nice work guys!

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Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT

Hello Ron,
Thanks for your explanation.
I understood how the statement (1) is sufficient but i could not relate the ratio short cut and statement(2).
Can you please explain how we can prove the statement(2) to be sufficient from here on.
thanks

sure

the key to proving statement 2 sufficient (without using the number line shortcut) lies in realizing that you don't need the two variables 'x' and 'y' anymore.

if you have statement 2, then you know that x and y must add up to 16 (since 'z' is the total number of tons when x and y are combined).
therefore, take out 'y' and just call it '16 - x'.

in fact, this is probably the single most important strategy in all of word translations:
NEVER use more variables than you absolutely NEED to use.
in particular, if two or more quantities are connected by some sort of simple relationship, then you generally shouldn't need to designate a separate variable for each quantity.

--

once you've done that, it's a pretty standard setup:
0.10(x) + 0.02(16 - x) = 0.05(16)

this is an equation that you can solve for x; since this is a data sufficiency problem, you don't actually have to solve the equation. (on the other hand, it's good practice to carry out the steps at least to the point where you can be sure that x won't cancel out of the equation!)

Hello Ron,
Thanks for your explanation. Can you also show some light on how to get X using ratio method when only statement(2) is considered. I understood the solution for the statement(1) but i am confused with statement(2).
thanks

Hi,

Good question. A few have discussed this already, but statement (2) provides the value of z. From the question text we know that z = x + y. From there then, we can still apply the same methodology Ron applied to tackle statement 1.

Please let us know whether that clears things up for you!

Best regards,
Chris

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Chris Brusznicki
MGMAT Instructor
Chicago, IL