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total work = 100x

maya = 25x
felix = 50x
nora = 25x

total time. = a hrs
time for nora = 2 hrs
time for felix = t hrs
time for maya = a-2-t

time for maya is 50% of total time = a-2-t = (a/2)
a= 2t+4

so time for maya = t+2

need to find time taken by maya and felix if they work together from start.

S-1
time for F = 4 hrs.

so time for M = 6 hrs.

rate for F = 50x/4
rate for M = 25x/6

100x = (50x/4 + 25x/6) * t

its sufficient

S-2

Mt + Nt = 2*Ft
t+2+2= 2t
t= 4
so time for F = 4
so time for M = 6

this gives same stuff as above.
hence sufficient.

Choice D

Bunuel
Maya, Felix, and Nora painted a mural at a community center in consecutive shifts, each at a constant hourly rate. Maya painted the first 25% of the mural, Felix painted the next 50%, and Nora painted the remainder. If Maya’s shift accounted for 50% of the total time spent on the mural and Nora worked for 2 hours, how many hours would it have taken Maya and Felix to complete the entire mural if they had worked together from start to finish at their same respective constant rates?

(1) Felix worked on the mural for 4 hours.
(2) The total time Maya and Nora spent on the mural was twice the time Felix spent on the mural.


 


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WTR
MAYAx/4t/2x/2t
FELIX3x/8t/2 -23x/4(t-4)
NORA3x/823x/16t
M+Fx??x/2t + 3x/4t(t-4)

i.e., we get any idea about total time taken by them we can find out the result.

Considering statement 1 alone,
t/2 -2 =4
.: we can find t.
.: Statement 1 alone is sufficient.
We have A& D option.

Considering statement 2 alone,
t/2 +2=2* (t/2 -2)
.: We can find t from this.
statement 2 is alone sufficient.

.: D is the correct answer.
Bunuel
Maya, Felix, and Nora painted a mural at a community center in consecutive shifts, each at a constant hourly rate. Maya painted the first 25% of the mural, Felix painted the next 50%, and Nora painted the remainder. If Maya’s shift accounted for 50% of the total time spent on the mural and Nora worked for 2 hours, how many hours would it have taken Maya and Felix to complete the entire mural if they had worked together from start to finish at their same respective constant rates?

(1) Felix worked on the mural for 4 hours.
(2) The total time Maya and Nora spent on the mural was twice the time Felix spent on the mural.


 


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Assume the total work is 100 unts
Lets also assume the total time taken by the three is t
So Maya takes 1/2t, N=2 Hrs and Felix would be 1/2t-2
All we need is to find the value of t and we can derive each individual rates
S1 Since Felix time is 1/2t-4 which equals 4 we can easily find t meaning S1 is sufficient
S2 Maya and Nora equals 1/2t+2 while Felix is 1/2t-2. Equating the two by multiplying Felix time by 4 we can easily get t hence sufficient
Ans D
Bunuel
Maya, Felix, and Nora painted a mural at a community center in consecutive shifts, each at a constant hourly rate. Maya painted the first 25% of the mural, Felix painted the next 50%, and Nora painted the remainder. If Maya’s shift accounted for 50% of the total time spent on the mural and Nora worked for 2 hours, how many hours would it have taken Maya and Felix to complete the entire mural if they had worked together from start to finish at their same respective constant rates?

(1) Felix worked on the mural for 4 hours.
(2) The total time Maya and Nora spent on the mural was twice the time Felix spent on the mural.


 


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D - Each statement alone is sufficient.

Let total time be T hrs,
Maya -- 25% -- 0.5T hrs
Felix -- 50% -- 0.5T - 2 hrs
Nora -- 25% -- 2 hrs

Statement 1 - Felix worked on the mural for 4 hours.
We can calculate T = 12 hrs
Using that, we can calculate the rates of Maya and Felix, considering total work as 100.
We have combined rates of Maya and Felix, we have total work, we can calculate the time taken by Maya and Felix.
Hence, Statement 1 is sufficient.

Statement 2 - Maya and Nora spent twice the time Felix spent.
Using the equation above,
0.5T + 2 hrs = 2* (0.5T - 2 hrs)
We can calculate T = 12 hrs.
We can calculate individual rates of Maya and Felix now, and then the combined rates of Maya and Felix, and finally the time taken by them together.
Statement 2 is also sufficient.
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Time taken to complete their respective work, Maya- x, felix- y, nora- z
R |. T. |. W
M. 25/x| x = 2+y| 25
F. 50/y|. y | 50
N. 25/z| z | 25

x=(x+y+z)/2 = (x+y+2)/2
=> 2x = x+y+2 => x= 2+y
100/(1/x+1/y) = ?
1) y=4, we can easily get x and y both. so this is sufficient.
2) x+2 = 2y => 2+y+2 = 2y => y=4. Again sufficient.

So answer is D.

Bunuel
Maya, Felix, and Nora painted a mural at a community center in consecutive shifts, each at a constant hourly rate. Maya painted the first 25% of the mural, Felix painted the next 50%, and Nora painted the remainder. If Maya’s shift accounted for 50% of the total time spent on the mural and Nora worked for 2 hours, how many hours would it have taken Maya and Felix to complete the entire mural if they had worked together from start to finish at their same respective constant rates?

