While Alaska, one of the 50 states in the United States, has fully vac

Question

﻿While Alaska, one of the 50 states in the United States, has fully vaccinated 16 percent of its population, the highest rate in the country, the state ranks 46th in vaccine administration, having used only 69 percent of its supply. Hence, Alaska has vaccinated more people than has any other state. Note, the vaccine is a single-shot vaccine, and a state is only allowed to vaccinate its residents.
Which of the following is required for the assertion above to be true?
A. More vaccines have been delivered to Alaska than to most other states.
B. People in Alaska are more willing to get vaccinated than in other states.
C. California that ranks behind Alaska in the proportion of people vaccinated does not have a higher population.
D. Alaska's population is higher than that of other states.
E. Alaska has more locations that deliver the vaccine than do most other states.

gmatophobia · Accepted Answer

A lot of moving parts to this question. Let's try to understand the facts presented -

Alaska has vaccinated more people than has any other state
 Inference: Out of the 50 states in the US, the number of people (residents) vaccinated in Alaska is higher than that in other states. We cannot infer much about the population of the state at this point. We can, however, infer that Alaska has used a higher number of vaccines than other states have. We can infer this because the premise states that a greater number of people were vaccinated in Alaska than in other states.

% of people vaccinated = number of residents vaccinated / total number of residents. 
  
 Alaska ranks 46th in vaccine administration
 Inference: Out of the 50 states in the US, Alaska stands at 46th position in the percentage of vaccines used. Let's assume that 100 vaccines were sent to each state, a state which uses the maximum number of vaccines ranks one (highest), and the state that uses the least number of vaccines ranks last (50th). Hence, we can infer, that the percentage of vaccines Alaska used was lower than that of many other states, i.e. 45 states used a higher percentage of vaccines sent to those states.

% of vaccines used = number of vaccines used (equals to the number of residents vaccinated) / total number of vaccines that the state has received.

Alaska used 69 percent of its supply
 Inference: 69% of the supplies were used to vaccinate the residents of Alaska. Combining this information with the first two points, we can further infer that to vaccinate 16% population, the state has used 69% of its supplies. We also know that the number of people vaccinated in Alaska is greater than that of other states, however, the ranking of vaccine administration is lower than many other states. A possible explanation for this paradox can be that the state received more supplies than other states. Hence, while it used more supplies than other states did, the ranking of vaccine administration wasn't that great. Let's hold on to this thought.

Answer choice elimination -

Let's start with Option B

B. People in Alaska are more willing to get vaccinated than in other states.

This option is out of scope and relies on common knowledge. The passage doesn't share the reason for vaccination. Was the reason to get vaccinated sheer willingness or the residents were incentivized or something else, we have no idea. We can eliminate this option.

C. California that ranks behind Alaska in the proportion of people vaccinated does not have a higher population.

% of people vaccinated = # of residents vaccinated / total number of residents.

From the premise, we know that the value of the numerator is highest for Alaska. This statement presents us with the rate of people vaccinated between the two states.

Multiple possibilities exist for this observation -

1) Population of Alaska is lower than the population of California 
2) Number of people vaccinated is lower in California and the population is the same as that of Alaska.
3) Number of people vaccinated is lower in California and the population is more than that of Alaska.

Hence, we can eliminate this possibility.

P.S. The use of 'that' in the statement is incorrect. Better construction -

California,  which  ranks behind Alaska in the proportion of people vaccinated, does not have a higher population.

D. Alaska's population is higher than that of other states.

This may be true. However, we cannot this must not be true for the statements to hold true. It's well possible that all states share the same population and the number of people vaccinated in Alaksa was greater than that of the other states.

Hence, we can eliminate this possibility.

E. Alaska has more locations that deliver the vaccine than do most other states

Not relevant. Hence, we can eliminate this option.

A. More vaccines have been delivered to Alaska than to most other states.

We know while Alaska used a greater number of vaccines than other states did, however, it ranked quite lower than most other states in vaccine administration. Let's revisit the formula again

% of vaccines used = number of vaccines used (equals to the number of residents vaccinated) / total number of vaccines that the state has received.

The numerator is highest for Alaska and the % of vaccines used is lower than most other states (as Alaska ranks 46th). This observation is possible when the value of the denominator is higher. Hence, the state must have received more supplies of vaccines than most other states.

Option A.

druparel · Answer

I selected option D. Here's why:

We want this assertion to be true: "Hence, Alaska has vaccinated more people than has any other state." If Alaska's population is higher than that of other states, that means that the number of vaccinated residents is higher for Alaska than any other state (since 16% vaccinated is the highest). Thus, making the assertion true.

Option A - More vaccines have been delivered to Alaska than to most other states - explains why '69% vaccine administration' is so low and ranks 46th, but that's not the assertion we want to make.

Can you explain to me why my logic is incorrect?

VerbalBot · Answer

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While Alaska, one of the 50 states in the United States, has fully vac

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