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Maya: 25%, Felix: 50%, Nora: 25%
Maya: 50% of time, Nora: 2 hours
(1)
50% of time + 4 + 2 = time
50% of time = 6
time = 12
constant rate of Felix: work/time = (1/2)/4 = 1/8
constant rate of Maya: work/time = (1/4)/6 = 1/24
constant rate working together: 1/8+1/24 = 1/6
rate=1/6 means that they complete the work in 6 hours
Condition (1) is sufficient
(2)
50% of time + time of Felix + 2 = time
50% of time + (50% of time + 2)/2 + 2 = time
time + 50% of time + 2 + 4 = 2*time
50% of time = 6
time = 12
we just calculated rates previously with this info, so the answer is 6 hours.
Condition (2) is sufficient
The answer is D
Maya: 50% of time, Nora: 2 hours
(1)
50% of time + 4 + 2 = time
50% of time = 6
time = 12
constant rate of Felix: work/time = (1/2)/4 = 1/8
constant rate of Maya: work/time = (1/4)/6 = 1/24
constant rate working together: 1/8+1/24 = 1/6
rate=1/6 means that they complete the work in 6 hours
Condition (1) is sufficient
(2)
50% of time + time of Felix + 2 = time
50% of time + (50% of time + 2)/2 + 2 = time
time + 50% of time + 2 + 4 = 2*time
50% of time = 6
time = 12
we just calculated rates previously with this info, so the answer is 6 hours.
Condition (2) is sufficient
The answer is D
Posts: 36
Rate of each individual:
Maya = 1/M
Felix = 1/F
Nora = 1/N
Work done by each individual (Work=1) (not rate or time of work!)
Maya= 1/4
Felix= 50% of the remaining = 1-(1/4)=0.75 or 3/4 and 1/2 of 3/4 =0.75 or 3/8
Nora= Remaining job = (3/4)-(3/8) = 3/8
How long did each person work (Duration of each persons shift) ?
If total work duration = T
Maya =T/2
Felix=T-(T/2)-2= (T-4)/2
Nora= 2 hours
What does the question ask?
(1/((1/M)+(1/F)) -----> Hours Maya and Felix working together to finish the entire job
Rates of Each individual (Since we have time and work of each individual we can find out distinct rates)
Maya = (1/M)*(T/2)=(T/2M)
Felix= (T-4)/(2F)
Nora=(2/N)
Statement 1: Felix worked 4 hours on mural ------> T of Felix= (T-4/2) = 4 T= 12 ------> If we know T we can calculate individual rate of each person ------> in 4 hours Felix completed 3/8 of job = Rate of Felix is = 8/2F -----> (3/8)/(8/2F)=4 from this point on we don't need to do whole calculation we know it is sufficient
Statement 2: 2((T-4)/(2))=2+(T/2) -----> T=12 with T we can calculate each persons rate and reach the answer
Ans. D
IMO
Maya = 1/M
Felix = 1/F
Nora = 1/N
Work done by each individual (Work=1) (not rate or time of work!)
Maya= 1/4
Felix= 50% of the remaining = 1-(1/4)=0.75 or 3/4 and 1/2 of 3/4 =0.75 or 3/8
Nora= Remaining job = (3/4)-(3/8) = 3/8
How long did each person work (Duration of each persons shift) ?
If total work duration = T
Maya =T/2
Felix=T-(T/2)-2= (T-4)/2
Nora= 2 hours
What does the question ask?
