After 2/9 of the Numbers in a Data Set A were Observed GMAT Problem Solving

Question: 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 is 2 to 1?

1. 11/14
2. 13/18
3. 4/7
4. 3/7
5. 3/14

Correct Answer: A
Solution and Explanation:
Approach Solution 1:

When picking a variable for set A, there will be too many fractions to deal with, so pick a number that makes sense.

For example, let's say set A has 18 numbers.
"2/9 of the numbers in a data set A were observed."

This means that 4 numbers were seen, and there are still 18 - 4 = 14 numbers to see.

"3/4 of those numbers weren't negative," so 3 of the numbers weren't negative and 1 was.

For the ratio of negative numbers to non-negative numbers to be 2:1, there should be a total of 182/3 = 12 negative numbers. This means that there should be 11 negative numbers in the part that hasn't been seen yet, which is 121 = 11. This means that 11/14 of the numbers left in set A must be negative.

A is the correct answer.

Approach Solution 2:

Find the LCM of 4 and 9: 36 (Let total)
So, 2/9 of 36 is 8, which was seen.

Six out of the eight were not negative. So, the number was -2.

The ratio of negative to non-negative numbers must be 2:1.

So the total number of negatives will be 2/3 of 36, or 24, and the number of positives will be 12.

So, new negative numbers must be =24-2 =22 (Because we already know two from what we have seen)
Remaining numbers = 36-8 = 28 (Our goal is to figure out how many numbers are left. The numbers we haven't seen yet are what we mean by "remaining."

fraction =22/28 = 11/14

A is the correct answer.

“After 2/9 of the numbers in a data set A were observed" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT problem solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude for reasoning and mathematics. The GMAT Quantitative Test's Club Test Phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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