chiragatara
Is the number of seconds required to travel d1 feet at r1 feet per second greater than the number of seconds required to travel d2 feet at r2 feet per second?
(1) d1 is 30 greater than d2.
(2) r1 is 30 greater than r2.
Is \(\frac{d_1}{r_1}>\frac{d_2}{r_2}\)?
Obviously each statement alone is not sufficient.
When taken together we'l have: is \(\frac{d_2+30}{r_2+30}>\frac{d_2}{r_2}\)? --> cross multiply (we can safely do that as in both fractions denominator and nominator are positive): \(d_2*r_2+30r_2>d_2*r_2+30d_2\) --> is \(r_2>d_2\)? so we have that \(\frac{d_2+30}{r_2+30}>\frac{d_2}{r_2}\) holds true when \(r_2>d_2\), but we don't know whether that's true so even taken together statements are not sufficient.
Answer: E.
Generally if \(a\), \(b\) and \(c\) are positive numbers and \(a>b\) then \(\frac{a}{b}>\frac{a+c}{b+c}\) (or as you mention \(\frac{a+c}{b+c}\) is closer to 1 then \(\frac{a}{b}\), but as \(\frac{a}{b}>1\) then \(\frac{a+c}{b+c}\) is getting less to be closer to 1). For example: \(\frac{3}{2}>\frac{3+30}{2+30}\);
But if \(a\), \(b\) and \(c\) are positive numbers and \(a<b\) then \(\frac{a}{b}<\frac{a+c}{b+c}\) (again \(\frac{a+c}{b+c}\) is closer to 1 then \(\frac{a}{b}\), but as \(\frac{a}{b}<1\) then \(\frac{a+c}{b+c}\) is getting bigger to be closer to 1). For example: \(\frac{4}{5}<\frac{4+30}{5+30}\).
Hope it's clear.