Question

Directions: The following table shows the percentage population of six states (A to F) that lives below the poverty line, along with the male to female ratio among the population below the poverty line and above the poverty line, for each state.

State	% Population below poverty line	Below Poverty line M:F	Above Poverty line M:F
A	16	2:3	3:4
B	10	4:3	5:2
C	14	3:4	2:3
D	20	5:2	4:3
E	25	4:1	2:1
F	20	2:3	4:1

If the number of females below the poverty line in state F is 16000, what is the number of males below the poverty line in that state?

• A. 8000
• B. 6000
• C. 12000
• D. NOTA

Hint:

Use the 2:3 male to female ratio below poverty line in F to convert the given female count of 16000 into a male count, then compare with the options.

Answer 1

The Correct Option is D

To find the number of males below the poverty line in state F, we begin by analyzing the given data:

The male-to-female ratio below the poverty line in state F is given as \(\frac{2}{3}\). This means that for every 2 males, there are 3 females.

We are informed that there are 16,000 females below the poverty line in state F.

We establish equal comparability using the ratios. So, if the number of females is 16,000, we can express the males as follows:

1. Since the ratio is \(2:3\) (males:females), let the common ratio factor be x.
2. The number of males = \(2x\).
3. The number of females = \(3x = 16000\). 

Now, solve for x:

\(3x = 16000\)

Divide both sides by 3 to find x:

\(x = \frac{16000}{3} = 5333.333\) (approximately)

This represents the factor for the ratio.

Using this factor, find the number of males:

\(2x = 2 \times 5333.333 = 10666.666\) (approximately)

Since the number of males must be expressed as a whole number, and no option matches this, the correct answer is indeed NOTA (None of the Above).

Answer 2

Step 1: Set up the total population of state F.
Let the total population of F be \(100x\). Since 20% of F is below the poverty line, the population below poverty line is \(20x\).

Step 2: Use the M:F ratio below poverty line to find \(x\).
The M:F ratio below poverty in F is \(2:3\), so females are \( \frac{3}{5}\) of that group. Females below poverty in F \( = \frac{3}{5} \times 20x = 12x\). We are told this equals 16000, so \(12x = 16000\), giving \(x = \frac{16000}{12} = 1333.33\).

Step 3: Find the number of males below poverty line.
Males are \( \frac{2}{5}\) of the below poverty group: males below poverty in F \( = \frac{2}{5} \times 20x = 8x = 8 \times 1333.33 = 10666.66\). This is not a whole number of people and it does not match 8000, 6000, or 12000.

Final Answer:
Since the exact male count below poverty line in F is about 10666.66, which matches none of the given numeric options, the correct choice is NOTA. \[ \boxed{10666.66 \Rightarrow \text{NOTA}} \]