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 males below the poverty line in state C is 6000 and in state E is 1000, what is the ratio of the total population of state C to state E?

• A. 2:1
• B. 3:5
• C. 11:5
• D. NOTA

Hint:

Find what percent of each state's total population the given male count represents, then divide the two totals.

Answer 1

The Correct Option is D

To find the ratio of the total population of state C to state E, we must first determine the total population of each state. We are provided with the male population below the poverty line for both states, as well as the percentage of the population below the poverty line and the male-to-female ratios. 

1. Find the total population below the poverty line for state C:
   • The ratio of males to females below the poverty line in state C is \(3:4\) and the number of males is 6000.
   • Therefore, the female population can be calculated using: \(\frac{3}{4} = \frac{6000}{\text{Females}}\) ⟹ \(\text{Females} = \frac{6000 \times 4}{3} = 8000\)
   • The total population below the poverty line in state C is: \(6000 + 8000 = 14000\).
2. Calculate the total population of state C:
   • Given that 14% of state C's population is below the poverty line, thus representing 14,000 people.
   • The entire population can be calculated using the formula: \(\frac{14}{100} \times \text{Total Population} = 14000\) ⟹ \(\text{Total Population} = \frac{14000 \times 100}{14} = 100000\)
3. Find the total population below the poverty line for state E:
   • The ratio of males to females below the poverty line in state E is \(4:1\). The number of males is 1000.
   • The female population can be calculated using: \(\frac{4}{1} = \frac{1000}{\text{Females}}\) ⟹ \(\text{Females} = \frac{1000 \times 1}{4} = 250\)
   • The total population below the poverty line in state E is: \(1000 + 250 = 1250\).
4. Calculate the total population of state E:
   • Given that 25% of state E's population is below the poverty line, thus representing 1250 people.
   • The entire population can be calculated using the formula: \(\frac{25}{100} \times \text{Total Population} = 1250\) ⟹ \(\text{Total Population} = \frac{1250 \times 100}{25} = 5000\)
5. Determine the ratio of the total population of state C to state E:
   • State C population is 100000, and state E population is 5000.
   • The ratio is: \(\frac{100000}{5000} = 20:1\)

The ratio of the total population of state C to state E is \(20:1\), which confirms that the correct answer is NOTA.

Answer 2

Step 1: Set up the total population of state C using its male count below poverty line.
Let the total population of C be \(100x\). Below the poverty line, that is \(14x\) people (since C has 14% below poverty). The M:F ratio below poverty in C is \(3:4\), so males are \( \frac{3}{7}\) of that group: males below poverty in C \( = \frac{3}{7} \times 14x = 6x\). We are told this equals 6000, so \(6x = 6000\), giving \(x = 1000\). Total population of C \( = 100x = 100000\).

Step 2: Set up the total population of state E the same way.
Let the total population of E be \(100y\). Below the poverty line, that is \(25y\) people (since E has 25% below poverty). The M:F ratio below poverty in E is \(4:1\), so males are \( \frac{4}{5}\) of that group: males below poverty in E \( = \frac{4}{5} \times 25y = 20y\). We are told this equals 1000, so \(20y = 1000\), giving \(y = 50\). Total population of E \( = 100y = 5000\).

Step 3: Find the ratio of the two total populations.
Ratio of C to E \( = 100000 : 5000 = 20 : 1\). This value does not match \(2:1\), \(3:5\), or \(11:5\).

Final Answer:
The ratio of the total population of C to E is 20:1, which is not listed, so the correct choice is NOTA. \[ \boxed{20:1 \Rightarrow \text{NOTA}} \]