Working together rates ...

II · Posted: Thu Aug 07, 2008 1:04 pm Post subject: Working together rates ...

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

Thanks in advance.

Stuart Kovinsky · Posted: Thu Aug 07, 2008 1:39 pm Post subject:

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 · Posted: Thu Aug 07, 2008 2:06 pm Post subject:

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 Kovinsky · Posted: Thu Aug 07, 2008 2:24 pm Post subject: