Is T/S F/G? (1) T G

Question

Competition Mode Question

Is  \frac{T}{S} > \frac{F}{G} ?

(1)  T < S

(2)  F > G

shridhar786 · Answer

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

EncounterGMAT · Answer

Is  \frac{T}{S}   > \frac{F}{G} ?

(1) T<S
Nothing about F and G to find which fraction is greater. INSUFFICIENT!

(2) F>G
Nothing about T and S to find which fraction is greater. INSUFFICIENT!

(1) + (2)
If T=1, S=2, F=4, G=3, then  \frac{1}{2}   > \frac{4}{3} ? NO
If T=4, S=3, F=1, G=2, then  \frac{4}{3}   > \frac{1}{2} ? YES
Different possibilities. INSUFFICIENT!

IMO answer is option E

Bunuel · Answer

Is \frac{T}{S} > \frac{F}{G} ? (1) T < S This statement is clearly insufficient, as we know nothing about F and G. (2) F > G Similarly, this statement is clearly insufficient, as we know nothing about T and S. (1)+(2) It's crucial to note that we don't know the signs of T, S, F, and G. If we were given that S and G are positive, then from (1) we'd infer that \frac{T}{S} < 1 , and from (2) we'd infer that \frac{F}{G} > 1 , which would lead to \frac{T}{S} < 1 < \frac{F}{G} . For instance, consider T = 1 , S = 2 , G =1 and F = 2 . However, if S and G are negative, then from (1) we'd infer that \frac{T}{S} > 1 , and from (2) we'd infer that \frac{F}{G} < 1 , which would lead to \frac{T}{S} > 1 > \frac{F}{G} . For instance, consider T = -2 , S = -1 , G =-2 and F = -1 . Not sufficient. Answer: E

QuantMadeEasy · Answer

Understanding Statement 1 alone:
As relation between F and G is not known, the statement alone is insufficient.

Understanding Statement 2 alone:
As relation between T and S is not known, the statement alone is insufficient.

Understanding Statement 1 and 2 together:
Using values:
When T = 4, S = 5, G = 1 and F = 2, then T/S>F/G is true
When T = -4, S = 5, G = 1 and F = 2, then T/S>F/G is false
Insufficient

E is correct

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

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