(1) Felix worked on the mural for 4 hours.
(2) The total time Maya and Nora spent on the mural was twice the time Felix spent on the mural.


 


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from the passage we have the following info:- let total time be T.

rate of work :- Maya= 0.25/ 0.5t
Felix= 0.5/t-(0.5t+2)
Nora= 0.25/2

From statement 1:- We can calculate the value of T .:- T- 0.5t -2= 4, so statement 1 alone is sufficient.

From statement 2:- We can calculate the value of T:- 0.5t + 2= 2(t-0.5t-2), so statement 2 is alone is sufficient.
Bunuel
Maya, Felix, and Nora painted a mural at a community center in consecutive shifts, each at a constant hourly rate. Maya painted the first 25% of the mural, Felix painted the next 50%, and Nora painted the remainder. If Maya’s shift accounted for 50% of the total time spent on the mural and Nora worked for 2 hours, how many hours would it have taken Maya and Felix to complete the entire mural if they had worked together from start to finish at their same respective constant rates?

(1) Felix worked on the mural for 4 hours.
(2) The total time Maya and Nora spent on the mural was twice the time Felix spent on the mural.


 


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M time= T/2
M rate= (1/4)/(T/2)=1/2T
N time= 2 hours
F time= T-T/2 -2 =T/2 -2
F rate= (1/2)/(T/2)-2 =1/(T-4)
M & F combined rate = (1/2T)+1/(T-4)

1) F time=4 hrs
(T/2)-2=4
T=12 hours
Combined rate = (1/24)+1/8 =1/6
Combined Time= 6 hours
It is sufficient

2) (T/2)+2 =2((T/2)-2)
T=12 hours Combined
Combined rate= 1/6 and combined time= 6 hours
It is sufficient

D. Each statement alone is sufficient
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So we've got a Work, Rate and Time problem which can be solved largely before getting to Statement 1. In fact, it's probably best to try and solve as much of the problem as possible before getting into the Statements.

We have M-> 25% of W
F -> 50% of W
N -> 25% of W

Let's take the total Work as 100.
The Total time taken = t

M -> 1/2t

Therefore F + N = t(F) + 2 Hrs

Now that we have derived the statements, let's take Statement No. 1

Felix worked 4 Hours

M = 1/2t
N+F = 1/2t

Which means 2 - Nora + 4 - Felix = 6 Hours = 1/2t

That means that we can now calculate the rate for Maya and Felix as Rate = Work / Time
R = 25/6 + 50/4 or 200 / 12 or 100 /6 -> Hence it will take them 6 hours working together to paint the mural. As such Statement 1 is sufficient

We move on to Statement 2

M + N = 2(F)
M = 1/2t = N +F

N+F + N = 2F
F+2+2 = 2F
F+4 = 2F
F = 4 Hours

Hence we have got the time for Felix. Using this we can again calculate the hours taken by Maya + Felix if they worked together at the constant rate to paint the mural. Hence Statement 2 is also sufficient.

As such, both Statement 1 and Statement 2 are held to be sufficient. . Answer is D.
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We are given that:
Maya does 25% of the work, Felix does 50% and hence Nora does the rest i.e. 25%
Let the time taken by Maya, Felix and Nora be m, f and n respectively. And let their respective contant rates of work be M, F and N
We are also given that n = 2 hours and Maya accounts for half of the total time (m+f+n)
Thus, we know
m = (1/2)*(m+f+n) ==> 2m = m+f+n ==> m = f+n ==> m = f+2

Now, what we need to find is the time that Maya and Felix would take to complete the mural if they work on it together, simultaneously and at their constant work rates.
Thus, the rate of work will be a sum of their individual rates i.e M+F and the time taken will simply be 1/(M+F)

By the rate formula, we know that R = Work/time
We are given that,
M = 0.25/m = = 0.25/(f+2)
F = 0.5/f

Thus, we can see that if using the statements, we can find the value of f, we should be able to calculate the time taken by Maya and Felix

Statement 1: Felix worked for 4 hours
We are directly given f=4. Thus, this statement should be sufficient. We can eliminate B, C and E.

Statement 2: Total time spent by Maya and Nora is twice that of Felix
Thus, m+n = 2f
But we know, m = f+2 and n = 2
Thus, f + 2 + 2 = 2f
f = 4
Thus, this statement is also sufficient. So we can eliminate A.

Thus D is the correct answer choice
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Translating the given information:

If there are 100 units, then Maya completed 25, F did 50 and N did 25

No. of hours by M= 25/m, F = 50/f, N = 2 hours

25/m = 1/2 (25/m + 50/f + 2)- (1)

Statement 1- F worked for 4 hours, we can get f's rate of work which we can put in (1) and get m which will give us their combined work rate to satistify in the following equation and get the answer- 100/m+f

Statement 2- Total time sped by Maya and N = 25/m + 2 = 2 (50/f) - (2)

Now, we have two equations with two variables m and f, we can solve them to get m and f and satisfy the third equation- 100/m+f

(D) Each statement alone is sufficient
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IMO : D
I ) f = 4
m= f+2 = 6
Rm =1/24 , Rf = 1/8
1/24 +1/8 = 1/6
time = 1/ 1/6 = 6 hours
therefore sufficient

II) m +2 = 2f
m = f + 2
f+2+2 = 2f
f 4
m= 6 therefore, suffuecient

hence D
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T: total time

Maya 25%=1/4 -> 0.5T
Felix 50%=1/2
Nora 100%-25%-50% = 25%=1/4 -> 2 hours

hours Maya and Felix together?

