Yves can paint a certain fence in 1/2 the time it takes Marcel to pain

regarding statement2:
Say Marcel can finish the work in x hrs. Then Vyes can finish the same work in 2x hrs. So they together can finish the work in
(2x^2)/3x hrs
The statement says, this time is equal to 'half the time it would take Marcel alone'. Thus
(2x^2)/3x = 2x/2 --> 2/3 = 1 What'm I doing wrong here?

Dear experts,

Please advise how statement-2 is not suffcient

Remember that the stem asks us for the number of hours - an explicit value - it would take both of them to paint the fence. From the stem we know that Yves is twice as fast as Marcel, but we do not know what this is in hours. It could be that Yves alone uses 1 hour and Marcel 2 hours, or it could be that Yves alone uses 3 hours and Marcel 6 hours. This would give different answers to the combined time that they use to paint the fence. Therefore, as Statement 2 doesn't provide any explicit value - a value that we can relate the speed of Yves to that of Marcel - statement 2 is not sufficient.

This question is posted incorrectly. It should read:

Yves can paint a certain fence in 1/2 the time it takes Marcel to paint the same fence. If they work together, each at his own constant rate, how many hours will it take them to paint the fence?

(1) Yves can paint the fence by himself in 3 hours.
(2) Working together, each at his own constant rate, they can paint the fence in 1/3 the time it would take Marcel, working alone, to paint the fence.

___________________
Thank you. Edited.

My 2 cents:

Given in the stem:
Alone
Rate Time Work
Marcel R T=1/R 1 fence
Yves 2R T= 1/2R 1 Fence

Combined
3R 1/3R 1 Fence

How many hours will it take them to complete?

(1) Yves T = 3 hours
1/2R = 3
1= 6R
R = 1/6

we have Yves Rate and so we can plug this in to determine Marcel's Rate to determine T -->(S)

Eliminate BCE

(2)

3R = 1/3*1/2R = 1/6R

This only gives a relative rate. We have no value for R and so we cannot determine T. --> (IS)

Eliminate D

Answer (A)

I don't get why statement (2) is insufficient. please explain Bunuel

The second statement is not sufficient because it gives adds nothing new to what we already know from the stem

The stem says that Yves can paint a certain fence in 1/2 the time it takes Marcel to paint the same fence:

Say Yves can paint the fence in x hours, then Marcel can pain it in 2x hours. Their combined rate is 1/x + 1/(2x) = 3/(2x), which means that they need 2x/3 hours to pain the fence together (recall that time is reciprocal of rate). 2x/3, is 1/3rd of 2x, the time Marcel needs to pain the fence alone. So, (2) simply restates the fact we could derive ourselves from the stem.

For anyone unsure about the second statement

\(\frac{1}{t}+\frac{1}{2t}=\frac{3}{2t}\)

Notice that the \(t\) cancels out

Step 1: Analyse Question Stem

Let time taken by Yves to paint the fence = Y and time taken by Marcel to paint the same fence = M.
Then, as per the question data, Y = ½ M.

Let,
Rate at which Yves paints the fence = p
Rate at which Marcel paints the fence = q

Since time taken by Yves is half the time taken by Marcel, Rate of Yves = 2 * Rate of Marcel

Therefore, p = 2q

When both of them work together, their combined rate = p + q = 2q + q = 3q.

Time taken by them to paint the fence, working together = \(\frac{Total work }{ 3q}\).

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE

Statement 1: Yves can paint the fence by himself in 3 hours.

Therefore, Y = 3.

Let total work done = 1 unit; then, rate at which Yves works = p = \(\frac{1}{3}\) units per hour.

We know that p = 2q; therefore, 2q = \(\frac{1 }{ 3}\) or q = \(\frac{1}{6}\) units per hour.

Since we know the value of q and the total work, the time taken can be calculated.

The data in statement 1 is sufficient to find out a unique value for the time taken.
Statement 1 alone is sufficient. Answer options B, C and E can be eliminated.

Statement 2: Working together, each at his own constant rate, they can paint the fence in \(\frac{1}{3}\) the time it would take Marcel, working alone, to paint the fence.

Working together, combined rate of Yves and Marcel = 3q.

Time taken by them, working together = \(\frac{1 }{ 3q}\) (assuming total work = 1 unit)

Rate of Marcel = q and hence, time taken by Marcel, working alone = \(\frac{1 }{ q}\).

The information given in statement 2 says that,

\(\frac{1 }{ 3q}\) = \(\frac{1 }{ 3}\) * \(\frac{1}{q}\)

Clearly, that is not sufficient to find out the value of q. If we cannot find the value of q, the question cannot be answered.

The data in statement 2 is insufficient to find out a unique value for the time taken.
Statement 2 alone is insufficient. Answer option D can be eliminated.

The correct answer option is A.

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