(1/((1/M)+(1/F)) -----> Hours Maya and Felix working together to finish the entire job
Rates of Each individual (Since we have time and work of each individual we can find out distinct rates)
Maya = (1/M)*(T/2)=(T/2M)
Felix= (T-4)/(2F)
Nora=(2/N)
Statement 1: Felix worked 4 hours on mural ------> T of Felix= (T-4/2) = 4 T= 12 ------> If we know T we can calculate individual rate of each person ------> in 4 hours Felix completed 3/8 of job = Rate of Felix is = 8/2F -----> (3/8)/(8/2F)=4 from this point on we don't need to do whole calculation we know it is sufficient
Statement 2: 2((T-4)/(2))=2+(T/2) -----> T=12 with T we can calculate each persons rate and reach the answer
Ans. D
IMO
Posts: 44
Both Statements are sufficient on their own
Sol
M + F+ N = 1(Work)
M painted = 25% = 1/4
F Painted = 50% = 1/2
N Painted = 25% =1/4
Let their times be M , F,N
so M time is 50% of total time so M= F+N
Nora worked for 2 hrs so
M= F+2
rate of painting for rM= 1/4/M
rF = 1/2/F
Need to find 1/( 1/4/M + 1/2/F )
Statement 1 - F worked 4 hrs so putting the values
1/ 1/4/M + 1/2/4 = 1/6
6 hrs is time taken
So statement 1 is sufficient
Statement 2 Total time M and N spent on mural was 2x time spent by F
so M+N = 2F
since N = 2
so M +2 = 2F
we know M = F+2 , putting values
F+2+2 = 2F
F =4
, then M = 6
So it took 6 hours , statement 2 is also sufficient
Sol
M + F+ N = 1(Work)
M painted = 25% = 1/4
F Painted = 50% = 1/2
N Painted = 25% =1/4
Let their times be M , F,N
so M time is 50% of total time so M= F+N
Nora worked for 2 hrs so
M= F+2
rate of painting for rM= 1/4/M
rF = 1/2/F
Need to find 1/( 1/4/M + 1/2/F )
Statement 1 - F worked 4 hrs so putting the values
1/ 1/4/M + 1/2/4 = 1/6
6 hrs is time taken
So statement 1 is sufficient
Statement 2 Total time M and N spent on mural was 2x time spent by F
so M+N = 2F
since N = 2
so M +2 = 2F
we know M = F+2 , putting values
F+2+2 = 2F
F =4
, then M = 6
So it took 6 hours , statement 2 is also sufficient
Bunuel
Posts: 86
Ans Choice D: Maria,M painted 25% ; Felix, F painted 50% of rest (75%) = 37.5% and Nora, N painted 37.5%(rest). at thier respective constant hourly rates.
Total time spent = T hrs
Maya spent = T/2 hrs
Nora spent = 2 hrs
Felix spent = (T/2) - 2 hrs
If we can find Maya and Felix individual rates we can find combined rates also
Stmt 1: Felix worked for 4 hrs
T/2 - 2 = 4 ; T = 12hrs
F painted 37.5% in 4 hrs which gives F can complete total in 32/3 hrs
M painted 25% in 6 hrs which gives M can complete total in 24 hrs.
Therefore, combined M+F can be derived. Sufficient.
Stmt 2 : Time M and N spent is twice F spent ; T/2 +2 = 2*(T/2 - 2) ; T=12 hrs and same process like in Stmt2 can be followed. Hence Sufficient.
Total time spent = T hrs
Maya spent = T/2 hrs
Nora spent = 2 hrs
Felix spent = (T/2) - 2 hrs
If we can find Maya and Felix individual rates we can find combined rates also
Stmt 1: Felix worked for 4 hrs
T/2 - 2 = 4 ; T = 12hrs
F painted 37.5% in 4 hrs which gives F can complete total in 32/3 hrs
M painted 25% in 6 hrs which gives M can complete total in 24 hrs.
Therefore, combined M+F can be derived. Sufficient.
Stmt 2 : Time M and N spent is twice F spent ; T/2 +2 = 2*(T/2 - 2) ; T=12 hrs and same process like in Stmt2 can be followed. Hence Sufficient.
Bunuel
Posts: 34
Bunuel
Maya’s rate and work done: M*T/2 = 1/4
Felix’s rate and work done: F*X = 2/4
Nora’s rate and work done: N*2 = 1/4
The question asks us to find the time taken to complete the work if Maya and Felix work together.
1. This gives us Felix’s time (X). From here we can calculate Maya’s time (T=12) and arrive at the combined rate. Sufficient.
2. This gives us a relation between Maya’s, Felix’s, and Nora’s time. From here we can calculate Maya’s and Felix’s time and arrive at the combined rate. Sufficient.
Answer is D.