(1)
Felix -> 4 hours

0.5T+4+2=T
0.5T=6
T=12

rate Maya: (1/4)/6 = 1/24
rate Felix: (1/2)/4 = 1/8 = 3/24

combined: 1/24 + 3/24 = 4/24 = 1/6 -> 6 hours

Sufficient

(2)
0.5T+2+(0.5T+2)/2=T
T+4+0.5T+2=2T
0.5T=6
T=12

Same result as in (1), so the answer is 6 hours

Sufficient

IMO D
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let m time = m hrs
f time = f hrs
n = 2 hrs

m’s time is 50% of total

m = 1/2(m + f + 2)

2m = m + f + 2

m = f + 2

we need m and f rates

1) f = 4

so m = 6. both rates can be found.

sufficient

2) m + 2 = 2f

also m = f + 2

f + 2 + 2 = 2f

f = 4 and m = 6. both rates can be found

sufficient

each alone is sufficient.

ans: d


Bunuel
Maya, Felix, and Nora painted a mural at a community center in consecutive shifts, each at a constant hourly rate. Maya painted the first 25% of the mural, Felix painted the next 50%, and Nora painted the remainder. If Maya’s shift accounted for 50% of the total time spent on the mural and Nora worked for 2 hours, how many hours would it have taken Maya and Felix to complete the entire mural if they had worked together from start to finish at their same respective constant rates?

(1) Felix worked on the mural for 4 hours.
(2) The total time Maya and Nora spent on the mural was twice the time Felix spent on the mural.


 


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Given Maya painted 25%, Felix 50%, and Nora 25%.

Nora worked for 2 hours, and Maya's time was half of the total time.

Let Maya's time = Mand Felix's time = F.

Since Maya worked half the total time:
M = (M+F+2)/2
M = F + 2

S1 --> Felix worked for 4 hours.
So, F = 4 and M = 6

Rates: Maya = (1/4)/6 = 1/24 and Felix = (1/2)/4 = 1/8

Combined Rate = 1/24 + 1/8 = 1/6

Time Together = 6 hours (S1 is sufficient)

S2 --> M + 2 = 2F

Using M = F + 2
F + 2 + 2 = 2F
F = 4, so M = 6

S2 is sufficient

Answer D - Each statement alone is sufficient
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3 People -> Maya, Felix and Nora who paint a mural

Let the total work done to finish mural = W
Maya paints 25% of the mural = W/4
Felix paints 50% of the mural = W/2
Nora paints the remaining part, which is 25% of the mural = W/4

Let,
Time spent by Maya = M
Time spent by Felix = F
Time spent by Nora = N = 2 hrs

We know that,
M = 0.5(M+F+N)
=> M = F + 2

We need to find the time taken by Maya and Felix to complete the mural if they had worked together from start to finish

Let,
Rate of work by Maya = 0.25W/M = W/4M
Rate of work by Felix = 0.5W/F = W/2F

=> We need to find,
Time taken by both = W/(0.25W/M + 0.5W/F) = 1 / (0.25/M + 0.5/F)

We are given 2 statements,
Statement 1 ->

=> F = 4
=> M = F + 2
=> M = 6

=> Time taken by both = 1 / (1/24 + 1/8) = 1/ (1/6) = 6hrs

Statement 1 is sufficient

Statement 2 ->

=> M + 2 = 2F
Since,
M = F + 2

=> F + 2 + 2 = 2F
=> F = 4
=> M = 6

We got the same values as statement 1 and follow the same procedure after and get the combined time by Felix and Maya to finish work asa 6 hrs

Statement 2 is sufficient

D. Each statement alone is sufficient
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If we know either M or F time, the question is solvable

(A) F’s time given => sufficient
(B) We can derive F’s time => sufficient

(D) is the answer
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Maya paints 1/4 in TotalTime/2
Felix paints 1/2
Nora paints the remaining 25% in 2 hours

(1)
Time of Felix = 4

TotalTime = TotalTime/2 + 4 + 2
TotalTime = 12

Maya paints 1/4 in 12/2=6 hours, rate=1/24
Felix paints 1/2 in 4 hours, rate=1/8

1/24 + 1/8 = 1/6

Maya and Felix worked together complete the mural in 6 hours.

Condition sufficient

(2)
TotalTime/2 + 2 = 2*(TotalTime - (TotalTime/2 + 2)) = 2*(TotalTime/2 - 2) = TotalTime - 4
TotalTime/2 = 6
TotalTime = 12

Reasoning like in statement 1: 6 hours.

Condition sufficient

Answer D
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