Working together rates ...

[II]

Hi would be interested to see the approaches in solving this one ... especially in dealing with statement 2.

Thanks in advance.

[Stuart@KaplanGMAT]

Let's jot down the relevant formula:

Combined time (Y&M) = Y*M/(Y+M)

We know that Y=1/2(M), so:

Combined time (Y&M) = 1/2(M^2)/(1.5M)

So, if we can determine the individual time of either Y or M, we can answer the question.

(1) Y=3... exactly what we want, sufficient!

(2) Combined Tme (Y&M) = 1/3(M)

This might seem useful, but it actually tells us what we already knew!

Let's take our original equation a few steps further:

Combined time (Y&M) = 1/2(M^2)/(1.5M)

Combined time (Y&M) = (.5)/(1.5) * M^2/M

Combined time (Y&M) = 1/3 * M

So, we already knew the relationship described in statement 2 - therefore, it's completely useless.

(1) is sufficient, (2) isn't: choose (A).

As an aside, if you ever determine that a statement is completely useless, you can eliminate one more choice than usual.

Normally, if (2) is insufficient, we eliminate (b) and (d).

However, if (2) is completely worthless, then we can also eliminate (c), since there's no way that:

an insufficient statement + a worthless statement = sufficiency.

[II]

Thanks for the quick response Stuart.

I am just trying to get my head around the following:

Combined time (Y&M) = Y*M/(Y+M)

We know that Y=1/2(M), so:

Combined time (Y&M) = 1/2(M^2)/(1.5M)

Can you please elaborate ?

Thanks again !

[Stuart@KaplanGMAT]

Thanks for the quick response Stuart.

I am just trying to get my head around the following:

Combined time (Y&M) = Y*M/(Y+M)

We know that Y=1/2(M), so:

Combined time (Y&M) = 1/2(M^2)/(1.5M)

Can you please elaborate ?

Thanks again !

There are two formulae we can use for work problems.

First, there's the generic formula:

1/(combined time) = 1/x + 1/y + 1/z + ....

in which x, y, z and so on are the times of individual workers.

With exactly two workers, we can rearrange the formula to:

Combined Time of X&Y = x*y/(x+y),

which is a much easier formula to use on most work problems on the GMAT.

For example, if we know that x can finish a job in 4 hours and y can finish the same job in 5 hours, then we would calculate:

Combined time of X&Y = 4*5/(4+5) = 20/9 = 2 & 2/9 hours.

So, in the question you posted, if we call Y's individual time "y" and M's individual time "m",

Combined time of Y&M = y*m/(y+m)

and, since we know that y=(1/2)m, we can simply substitute in for y to get:

Comb Time (Y&M) = (1/2)m*m/(1/2m + m) = .5(m^2)/1.5(m)