Posts: 151
t = time to complete the entire mural
M: 1/4 in t/2, rate=1/2t
F: 1/2
N: 1/4 in 2 hours, rate=1/8
(1)
F: 2 hours
t = 4+2+t/2
t = 12
rate of F: (1/2)/4 = 1/8
rate of M: 1/2t = 1/24
together: 1/8+1/24=1/6
time together = 6 hours
Sufficient
(2)
t/2 + 2 + (t/2 + 2)/2 = t
t/2 + 2 = 2t/3
3t + 12 = 4t
t = 12
This is the same info given in st 1, so rates can be calculated too and time together = 6 hours.
Sufficient
The correct answer is D
M: 1/4 in t/2, rate=1/2t
F: 1/2
N: 1/4 in 2 hours, rate=1/8
(1)
F: 2 hours
t = 4+2+t/2
t = 12
rate of F: (1/2)/4 = 1/8
rate of M: 1/2t = 1/24
together: 1/8+1/24=1/6
time together = 6 hours
Sufficient
(2)
t/2 + 2 + (t/2 + 2)/2 = t
t/2 + 2 = 2t/3
3t + 12 = 4t
t = 12
This is the same info given in st 1, so rates can be calculated too and time together = 6 hours.
Sufficient
The correct answer is D
Free information:
Maya painted 25%
Felix 50%
Nora 25%
Let the total time be T. Maya took T/2
Nora took 2 hrs
So T= Tm+Tf+Tn
T= T/2+2+Tf
Tf=T-T/2-2
Tf=T/2-2
How much time would Maya and fix take
Find the time and their rates
St1. Tf = 4hr
4=T/2-2
6=T/2
T= 12 hrs
Rate for Maya= 25%/6=1/24
Rate for Felix= 50%/4=1/8
Combined rate = 1/6
So they will take 6 hrs sufficient
St2 Maya + Nora time= 2X Felix time
T/2+2=T(T/2-2)
6=T/2
T=12
We can calculate the rates hence st2 is sufficient too.
So D Answer
Maya painted 25%
Felix 50%
Nora 25%
Let the total time be T. Maya took T/2
Nora took 2 hrs
So T= Tm+Tf+Tn
T= T/2+2+Tf
Tf=T-T/2-2
Tf=T/2-2
How much time would Maya and fix take
Find the time and their rates
St1. Tf = 4hr
4=T/2-2
6=T/2
T= 12 hrs
Rate for Maya= 25%/6=1/24
Rate for Felix= 50%/4=1/8
Combined rate = 1/6
So they will take 6 hrs sufficient
St2 Maya + Nora time= 2X Felix time
T/2+2=T(T/2-2)
6=T/2
T=12
We can calculate the rates hence st2 is sufficient too.
So D Answer
Posts: 227
A is sufficent
Bcz we can find time of 1 which is T = 6+T/2 and Rate we know so A is suu And B is not
Bcz we can find time of 1 which is T = 6+T/2 and Rate we know so A is suu And B is not
Bunuel
GMAT Focus 1: 545 Q77 V77 DI77 
Posts: 82
My ans is A) Stat 1 is suff
Let total work be 40
We need to find x and y. Time spent by Maya and Felix working together= 40/(x+y)
1) Stat 1, with the given info we can find x and y. Hence sufficient
y= 20/4= 5
x=10/(4+2)= 10/6 (time taken by Maya is 50%= total time taken by Felix and Nora)
2) Stat 2, we cannot find both x and y hence Insufficient
Let total work be 40
| Work | Rate | Time | |
| Maya | 10 | x | |
| Felix | 20 | y | |
| Nora | 10 | 5 | 2 |
| Total | 40 |
We need to find x and y. Time spent by Maya and Felix working together= 40/(x+y)
1) Stat 1, with the given info we can find x and y. Hence sufficient
y= 20/4= 5
x=10/(4+2)= 10/6 (time taken by Maya is 50%= total time taken by Felix and Nora)
2) Stat 2, we cannot find both x and y hence Insufficient
Bunuel
Posts: 59
Similar Problem : https://gmatclub.com/forum/alan-botham- ... 17632.html
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