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jeffhicks05
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5 lb Practice Book, Ratios, Page 707, Number 34.

by jeffhicks05 Sat Aug 17, 2013 10:18 am

A quantitative comparison question.

Quantity A is "the fraction of the total distance x that is covered by Jane."

Quantity B is "(2/3)*x".

Quantity A is a constant (2/3), that is, Jane always covers two thirds of the distance, regardless of how large the distance is.

Quantity B is not a constant. If x is .5, than Quantity B is smaller. If x>1, the quantity B is larger.

By this reasoning the answer is D. The book says it is C.

Where am I going wrong in my reasoning?

Thanks!
tommywallach
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Re: 5 lb Practice Book, Ratios, Page 707, Number 34.

by tommywallach Wed Aug 21, 2013 4:45 pm

Hey Jeff,

I'm afraid I don't totally understand your reasoning. 2/3 of x and 2/3 of distance x mean the exact same thing. If Jane runs twice as fast as Dick, she'll always cover 2/3rds of the distance between them, and he'll cover 1/3. So the two columns are actually saying the exact same thing (they're both 2/3 * x).

Does that make sense, or am I missing something about what you think you're missing? : )

-t
jeffhicks05
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Re: 5 lb Practice Book, Ratios, Page 707, Number 34.

by jeffhicks05 Sun Aug 25, 2013 10:47 am

My thinking was this:

If x=12, than 2/3 of the distance is 8. This is equivalent to (2/3)*x, which is Quantity B.

Quantity A is simply 2/3 = .66666666

Or put differently, Quantity A is essentially the constant fraction of the distance (2/3), whereas Quantity B is the actual amount of distance, which depends on x.
tommywallach
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Re: 5 lb Practice Book, Ratios, Page 707, Number 34.

by tommywallach Fri Aug 30, 2013 7:47 am

Jeff!

You're totally right! I'm sorry; I didn't understand your question at first. This is absolutely an error. I'll send it on to errata. Well done!

-t