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# In a certain international contest the winners received only

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02 Feb 2014, 05:49
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66% (03:58) correct 34% (03:16) wrong based on 76 sessions

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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, 01:53, edited 1 time in total.
Renamed the topic and edited the question.
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03 Feb 2014, 02:10
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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.

Hope it helps.
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01 Jul 2014, 11:44
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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01 Jul 2014, 11:46
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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04 Nov 2014, 09:52
Thanks Bunuel! Making simultaneous equations definitely simplifies this significantly.
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04 Nov 2014, 22:56
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.
Attachments

medals.png [ 27.38 KiB | Viewed 481 times ]

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Re: In a certain international contest the winners received only   [#permalink] 04 Nov 2014, 22:56
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