Qn #80 in OG12

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.

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).

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!

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.