If A, B & C can build a wall in 4 hours,working together,

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

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).

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.

OA has to be B
correct me if i am wrong

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 )
_________________

The question says a, b,c can build in 4 hours not 4 days.
In statement 1 and 2, the duration mentioned is in days and not hours.

Posted from my mobile device

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.
_________________

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?

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

Lets say:
Rate of A = A
Rate of B = B
Rate of C = C

Given from question = 1Job(Wall) = (A+B+C) * 4, so Rate of A+B+C = 1/4

STMNT 1
B Build the Wall in more than 8 but less than 11 days.

So Rate of B = 1/8 (days) < RATE < 1/11 (days)

Clearly IS (Eliminate Choices A & D)

STMNT 2
Working Together B and C build the wall in 5 days

1Job(wall) = (B+C) * 5d --> Rate of B+C = 1/5
Now if we plug into A+B+C = 1/4 we get A+1/5 = 1/4 which gives us A = 1/20

But still IS. (Eliminate answer B)

STMNT 1 and 2 together
from Q: A+B+C = 1/4
From 2: A = 1/20
From 1: B = 1/8 < B < 1/11 , so B 1/9 OR 1/10

you could plug in for A and B to get C, but since you have B = 1/9 OR 1/10 you would get two solutions.

so still IS. (Eliminate answer C)

Hence Answer is E.

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.