Qn #80 in OG12

[papgust]

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?

[arzanr]

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.

[kstv]

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).

[papgust]

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!

[Testluv]

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.

[Scott@TargetTestPrep]

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