hours,working together, [#permalink]

Show Tags

13 Oct 2013, 00:46

innocous wrote:

If A, B & C can build a wall in 4 hours, working together, at their respective rates. If their working rates remain the same, who among the three can build the same wall in shortest amount of time working independently?

(1) Working alone B can build the same wall in more than eight but less than eleven days. (2) Working together B and C can build the same wall in five days.

I think there is a typo mistake in a question --- It has to be 4 days in the question and not 4 hours for the answer to be E.

Otherwise the answer would be B undoubtedly.

Bunuel Could you please look into this question once?

Anyways considering the question be 4 days, then

The more the rate of any individual the less time it takes to build the wall independently. Since Time is inversely proportional to Rate.

Question stem gives us 1 equation. Let A,B,C be the rates of the individuals.

Then \(Work = Rate * Time\)

Therefore Assuming Work to be done is 40 units.

Then \(40 = (A+B+C)*4\). Therefore \(A+B+C = 10 units/day\)

Therefore \(A+B+C = 10\)

Statement 1 :- \(11 > Time taken by B > 8\)

Therefore Rate of B will be \(\frac{40}{11} < B < \frac{40}{8}\)

Note :- (Inequalities change since T and R are inversely proportional. Also Considering Work as 40 units as did before)

that will be \(3.66 < B < 5\)

Now considering \(B = 3.7\)

\(A+C = 10 - 3.7 = 6.3\)

Therefore A can be 5.3 and C can be 1 (A will be the fastest)

Again considering B = 4.9 Then A+C = 5.1 (A can be 4.1 and C can be 1) --- B will be fastest

Hence 2 answers --- Not sufficient

Statement 2 :-

Time taken by B and C together is 5 days Then \(B+C = 40/5 = 8 units/day\)

Therefore A = 2 and B can be 3, C can be 5 --- C will be fastest And A = 2 and B can be 5, C can be 3 ---- B will be fastest

Hence insufficient

Considering both the statements :- \(A = 2; 3.66<b<5\)

a) A = 2; B = 3.7; C = 4.3 ---- C will be fastest b) A = 2; B = 4.9; C = 3.1 ---- B will be fastest

Still not sufficient..

Hence Answer is E

Consider Kudos if the post helps!! its a good way to motivate others and get as much contribution from others...

Re: If A, B & C can build a wall in 4 hours,working together, [#permalink]

Show Tags

03 Nov 2013, 14:03

shameekv wrote:

innocous wrote:

If A, B & C can build a wall in 4 hours, working together, at their respective rates. If their working rates remain the same, who among the three can build the same wall in shortest amount of time working independently?

(1) Working alone B can build the same wall in more than eight but less than eleven days. (2) Working together B and C can build the same wall in five days.

I think there is a typo mistake in a question --- It has to be 4 days in the question and not 4 hours for the answer to be E.

Otherwise the answer would be B undoubtedly.

Bunuel Could you please look into this question once?

Anyways considering the question be 4 days, then

The more the rate of any individual the less time it takes to build the wall independently. Since Time is inversely proportional to Rate.

Question stem gives us 1 equation. Let A,B,C be the rates of the individuals.

Then \(Work = Rate * Time\)

Therefore Assuming Work to be done is 40 units.

Then \(40 = (A+B+C)*4\). Therefore \(A+B+C = 10 units/day\)

Therefore \(A+B+C = 10\)

Statement 1 :- \(11 > Time taken by B > 8\)

Therefore Rate of B will be \(\frac{40}{11} < B < \frac{40}{8}\)

Note :- (Inequalities change since T and R are inversely proportional. Also Considering Work as 40 units as did before)

that will be \(3.66 < B < 5\)

Now considering \(B = 3.7\)

\(A+C = 10 - 3.7 = 6.3\)

Therefore A can be 5.3 and C can be 1 (A will be the fastest)

Again considering B = 4.9 Then A+C = 5.1 (A can be 4.1 and C can be 1) --- B will be fastest

Hence 2 answers --- Not sufficient

Statement 2 :-

Time taken by B and C together is 5 days Then \(B+C = 40/5 = 8 units/day\)

Therefore A = 2 and B can be 3, C can be 5 --- C will be fastest And A = 2 and B can be 5, C can be 3 ---- B will be fastest

Hence insufficient

Considering both the statements :- \(A = 2; 3.66<b<5\)

a) A = 2; B = 3.7; C = 4.3 ---- C will be fastest b) A = 2; B = 4.9; C = 3.1 ---- B will be fastest

Still not sufficient..

Hence Answer is E

Consider Kudos if the post helps!! its a good way to motivate others and get as much contribution from others...

I am missing something here.... if B+C can finish the wall in 5 days, and together with A they finish in 4 days, it has to mean the A has the fastest time, the highest rate or whatever you want to call it.... So why isn't the answer B?

Re: If A, B & C can build a wall in 4 hours,working together, [#permalink]

Show Tags

04 Dec 2013, 12:28

innocous wrote:

If A, B & C can build a wall in 4 hours, working together, at their respective rates. If their working rates remain the same, who among the three can build the same wall in shortest amount of time working independently?

(1) Working alone B can build the same wall in more than eight but less than eleven days. (2) Working together B and C can build the same wall in five days.

Rates : A,B,C so time will be 1/A,1/B,1/C Given:ABC/AB+BC+CA = 4 -- Equation1

Statement 1: 8<1/B<11. Insufficient .

BC/B+C = 5 Multiply & divide by A ABC/AB+AC = 5 AB+AC+BC-BC / ABC = 1/5 AB+BC+CA/ABC - BC/ABC = 1/5 1/4 - 1/A = 1/5 A = 20 We dont know the values of B & C. Insufficient . Combining .

Let B = 9 Putting in given equation 1, C ~ 11. Here B - lowest

Let B = 10 , c~ 10 Here B=C - lowest . Insufficient . Hence E

Re: If A, B & C can build a wall in 4 hours,working together, [#permalink]

Show Tags

30 Dec 2013, 15:21

Guys, Answer should be B. There is a typo in the question.

I checked out each one's calculations. Everyone says given as A+B+C = 1/4 when A, B, C are rates of each person. A+B+C = 6, not 1/4...... If you look closer, given A, B, and C can complete work in 4hrs, so 1/6th of a day..... Shameekv did observe this above and he gave the explanation too....

(2) Working together B and C can build the same wall in five days.

gmatclubot

Re: If A, B & C can build a wall in 4 hours,working together,
[#permalink]
30 Dec 2013, 15:21

This is the kickoff for my 2016-2017 application season. After a summer of introspect and debate I have decided to relaunch my b-school application journey. Why would anyone want...

Check out this awesome article about Anderson on Poets Quants, http://poetsandquants.com/2015/01/02/uclas-anderson-school-morphs-into-a-friendly-tech-hub/ . Anderson is a great place! Sorry for the lack of updates recently. I...

Time is a weird concept. It can stretch for seemingly forever (like when you are watching the “Time to destination” clock mid-flight) and it can compress and...