A local group working to get signatures for a petition to pass a new

Question

A local group working to get signatures for a petition to pass a new ordinance lists all signers in their database as either “residents” or “non-residents”. If the ratio of residents to nonresidents in the database is 3 : 5, how many signers are currently listed as non-residents in the database?

(1) If the next six signers are all residents, the ratio of residents to nonresidents in the database will be 1 : 1

(2) If three signers had been incorrectly assigned and were nonresidents rather than residents, the ratio of residents to nonresidents in the database would be 1: 3 once this was corrected.

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ThickRiver · Answer

Nice one, this is a set-up-two-equations-and-let-algebra-do-the-work question.

1. Let residents = 3k and non-residents = 5k right now, since the ratio is 3:5.

2. Statement 1: add six residents, and the ratio flips to 1:1. So 3k + 6 = 5k, which gives 6 = 2k, k = 3. Non-residents = 5k = 15. That's a full number, so sufficient.

3. Statement 2: three people who were logged as residents actually should have been non-residents. So residents become 3k - 3, non-residents become 5k + 3, and that new ratio is 1:3. Set it up: 3(3k - 3) = 5k + 3. That's 9k - 9 = 5k + 3, so 4k = 12, k = 3. Same answer, non-residents = 15. Also sufficient on its own.

Answer: D, each statement alone gets you there.

What I like about this one is that both statements are really just "correct the count and set the new ratio equal," and once you're comfortable translating word problems into a single variable k for the ratio unit, both statements resolve fast. Early on I used to rewrite R and N as two separate variables and solve a messier system. One variable for the ratio unit does the whole job here, and it's worth practicing that shortcut deliberately instead of hoping it shows up on its own under time pressure.

odionam · Answer

ratio of resident and non resident are given i.e 3:5 , R:NR =3:5
from St1 if R has another 6 then ratio becomes 1:1, 3k+6 : 5k = 1:1 so we can calculate each value easily it is sufficient 
from St2 if 3h has assigned from R to NR it becomes 3k-3 :5k+3 = 1:3 from here we can also calculate each value so each statement alone is sufficient answer is D

dhart · Answer

Either statement is sufficient to answer , option D

MarkGMATMentor · Answer

When conditions change in a ratio problem, often the quickest way to solve is by using a variable to represent the "ratio multiplier".

Since the prompt tells us that the ratio of residents to nonresidents is 3:5, we can think of the  actual number  of residents as 3x and the  actual number  of nonresidents as 5x. Once we know the value of x (the ratio multiplier), we'll also know the number of non-residents (and be able to answer the question).

Statement 1: 
If the next 6 signers are all residents, the new number of residents is 3x + 6. Now the ratio of residents to non-residents is:
 \frac{3x + 6}{5x} = \frac{1}{1}

This can be solved for one answer for x, so we'll be able to answer the question. No need to go through it.  Sufficient.

Statement 2: 
If 3 signers were incorrectly assigned as residents, to correct it we must subtract 3 from the residents (3x - 3) and add 3 to the non-residents (5x + 3). Now the ratio of residents to non-residents is:
 \frac{3x - 3}{5x + 3} = \frac{1}{3}

As with the first statement, this can be solved, so we'll be able to answer the question.  Sufficient.

The answer is D.

Using the ratio multiplier when conditions change is almost always faster than using two different variables (for example, r for residents and n for non-residents) and setting up multiple equations. And on a DS question, once you have a solveable one-variable linear equation, you know it's sufficient and don't need to calculate.

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