CR - Proportion VS Quantity

[bhugra.ashish]

A survey recently revealed a high correlation between a household's level of education and its library. Specifically, the more years of college and graduate school education received by the household's members, the more books in the household's library. The survey also indicated that the higher the education level of the household, the greater the percentage of books that are not works of fiction in its library.

Which of the following can be properly inferred from the survey results cited above?

a. People with a higher level of education prefer reading nonfiction to works of fiction.
b. Households with low education levels generally own more works of fiction than do households with high education levels.
c. Households with lower levels of education generally own more works of fiction than nonfiction.
d. The higher the education level of a household, the fewer works of fiction owned by the household.
e. Households with high education levels generally own more nonfiction books than do households with low education levels.

Correct Answer: E

Query: How are B, C and D.. wrong ? PLease explain for each answer choice.

To simplify I took the following example
Step1: High education guys have 100 books and Low education guys have 80 books
Step2: For HIGH EDU GUYS, 70% are NonFiction. Therefore, 70 NF and 30 Fiction (F).
Step3: For LOW EDU GUYS, 60% are Non Fiction. Therefore, 48 NF and 32 F
Therefore, number of HIGH NF will always be greater than LOW NF ....

By the same token, can't D be right ? -- I am definately missing something here...
Or is it that, D talks about FICTION books within the HIGH EDUCATION HOUSEHOLDS and not about LOW, therefore incorrect ?

[messi10]

Hi,

The language is a bit tricky on this one. I will try and give you my interpretation using examples.

First of all, the premises of the argument:

Strong association between households level of education and its library
More years of college and graduate education = More books
Higher the education level = Greater the percentage of books that are not fiction

The keyword in the last premise is "percentage". In my opinion, greater percentage here does not mean that 55% book are non fiction and 45% are fiction. It is actually a comparison between households. It means, for example: If household A has 40 years worth of higher education and household B has 35 years worth of higher education then household A will have more books. Also, household A is expected to have greater percentage of non fiction books compared to household B. Elaborating further, it means that in household A, if the percentage of non fiction books are 31% then household B is expected to have less than 31% non fiction books, say 29%.

Based on this logic, lets evaluate the answer choices:

Choice A talks about preference of reading. We cannot conclude their preference of reading based on the argument. They may higher percentage of non-fictional books but they may prefer reading fictional books.

Choice B: This choice talks about "numbers". Lets try and break this conclusion: Households with higher education may own a much greater "number" of books but percentage wise, they may own more non-fiction. e.g. - Household A owns a 1000 books out of which only 50 are fiction. Household B with less educational years owns only a 100 books out of which 40 are fiction. So the higher education household has more "number" of fictional books. The premise is still true but the conclusion falls.

Choice C: Again, the argument talks about a greater percentage in comparison to other households. Not greater percentage within its own inventory. There is no premise to support this.

Choice D: Once again, lets try and break this conclusion: e.g. - Household A has 40 years education and 50 fictional books out of 1000. Household B has 50 years education and 60 fictional books out of 2000. So household B has more fictional books but at the same time, a higher percentage of non-fictional books. Once again, we have managed to hold the premise but not the conclusion.

Choice E: We know that more years of higher education means more books. We also know that they own greater percentage of non fictional books. e.g.- Household A - 40 years - 1000 books - 75% non fiction. Household B - 50 years - 1001 books - >75% non fiction. Even if household B has 1 extra book, we know from the premise that it must have a higher percentage of non fiction books. And higher percentage means more books in this case. So this is the only choice that holds true.

Hope this helps

Regards

Sunil

[jnelson0612]

As always, Sunil has good thoughts. You want to be very, very careful about concluding actual numbers when you are only given percentages. Generally the GMAT test writers are setting traps in these circumstances.

b. Households with low education levels generally own more works of fiction than do households with high education levels.
Do we know this? No, we just know that higher education houses have a higher PERCENTAGE of books that are non-fiction. For example, maybe that means that high education have 50% non-fiction and 50% fiction, and low education have 49% non-fiction and 51% fiction. We also do know that higher education tend to have more books. Well, if high education have 1000 books and low education have 100 books, high education will have 500 fiction and low education will have 51 fiction. This shows how B is wrong.

c. Households with lower levels of education generally own more works of fiction than nonfiction.
Same explanation as answer B

d. The higher the education level of a household, the fewer works of fiction owned by the household. Same as B. Again, we can't generalize absolute numbers from percentages.

[messi10]

Thanks Jamie,

Yours is a much simpler and easier post to understand.

I think I went a bit overboard with this explanation and made it too complicated. :) In fact, I have also made a mistake in interpreting the percentages at the beginning of my post.

Thanks again

Regards

Sunil

[jnelson0612]

Anytime, Sunil. :-)

[shree.neve]

As always, Sunil has good thoughts. You want to be very, very careful about concluding actual numbers when you are only given percentages. Generally the GMAT test writers are setting traps in these circumstances.

b. Households with low education levels generally own more works of fiction than do households with high education levels.
Do we know this? No, we just know that higher education houses have a higher PERCENTAGE of books that are non-fiction. For example, maybe that means that high education have 50% non-fiction and 50% fiction, and low education have 49% non-fiction and 51% fiction. We also do know that higher education tend to have more books. Well, if high education have 1000 books and low education have 100 books, high education will have 500 fiction and low education will have 51 fiction. This shows how B is wrong.

c. Households with lower levels of education generally own more works of fiction than nonfiction.
Same explanation as answer B

d. The higher the education level of a household, the fewer works of fiction owned by the household. Same as B. Again, we can't generalize absolute numbers from percentages.

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Hi Jamie,

I guess 'c' will have a separate explanation than 'b'.
B compares two households while C discusses the proportion of books of fiction within one class of households only,

I marked E as the answer but still not very sure why C is incorrect,

Can you please explain?
Thanks!

[jnelson0612]

Hi Jamie,

I guess 'c' will have a separate explanation than 'b'.
B compares two households while C discusses the proportion of books of fiction within one class of households only,

I marked E as the answer but still not very sure why C is incorrect,

Can you please explain?
Thanks!

Hi Singh,
C makes the same mistake as B. The problem only gives us percentages, but C takes that and tries to conclude something about real numbers. Watch out! Please read my explanation again about why B is wrong; C is wrong for the same reason.