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In a certain international contest the winners received only

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In a certain international contest the winners received only [#permalink] New post 02 Feb 2014, 04:49
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In a certain international contest the winners received only gold and silver medals. In that contest, France received how many more medals than Spain did?

(1) If France were to give Spain half of its gold medals, and Spain were to give France half of its silver medals, then France would have a total of 26 more medals than Spain.

(2) If Spain were to give France half of its gold medals, and France were to give Spain half of its silver medals, then Spain would have a total of 22 more medals than France.

Which is the best approach to solve this "swap" questions? It seems like the question of Danny and its blue and red boxes...
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Feb 2014, 00:53, edited 1 time in total.
Renamed the topic and edited the question.
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Re: In a certain international contest the winners received only [#permalink] New post 03 Feb 2014, 01:10
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In a certain international contest the winners received only gold and silver medals. In that contest, France received how many more medals than Spain did?

France: \(Gold = g_1\), \(Silver = s_1\).
Spain: \(Gold = g_2\), \(Silver = s_2\).

Question asks to find \((g_1+s_1)-(g_2+s_2)\)

(1) If France were to give Spain half of its gold medals, and Spain were to give France half of its silver medals, then France would have a total of 26 more medals than Spain.

France: \(Gold = 0.5g_1\), \(Silver = s_1 +0.5s_2\).
Spain: \(Gold = g_2+0.5g_1\), \(Silver = 0.5s_2\).

\(0.5g_1+(s_1 +0.5s_2)=(g_2+0.5g_1)+0.5s_2+26\) --> \(s_1-g_2=26\).

Not sufficient.

(2) If Spain were to give France half of its gold medals, and France were to give Spain half of its silver medals, then Spain would have a total of 22 more medals than France.

France: \(Gold = g_1+0.5g_2\), \(Silver = 0.5s_1\).
Spain: \(Gold = 0.5g_2\), \(Silver =s_2+ 0.5s_1\).

\((g_1+0.5g_2) +0.5s_1=0.5g_2+(s_2+0.5s_1)-22\) --> \(g_1-s_2=-22\).

Not sufficient.


(1)+(2) \((g_1+s_1)-(g_2+s_2)=(g_1-s_2)+(s_1-g_2)=26-22=4\). Sufficient.

Answer: C.

Hope it helps.
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In a certain international contest the winners received only [#permalink] New post 01 Jul 2014, 10:44
In a certain international contest the winners received only gold and silver medals. In that contest, France received how many more medals than Spain did?

(1) If France were to give Spain half of its gold medals, and Spain were to give France half of its silver medals, then France would have a total of 26 more medals than Spain.
(2) If Spain were to give France half of its gold medals, and France were to give Spain half of its silver medals, then Spain would have a total of 22 more medals than France.
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Re: In a certain international contest the winners received only [#permalink] New post 01 Jul 2014, 10:46
Expert's post
goodyear2013 wrote:
In a certain international contest the winners received only gold and silver medals. In that contest, France received how many more medals than Spain did?

(1) If France were to give Spain half of its gold medals, and Spain were to give France half of its silver medals, then France would have a total of 26 more medals than Spain.
(2) If Spain were to give France half of its gold medals, and France were to give Spain half of its silver medals, then Spain would have a total of 22 more medals than France.


Merging similar topics. Please refer to the solution above.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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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: In a certain international contest the winners received only [#permalink] New post 04 Nov 2014, 08:52
Thanks Bunuel! Making simultaneous equations definitely simplifies this significantly.
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Re: In a certain international contest the winners received only [#permalink] New post 04 Nov 2014, 21:56
civi83 wrote:
In a certain international contest the winners received only gold and silver medals. In that contest, France received how many more medals than Spain did?

(1) If France were to give Spain half of its gold medals, and Spain were to give France half of its silver medals, then France would have a total of 26 more medals than Spain.

(2) If Spain were to give France half of its gold medals, and France were to give Spain half of its silver medals, then Spain would have a total of 22 more medals than France.

Which is the best approach to solve this "swap" questions? It seems like the question of Danny and its blue and red boxes...


C. please refer to the image.
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Re: In a certain international contest the winners received only   [#permalink] 04 Nov 2014, 21:56
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