In a recent town election, what was the ratio of the number of votes

Solution

To find:

• The ratio of the number of votes in favour to the number of votes against the proposal

Analysing Statement 1

• As per the information given in statement 1, there were 60 more votes in favor of the proposal than against the proposal

o If we assume the number of votes against the proposal to be n, then the number of votes in favour will be n + 60
o But we don’t know the value of n, hence, we can’t find the value of the ratio \(\frac{n+60}{n}\)

Hence, statement 1 is not sufficient to answer

Analysing Statement 2

• As per the information given in statement 2, there were 240 voters in favour of the proposal
o Only considering this statement, we don’t have any information about the number of votes against the proposal

Hence, statement 2 is not sufficient to answer

Combining Both Statements
If we combine both the statements, we can say:

• 240 votes were in favour of the proposal and it is 60 more than the votes against the proposal
• Therefore, we can find out the exact number of votes for and against the proposal, and thus, we can find out the required ratio

Hence, the correct answer is option C.

Answer: Cs

We are asking about Favored/Non-Favored

1. There were 60 more votes in favor of the proposal than against the proposal.

Lets assume, Non-favored = X
Favored= x+60

x+60/x?

We cannot find it since we dont know the value of X

2. Favored= 240. This is ALONE not sufficient since we dont know the value of Non-Favored


From Statement 1 and 2:
Favored = X+60 = 240 i.e. x=60 which is value of non-favored.

We can calc the ratio of these two.

Hi i am new and i answer every question correctly. However, I can only see the statement not the answers. Therefore, I cannot answer any of the questions...

These are the answer choices in DS questions:

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

Answer: Option C

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Solution:

Question Stem Analysis:

We need to determine the median of the annual salaries of the n employees at a certain company.

Statement One Alone:

Since we know the median salary is the 15th highest salary, we can determine the value of n is 29. That is, there are 29 employees in the company. However, we can’t determine the median of the annual salaries of the 29 employees. Statement one alone is not sufficient.

Statement Two Alone:

Knowing the sum of the annual salaries does not allow the median of the annual salaries of the n employees to be discerned. Statement two alone is not sufficient.

Statements One and Two Together:

With the two statements, we can determine the average (or mean) annual salary of the 29 employees. However, we still can’t determine the median annual salary since the mean and the median of a set of numbers are not necessarily the same value. Both statements together are not sufficient.

Answer: E

Solution:

Question Stem Analysis:

We need to determine the ratio of the number of votes in favor of a certain proposal to the number of votes against the proposal. We can let the number of votes in favor and against the proposal be f and a, respectively, so we need to determine the value of f/a.

Statement One Alone:

With the information in statement one, we can create the equation:

f = a + 60

With one equation and two variables, we can’t determine the value of f (or a). Hence, we can’t determine the value of f/a. Statement one alone is not sufficient.

Statement Two Alone:

With the information in statement two, we can create the equation:

f = 240

Without the value of a, we can’t determine the value of f/a. Statement two alone is not sufficient.

Statements One and Two Together:

With the two statements, we see that:

f = a + 60

and

f = 240

Substituting 240 for f in the first equation, we have:

240 = a + 60

180 = a

Therefore, the value of f/a = 240/180 = 4/3. In other words, the ratio of the number of votes in favor of the proposal to the number of votes against it is 4 to 3. Both statements together are sufficient.

Answer: C

EgmatQuantExpert Do we need to consider the voters who do not vote at all ? How we will know that there are only 2 categories - Favor of the proposal/against the proposal ?

Video solution from Quant Reasoning:
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So, we are to find the ratio of votes in favor to votes against.

St(1)There were 60 more votes in favor of the proposal than against the proposal.

So if favorable/Non favorable = x/y then x=y+60 but this does not give us a definite ratio.We can have any number of favorable and corresponding to it non favourable votes and have multiple possible answers.(Insufficient)

St(2) There were 240 votes in favor of the proposal.

No information about non favorable or total votes (Insufficient)

On combining both we have favourable =240 and unfavourable = 240-60 =180

=>Ratio of votes in favour to votes against = 240/18024/18 (Sufficient) (option c)

Devmitra Sen
GMAT SME

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