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m12#05 - DS

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m12#05 - DS [#permalink] New post 12 Jun 2010, 04:40
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] New post 12 Jun 2010, 07:47
Expert's post
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] New post 12 Jun 2010, 07:56
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] New post 12 Jun 2010, 08:21
Expert's post
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 MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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.


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Re: m12#05 - DS   [#permalink] 12 Jun 2010, 08:21
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