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OG (12th ed) DS Prob #80

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OG (12th ed) DS Prob #80

by junkbond » Thu Apr 19, 2012 3:01 pm
The questions is:

If r>0 and s>0, is r/s < s/r?

I chose answer B, however OG says the answer is D. My rationale...

2) is correct

1) r/3s = 1/4

Once you cross multiply you get r = 3s/4. If r is any number above 1, than r>s and the statement is sufficient. However, if r is a fraction then s>r, making it insufficient.

For instance, if 1/2 = 3s/4, then s=2/3, correct? So, why does OG not take into consideration fractions here? It just says r & s are greater than 0....not 1.

What am I missing?
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Source: — Data Sufficiency |

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by Anurag@Gurome » Thu Apr 19, 2012 5:29 pm
junkbond wrote:The questions is:

If r>0 and s>0, is r/s < s/r?

I chose answer B, however OG says the answer is D. My rationale...

2) is correct

1) r/3s = 1/4

Once you cross multiply you get r = 3s/4. If r is any number above 1, than r>s and the statement is sufficient. However, if r is a fraction then s>r, making it insufficient.

For instance, if 1/2 = 3s/4, then s=2/3, correct? So, why does OG not take into consideration fractions here? It just says r & s are greater than 0....not 1.

What am I missing?
Question is: If r > 0 and s > 0, is r/s < s/r?

(1) r/3s = 1/4
(2) s = r + 4

Explanation:

(1) r/3s = 1/4 or r/s = 3/4. Also we can say that s/r = 4/3
So, r/s < s/r
This means the answer to the main question is "yes"; SUFFICIENT.

(2) s = r + 4 implies s > r as it is given that r > 0.
So, s > r > 0, which implies s/r > 1 > r/s or r/s < s/r
This means the answer to the main question is "yes"; SUFFICIENT.

The correct answer is D.
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by junkbond » Thu Apr 19, 2012 6:05 pm
Yes, but r and s can be fractions, can they not? In which case r/s < s/r, which makes 2) insufficient.
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by junkbond » Thu Apr 19, 2012 6:13 pm
Welp - never mind. This makes sense. Thanks for the response.
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by Poisson » Sun Aug 21, 2016 7:27 am
Please help. I'm really confused with this one. Since R and S are both positive, I cross-multiplied the information in the prompt and to get "is r^2 < s^2"? For Statement 1, I tested fractions R= 0.3 and S = 0.4. I got 0.09 is not less than 0.16. When I tested whole numbers, I got 9 is less than 16. I'm confused about why cross-multiplication yielded two different answers. Attached is my work. Please help me understand what I'm doing wrong. Thanks so much.
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by [email protected] » Sun Aug 21, 2016 9:30 am
Hi Poisson,

You did all of the work correctly; however, .09 IS LESS than .16, so your second example also provides a "YES" answer. For this prompt, the information in Fact 2 will ALWAYS lead to a "yes" answer, so that Fact is SUFFICIENT.

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