Qn #80 in OG12

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papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pm; Thanked: 653 times; Followed by:252 members

Qn #80 in OG12

by papgust » Fri Feb 26, 2010 8:03 pm

If r > 0 and s > 0, is r/s < s/r?
(1) r / 3s = 1/4
(2) s = r + 4

OA: D

I know that statement 1 is sufficient, but i thought that II is insufficient. As the qn does not mention whether r and s are integers, i plugged in both fractions and integers and was convinced that i get 2 different answers.

If r=2, then s = 4+2 = 6.
2/6 < 6/2. YES

If r=1/2, then s = 1/4.
r/s = 4/2. s/r = 2/4. So, r/s > s/r. NO

Can someone explain where i'm wrong?

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Source: Beat The GMAT — Data Sufficiency | Fri Feb 26, 2010 8:03 pm

arzanr: Senior | Next Rank: 100 Posts; Posts: 60; Joined: Wed Jan 07, 2009 1:56 pm; Thanked: 12 times; GMAT Score:750

by arzanr » Fri Feb 26, 2010 8:16 pm

If r=1/2, then s = 1/4.

With s = r + 4, If r = 1/2 then S would be equal to 4 1/2 (1/2 + 4)

Btw, for #2 you don't need to try any numbers, when s is greater than r then the fraction with s as the numerator would always be greater than the fraction with s as the denominator.

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kstv: Legendary Member; Posts: 610; Joined: Fri Jan 15, 2010 12:33 am; Thanked: 47 times; Followed by:2 members

by kstv » Fri Feb 26, 2010 9:53 pm

If r > 0 and s > 0, is r/s < s/r?
(1) r / 3s = 1/4
(2) s = r + 4

(1) r/s = 3/4 so when r= 3 s = 4 , s/r =4/3

or when r= 1/4 s= 1/3 s/r = 3/4 not suff

(2) s= r + 4 or s/r = 1 + 4/r plug the same values r= 3 s = 4 , s/r =4/3
s/r = 4/3 = 1+ 4/3 not possible

s/r = 3/4 = 1+4*4 when r= 1/4 s= 1/3 s/r = 3/4 not possible

so D.

I read somewhere that (1) and (2) should be compatible if E is the option. Leads me think that we should use the same values in (1) and (2).

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papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pm; Thanked: 653 times; Followed by:252 members

by papgust » Fri Feb 26, 2010 10:01 pm

arzanr wrote:
If r=1/2, then s = 1/4.
With s = r + 4, If r = 1/2 then S would be equal to 4 1/2 (1/2 + 4)

Btw, for #2 you don't need to try any numbers, when s is greater than r then the fraction with s as the numerator would always be greater than the fraction with s as the denominator.

True arzanr. I completely agree!

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Testluv: GMAT Instructor; Posts: 1302; Joined: Mon Oct 19, 2009 2:13 pm; Location: Toronto; Thanked: 539 times; Followed by:164 members; GMAT Score:800

by Testluv » Sun Feb 28, 2010 11:00 am

Simplify the question stem.

Because we know that both r and s are positive, we don't have to worry about the inequality sign flipping, and we can rearrange the inequality being asked about:

Is r/s < s/r?

Is r^2 < s^2?

Is r < s?

If we rephrase the question this way, then it is clear that both statements are sufficient by themselves.

Kaplan Teacher in Toronto

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: Qn #80 in OG12

by Scott@TargetTestPrep » Fri May 14, 2021 6:46 am

papgust wrote: ↑
Fri Feb 26, 2010 8:03 pm
If r > 0 and s > 0, is r/s < s/r?
(1) r / 3s = 1/4
(2) s = r + 4

OA: D

Solution:

Question Stem Analysis:

We need to determine whether r/s < s/r given that both r and s are positive. Notice that r/s < s/r if r < s when both r and s are positive. Therefore, we really need to determine whether r < s.

Statement One Alone:

r/(3s) = 1/4

4r = 3s

r = 3s/4

We see that r is ¾ of s. Given that both r and s are positive, we see that r < s. Therefore, r/s < s/r. Statement one alone is sufficient.

Statement Two Alone:

Since s = r + 4, r < s. Therefore, r/s < s/r. Statement two alone is sufficient.

Answer: D

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