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Is a/b < c/d?

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catty2004 Newbie | Next Rank: 10 Posts Default Avatar
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Is a/b < c/d?

Post Sun Jul 08, 2012 5:19 pm
If a, b, c, and d, are positive numbers, is a/b < c/d?

1) 0 < (c-a) / (d-b)

2) (ad/bc)^2 < (ad)/(bc)

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Post Sun Dec 27, 2015 5:16 pm
There is, but it's a little time consuming. I think S1 is mostly there to test your understanding of fractions; i.e. whether you recognize that (c/d) - (a/b) is NOT the same thing as (c - a)/(d - b).

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Post Mon Oct 09, 2017 7:45 am
Nina1987 wrote:
Is it possible to prove St1 insufficient w/o resorting to number picking? thanks
This problem can be solved without choosing numbers, if you rephrase the question:
a/b < c/d --> Because all of these variables are positive, we're allowed to cross-multiply here:
ad < bc

Target question: is ad < bc?
Often it's easier to deal with products than with ratios on DS questions.

Statement 1: 0 < (c-a)/(d-b)
Here, we can't cross-multiply, because we don't know if (d - b) is positive or negative. Our question was asking us about ratios/products... in other words, PROPORTIONAL relationships. This statement is giving us information about DIFFERENCES, which cannot answer a proportion question. (You can certainly test numbers to prove the point, though, as Mitch pointed out).
Insufficient

[color=]Statement 2: (ad/bc)² < (ad)/(bc) [/color]
Here, we're given a proportion, which is already more helpful. Let's rephrase:
(ad/bc)² < (ad)/(bc) Because everything is positive, we know that all products and ratios will be positive. If the square of the ratio (ad/bc) is less than the ratio itself, what does that mean? It means the ratio must be a POSITIVE FRACTION.
ad/bc < 1
Multiply both sides by bc:
[color=]ad < bc [/color]
This is our target question. Sufficient.

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Post Sun Dec 27, 2015 5:16 pm
There is, but it's a little time consuming. I think S1 is mostly there to test your understanding of fractions; i.e. whether you recognize that (c/d) - (a/b) is NOT the same thing as (c - a)/(d - b).

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Post Mon Oct 09, 2017 7:45 am
Nina1987 wrote:
Is it possible to prove St1 insufficient w/o resorting to number picking? thanks
This problem can be solved without choosing numbers, if you rephrase the question:
a/b < c/d --> Because all of these variables are positive, we're allowed to cross-multiply here:
ad < bc

Target question: is ad < bc?
Often it's easier to deal with products than with ratios on DS questions.

Statement 1: 0 < (c-a)/(d-b)
Here, we can't cross-multiply, because we don't know if (d - b) is positive or negative. Our question was asking us about ratios/products... in other words, PROPORTIONAL relationships. This statement is giving us information about DIFFERENCES, which cannot answer a proportion question. (You can certainly test numbers to prove the point, though, as Mitch pointed out).
Insufficient

[color=]Statement 2: (ad/bc)² < (ad)/(bc) [/color]
Here, we're given a proportion, which is already more helpful. Let's rephrase:
(ad/bc)² < (ad)/(bc) Because everything is positive, we know that all products and ratios will be positive. If the square of the ratio (ad/bc) is less than the ratio itself, what does that mean? It means the ratio must be a POSITIVE FRACTION.
ad/bc < 1
Multiply both sides by bc:
[color=]ad < bc [/color]
This is our target question. Sufficient.

_________________


Ceilidh Erickson
Manhattan Prep GMAT & GRE instructor
EdM in Mind, Brain, and Education
Harvard Graduate School of Education


Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience.
Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry!

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Nina1987 Senior | Next Rank: 100 Posts Default Avatar
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Post Sun Dec 27, 2015 7:05 am
Is it possible to prove St1 insufficient w/o resorting to number picking? thanks

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