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# In a certain international contest the winners received only

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Intern
Joined: 13 Dec 2013
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02 Feb 2014, 05:49
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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, 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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Expert's post
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
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 839 times ]

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30 May 2017, 03:49
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In a certain international contest the winners received only   [#permalink] 30 May 2017, 03:49
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