# Having trouble interpreting the language behind some of the qualitative questions?

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In 2008, more members of the U.S. population in the 45 to 54 years old age group had health insurance than in the 35 to 44 years old age group

This was a problem I encountered while taking the Manhatten practice test. I've noticed I've been having a problem interpreting the language in the quantitative questions "correctly". The above statement I view as being true, based on the graph. The bar is higher for the 45 to 54 years age group than the 35 to 44 years age group. However, it is false. The reason they gave is:

"For the two age groups mentioned, look at the middle graph.  The year 2008 is represented by the light gray bars.  This bar is higher for the 45 to 54 category than for the 35 to 44 category, so you might be tempted to conclude that there were more 45- to 54-year-olds who have health insurance than there are 35- to 44-year-olds in 2008.  Watch out!  This is a case in which you cannot take "percent of population" comparisons and make "number of people" inferences from them, because we don't know the total number of people in each age range.

For example, there might have been 50 million 45- to 54-year-olds in 2008.  According to the chart, about 84% of them had health insurance, for a possible total of 42 million insured.  There might have been 55 million 35- to 44-year-olds in 2008.  According to the chart, about 81% of them had health insurance, for a possible total of 44.55 million insured.  The number of people insured could be greater in the group with the lower percent insured, if there are more people total in that group.

Since we don't know population by age group, this statement might be false (as shown above) or might be true (with different numbers tested for the populations)."

The title of the graph, the "percent of U.S. population with Health insurance by Age", to me means all the percentages are based on a constant number, that number being the total U.S. population. If there's 81% of the U.S. population (let's say 320 million) with Health Insurance, that is less than 84% of the U.S. population, so you could know that more members in the higher age group had health insurance, since both are a percentage based on a constant number (320 million, the U.S. population).

The language a lot of these qualitative questions uses is subjective?

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I remember seeing this same question. The "trick" (not really a trick) here is to understand that when they refer to a "percentage of the population", they are talking about percentages of subsets of the population. This bar graph shows the population broken down by age. The percentages refer to the percent of people within that age group. As explained in the solution, comparing the percentages of these subsets is not going to give you the correct answer since the subsets have different (and unknown) absolute totals. Another key here is to notice that these are not percentages of the same number (total US population)-- if it was, your total sum of percentages across each of the years would be 100%.

To give a simpler example, say in a graduating class of 600 students, 80% of the history majors are female and 50% of the chemistry majors are female. Notice that this mirrors the question above, but the subgroups are academic majors instead of age groups. Here, it would be incorrect (with this being the only information given) to say that there are more female history majors than female chemistry majors. It is easy to see that you might have a case where there are 70 chemistry majors (35 of which are female), but only 10 history majors (8 of which would be female)--there are actually more female chemistry majors. So it is incorrect to simply compare the percentages to each other because this is not capturing the full picture of the data.

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Percentage of health insurance by age means percentage out of total number of people in that age group. If you get confused, look at the chart. The trick to nail GRE IS to realize it's trickery and word play. It is a simple bar chart, simply comparing the value of percentages, and not the actual number of people.

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If there's 81% of the U.S. population (let's say 320 million) with Health Insurance, that is less than 84% of the U.S. population, so you could know that more members in the higher age group had health insurance, since both are a percentage based on a constant number (320 million, the U.S. population).

So, by that logic, if 81% of the US population falls into the 34-44 age group, and 84% of the US population falls into the 45-54 age group, then together they make up 165% of the US population?

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The GRE Q questions uses technical language that they expect you to understand. This might be tricky for someone who is not very familiar with this type of language but understanding the description/question is actually part of the test! However, I would not call it "trickery" or "wordplay", just precise language ("jargon" perhaps). It's an important skill to properly interpret academic quantitative work.

For future/similar questions, remember to read all parts of the graph very carefully. In this case, you see the title says "Percentage of U.S. Population with Health Insurance by age". Whenever we make a bar graph like this and we talk about a percentage or fraction of a certain quantity by age (or any other quantity, it could be gender, academic major, profession, etc.), the percentage or fraction in each group only applies to that age group (or gender, or major, or profession etc.). (The above advice to check that the numbers don't add up to 100% like you originally interpreted is also a good strategy!)

Practice, practice, practice is what I would recommend if you are new to this type of language. Make sure you read every piece of information carefully and decide what is important and what isn't important for the question. It will come more naturally once you are more familiar with the questions!

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