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# M05-19

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Math Expert
Joined: 02 Sep 2009
Posts: 56307

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16 Sep 2014, 00:25
00:00

Difficulty:

45% (medium)

Question Stats:

56% (01:07) correct 44% (00:54) wrong based on 98 sessions

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

(1) $$T \lt S$$

(2) $$F \gt G$$

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 56307

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16 Sep 2014, 00:25
Official Solution:

Statement (1) by itself is insufficient.

Statement (2) by itself is insufficient.

Statements (1) and (2) combined are insufficient. Positive and negative numbers do not work. For example,

$$\frac{-5}{10}$$ and $$\frac{2}{-4}$$ or

$$\frac{5}{10}$$ and $$\frac{2}{-4}$$

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Intern
Joined: 02 Aug 2014
Posts: 4

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15 Jul 2015, 18:27
Bunuel wrote:
Official Solution:

Statement (1) by itself is insufficient.

Statement (2) by itself is insufficient.

Statements (1) and (2) combined are insufficient. Positive and negative numbers do not work. For example,

$$\frac{-5}{10}$$ and $$\frac{2}{-4}$$ or

$$\frac{5}{10}$$ and $$\frac{2}{-4}$$

(1) can be written as T/S < 1 and (2) can be written as F/G >1
obviously F/G > T/ S. Hence C should be the correct answer rite?? Please explain
Math Expert
Joined: 02 Sep 2009
Posts: 56307

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16 Jul 2015, 01:13
3
shanti47 wrote:
Bunuel wrote:
Official Solution:

Statement (1) by itself is insufficient.

Statement (2) by itself is insufficient.

Statements (1) and (2) combined are insufficient. Positive and negative numbers do not work. For example,

$$\frac{-5}{10}$$ and $$\frac{2}{-4}$$ or

$$\frac{5}{10}$$ and $$\frac{2}{-4}$$

(1) can be written as T/S < 1 and (2) can be written as F/G >1
obviously F/G > T/ S. Hence C should be the correct answer rite?? Please explain

That's not correct.

T < S means T/S < 1 only if S is positive, if S is negative, then T/S > 1. The same for F < G.
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Director
Joined: 06 Jan 2015
Posts: 682
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)

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01 Apr 2018, 03:50
Bunuel wrote:
Is $$\frac{T}{S} \gt \frac{F}{G}?$$

(1) $$T \lt S$$

(2) $$F \gt G$$

HI chetan2u, Bunuel,

Can't we modify question as TG > FS ?

Using 1 & 2 Gives us TG > FS?
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आत्मनॊ मोक्षार्थम् जगद्धिताय च

Resource: GMATPrep RCs With Solution
Math Expert
Joined: 02 Aug 2009
Posts: 7763

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01 Apr 2018, 04:35
NandishSS wrote:
Bunuel wrote:
Is $$\frac{T}{S} \gt \frac{F}{G}?$$

(1) $$T \lt S$$

(2) $$F \gt G$$

HI chetan2u, Bunuel,

Can't we modify question as TG > FS ?

Using 1 & 2 Gives us TG > FS?

No, that will not be ok..
You can cross Multiply only when you know all variables are POSITIVE..
Say 2/4 > 1/-2 does not mean 2*(-2)>1*4
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Intern
Joined: 30 Apr 2013
Posts: 8

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02 Sep 2018, 23:41
Bunuel wrote:
shanti47 wrote:
Bunuel wrote:
Official Solution:

Statement (1) by itself is insufficient.

Statement (2) by itself is insufficient.

Statements (1) and (2) combined are insufficient. Positive and negative numbers do not work. For example,

$$\frac{-5}{10}$$ and $$\frac{2}{-4}$$ or

$$\frac{5}{10}$$ and $$\frac{2}{-4}$$

(1) can be written as T/S < 1 and (2) can be written as F/G >1
obviously F/G > T/ S. Hence C should be the correct answer rite?? Please explain

That's not correct.

T < S means T/S < 1 only if S is positive, if S is negative, then T/S > 1. The same for F < G.

Can you please explain this. Still not clear
Math Expert
Joined: 02 Sep 2009
Posts: 56307

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02 Sep 2018, 23:47
T < S means T/S < 1 only if S is positive, if S is negative, then T/S > 1. The same for F < G.

Can you please explain this. Still not clear[/quote]

We cannot multiply x/y < 1 by y and write x < y because we don't know the sign of y. If y is positive, then yes, from x/y < 1, we can get x < y (keep the sign when multiplying by positive value) but if y is negative, then when we multiply by negative value, we should flip the sign and we'll get x > y (recall that we should flip the sign of an inequality if we multiply/divide it by negative value)..

Never multiply (or reduce) an inequality by a variable (or the expression with a variable) if you don't know its sign.

9. Inequalities

For more check Ultimate GMAT Quantitative Megathread

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Intern
Joined: 23 Jul 2017
Posts: 5

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08 Feb 2019, 00:52
What would be the algebraic way to address this question, since hitting the right numbers might consume time or worse some case might be left.

Thanks
Re: M05-19   [#permalink] 08 Feb 2019, 00:52
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# M05-19

Moderators: chetan2u, Bunuel