buoyant wrote:After 2/9 of the numbers in a data set A were observed, it turned out that 3/4 of those numbers were non-negative. What fraction of the remaining numbers in set A must be negative so that the total ratio of negative numbers to non-negative numbers be 2 to 1?

a)11/14
b)13/18
c)4/7
d)3/7
e)3/14

[spoiler]OA:A[/spoiler]

Let's PLUG IN a nice value for the total number of values in set A.
Since we need to deal with the fractions 2/9 and 3/4, it may be useful to choose a value that is the LOWEST COMMON DENOMINATOR of 9 and 4, which is 36.

So, let's say that there are 36 numbers in set A.

2/9 of the numbers in a data set A were observed....
2/9 of 36 is 8
So, 8 numbers were observed, which means 28 numbers were NOT OBSERVED

.... 3/4 of the observed numbers were non-negative
3/4 of 8 is 6
So, 6 numbers were non-negative.
This means that 2 of the observed numbers were NEGATIVE

What fraction of the remaining numbers in set A must be negative so that the total ratio of negative numbers to non-negative numbers be 2 to 1?
We have a total of 36 numbers, and we want the negative numbers to non-negative numbers ratio to be 2 to 1.
In other words, we want there to be a TOTAL of 24 negative numbers and 12 non-negative numbers [since 24:12 = 2:1]
We have already observed 2 negative numbers, so we need 22 more negative numbers from the NON-OBSERVED portion.

In other words, we want 22 of the unobserved 28 numbers to be negative.
22/28 = [spoiler]11/14 = A[/spoiler]

Cheers,
Brent

Hi buoyant,

I'm a big fan of TESTing VALUES (the approach that Brent showed). This question can also be solved algebraically; you just have to be careful about labeling your work.

We're told that 2/9 of a group of numbers are observed and that 3/4 of that group were NON-negative.

X = total number of terms

(2/9)X = number of terms observed

(3/4)(2/9)X = (6/36)X = 1/6X of the terms in the set are NON-negative....so far....

We're asked what fraction of the remaining (7/9) terms must be NEGATIVE so that the ratio of NEGATIVE to NON-negativei is 2:1

With a ratio of 2:1, that translates into 2/3 NEGATIVE, 1/3 NON-negative

Since we already have data about the number of NON-negative terms (1/6 so far), I'm going to stay focused on the number of NON-negative terms...We need ANOTHER 1/6 of the X terms to be NON-negative (since 1/6 + 1/6 = 1/3.

We need to calculate what the fraction of the remaining (7/9) terms would have to be NON-negative to give us the extra 1/6 that we're looking for. That calculation would be....

Y(7/9) = 1/6
Y = 9/42
Y = 3/14

This is the fraction that would have to be NON-negative. The question asks us for the fraction that would have to be NEGATIVE though, so there's one more step...

1 - 3/14 = 11/14

Final Answer: A

GMAT assassins aren't born, they're made,
Rich