Is T/S > F/G? (1) T < S (2) F > G

is \(\frac{T}{S}\) > \(\frac{F}{G}\) ?


STATEMENT (1)- T < S
but we don't know anything about F and G
suppose F = 14 G = 7
T = 2 S = 4
then \(\frac{T}{S}\)<\(\frac{F}{G}\)---is \(\frac{T}{S}\) > \(\frac{F}{G}\) ?---NO

if F =14 G = 7
T =-12 S = -3
then \(\frac{T}{S}\)>\(\frac{F}{G}\)---is \(\frac{T}{S}\) > \(\frac{F}{G}\) ?---YES

so, this statement is INSUFFICIENT

STATEMENT (2)- F > G
but we don't know anything about T and S
suppose T =14 S = 7
F = 3 G = 2
then \(\frac{T}{S}\)>\(\frac{F}{G}\)---is \(\frac{T}{S}\) > \(\frac{F}{G}\) ?---YES

if F =14 G = 7
T = 3 S =2
then \(\frac{T}{S}\)<\(\frac{F}{G}\)---is \(\frac{T}{S}\) > \(\frac{F}{G}\) ?---NO

so, this statement is INSUFFICIENT

combining STATEMENT (1)&STATEMENT (2)
we know T < S and F > G
now
if T = 2 S = 3
F = 12 G =3
then \(\frac{T}{S}\)<\(\frac{F}{G}\)---is \(\frac{T}{S}\) > \(\frac{F}{G}\) ?---NO

if T = -12 S= -3 (since T < S)
F =4 G =2
then \(\frac{T}{S}\)>\(\frac{F}{G}\)---is \(\frac{T}{S}\) > \(\frac{F}{G}\) ?---YES

so, combining both statements is INSUFFICIENT

E is the correct answer