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Math Expert V
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Is T/S > F/G? (1) T < S (2) F > G  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 63% (00:59) correct 37% (00:59) wrong based on 54 sessions

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Competition Mode Question

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

(1) $$T < S$$

(2) $$F > G$$

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Re: Is T/S > F/G? (1) T < S (2) F > G  [#permalink]

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2
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

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Re: Is T/S > F/G? (1) T < S (2) F > G  [#permalink]

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1
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!

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Re: Is T/S > F/G? (1) T < S (2) F > G  [#permalink]

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We are to determine if T/S > F/G
It is worth noting that there is no definition of the values of T, S, F, and G. This means that the denominators S and G can assume the values of 0 which will make the T/S or F/G undefined.

1. T<S
not sufficient, because no information is provided about F and G.
2. F>G
not sufficient, since no information is provided about T and S.

1+2
still not sufficient because we don't know whether the signs of F, G, S, and T, which is very important when dealing with inequalities. In addition, there is no information given in connection with the relationship between F and G with T and S. This means we can choose infinite number combinations of F, G, S, and T which will lead to T/S > F/G and also F/G>T/S.

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Is T/S > F/G? (1) T < S (2) F > G  [#permalink]

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Is T/S>F/G?

(1) T<S
Since there is no information about signs of T & S
T/S & F/G are unknown
NOT SUFFICIENT

(2) F>G
Since there is no information about signs of F & G.
T/S & F/G are unknown
NOT SUFFICIENT

Combining (1) & (2)
(1) T<S
Since there is no information about signs of T & S
T/S & F/G are unknown
(2) F>G
Since there is no information about signs of F & G.
T/S & F/G are unknown

IMO E
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Originally posted by Kinshook on 10 Sep 2019, 23:43.
Last edited by Kinshook on 11 Sep 2019, 22:24, edited 1 time in total.
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Re: Is T/S > F/G? (1) T < S (2) F > G  [#permalink]

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Is T/S > F/G?

(1) T < S
Nothing is given about F and G i.e. no relation between F and G or about their signs(+/-). Also, there is no relation between F/G and T/S.
INSUFFICIENT.

(2) F > G
Nothing is given about T and S i.e. no relation between T and S or about their signs(+/-). Also, there is no relation between T/S and F/G.

INSUFFICIENT.

Together 1) and 2)
Attachment: TSFG.JPG [ 26.53 KiB | Viewed 445 times ]

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Re: Is T/S > F/G? (1) T < S (2) F > G  [#permalink]

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Quote:
Is T/S>F/G?

(1) T<S
(2) F>G

(1) no info about f,g; insufic.
(2) no info about t,s; insufic.

(1&2) T<S and F>G: insufic.
T: S: F: G: T/S>F/G:
-3…4…4…3… -0.75>1.333…no
3…4…4…-5… 0.75>-0.8…yes

Manager  S
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Re: Is T/S > F/G? (1) T < S (2) F > G  [#permalink]

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Is T/S >F/G ?

We don't have any info about T, S, F, or G, so work with (1) & (2)
(1) T<S --> T/S <1, but no info on F/G --> (1) is not sufficient

(2) F>G --> F/G >1, but no info on T/S --> (2) is not sufficient

(1) & (2)
T/S > F/G
(<1 from (1)) > (>1 from (2)), so this inequality is wrong, we have definite answer --> (1) & (2) are sufficient --> answer C
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Re: Is T/S > F/G? (1) T < S (2) F > G  [#permalink]

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#1 no relation or value of F&G ; insufficient
#2
no value or relation with T/S
insufficient
from 1 &2
we cannot conclusively say that T/S>F/G as no relation provided among all 4 characters
IMO E

Is T/S>F/G?

(1) T<S

(2) F>G Re: Is T/S > F/G? (1) T < S (2) F > G   [#permalink] 11 Sep 2019, 08:29
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