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13 May 2021, 00:15
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C
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Difficulty:
45%
(medium)
Question Stats:
72% (02:31) correct
28%
(02:20)
wrong
based on 150
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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.
(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.
14 May 2021, 01:15
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Bunuel
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.
General Discussion
13 May 2021, 00:54
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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?
Let, F = \(F_g + F_s & S = S_g + S_s\)
Stat1: 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.
F = \(F_g /2 + F_s + S_s/2\)
&, S = \(S_g + F_g/2 + S_s/2\)
So, F-S = 26 or, \(F_s - S_g \)= 26. Not sufficient.
Stat2: 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.
F = \(F_g + F_s /2+ S_g/2\)
&, S = \(S_g/2 + F_s/2 + S_s\)
So, S-F = 22 or, \(S_s - F_g \)= 22. Not sufficient.
Combining both, we can calculate, F-S = \((F_g+ F_s) - (S_g+ S_s)\). Sufficient.
I think C.
Let, F = \(F_g + F_s & S = S_g + S_s\)
Stat1: 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.
F = \(F_g /2 + F_s + S_s/2\)
&, S = \(S_g + F_g/2 + S_s/2\)
So, F-S = 26 or, \(F_s - S_g \)= 26. Not sufficient.
Stat2: 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.
F = \(F_g + F_s /2+ S_g/2\)
&, S = \(S_g/2 + F_s/2 + S_s\)
So, S-F = 22 or, \(S_s - F_g \)= 22. Not sufficient.
Combining both, we can calculate, F-S = \((F_g+ F_s) - (S_g+ S_s)\). Sufficient.
I think C.
