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m12#05 - DS

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m12#05 - DS [#permalink]

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New post 12 Jun 2010, 05:40
If \(a,b,c,d\) are positive numbers, is \(\frac{a}{b}<\frac{(a+c)}{(b+d)}\)?

1. \(\frac{a}{b}<\frac{c}{d}\)
2. \(a+c<b+d\)

The OA is A, but, I have one doubt:
From S1, we can say \(\frac{a}{c}<\frac{b}{d}\)

On adding 1 on both sides, the equation becomes:
\(\frac{(a+c)}{c}<\frac{(b+d)}{d}\)
\(\frac{(a+c)}{(b+d)}<\frac{c}{d}\)

But, we are given \(\frac{a}{b}<\frac{c}{d}\)

So, S1 is insufficient. Please explain where I am missing the point.
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Re: m12#05 - DS [#permalink]

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New post 12 Jun 2010, 08:47
ykaiim wrote:
If \(a,b,c,d\) are positive numbers, is \(\frac{a}{b}<\frac{(a+c)}{(b+d)}\)?

1. \(\frac{a}{b}<\frac{c}{d}\)
2. \(a+c<b+d\)

The OA is A, but, I have one doubt:
From S1, we can say \(\frac{a}{c}<\frac{b}{d}\)

On adding 1 on both sides, the equation becomes:
\(\frac{(a+c)}{c}<\frac{(b+d)}{d}\)
\(\frac{(a+c)}{(b+d)}<\frac{c}{d}\)

But, we are given \(\frac{a}{b}<\frac{c}{d}\)

So, S1 is insufficient. Please explain where I am missing the point.


Given: \(a\), \(b\), \(c\), and \(d\) are positive numbers. Question: is \(\frac{a}{b}<\frac{(a+c)}{(b+d)}\)? --> as all numbers are positive we can safely crossmultiply --> is \(ab+ad<ab+bc\)? --> is \(ad<bc\)? is \(\frac{a}{b}<\frac{c}{d}\)?

(1) Directly gives the answer. Sufficient.
(2) Not sufficient.

Answer: A.

We can get the answer the way you were doing too: \(\frac{a}{b}<\frac{c}{d}\) --> \(\frac{d}{b}<\frac{c}{a}\) --> add 1 to both sides --> \(\frac{d}{b}+1<\frac{c}{a}+1\) --> \(\frac{d+b}{b}<\frac{c+a}{a}\) --> \(\frac{a}{b}<\frac{a+c}{b+d}\).

Hope it helps.
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Re: m12#05 - DS [#permalink]

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New post 12 Jun 2010, 08:56
Bunuel,

Thanks for the explainations. But, I am still not clear where in my explaination I am missing. Can you please check?
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Re: m12#05 - DS [#permalink]

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New post 12 Jun 2010, 09:21
ykaiim wrote:
Bunuel,

Thanks for the explainations. But, I am still not clear where in my explaination I am missing. Can you please check?


You are not missing anything.

If we are given that \(a\), \(b\), \(c\), and \(d\) are positive numbers and \(\frac{a}{b}<\frac{c}{d}\), then \(\frac{(a+c)}{(b+d)}<\frac{c}{d}\) (the inequality you derived) is true. We are just asked to derive another inequality (the one I derived) not this one.
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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Kudos [?]: 132521 [0], given: 12324

Re: m12#05 - DS   [#permalink] 12 Jun 2010, 09:21
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