In a certain international contest the winners received only

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AAPL: Moderator; Posts: 2636; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Fri Sep 27, 2019 12:46 am

Economist GMAT

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.

OA C

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Source: Beat The GMAT — Data Sufficiency | Fri Sep 27, 2019 12:46 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

by deloitte247 » Sun Sep 29, 2019 7:49 am

Let the gold medals received by France = gf
Let the silver medals received by France = sf
Let the gold medals received by Spain = gs
Let the silver medals received by Spain = ss
Question; France received how many more medals than Spain?
i.e. Find (Total France medals) - (Total Spain medals)
Total France medals = gf + sf
Total Spain medals = gs + ss
Statement 1: If France were to give Spain half of its gold medals, and Spain was to give France half of its silver medals, then France would have a total of 26 more medals than Spain.
i.e. (Total France medals) = (Total Spain medals) + 26
gf= 0.5gf (This is because 0.5gf was given to Spain)
sf= sf + 0.5ss
gs= gs + 0.5gf
ss= 0.5ss (This is because 0.5ss was given to France)
Therefore, (0.5gf + sf + 0.5ss) = (gs + 0.5gf + 0.5ss) + 26
sf - gs = 26
We cannot get the value of total Spain medal from this expression, hence, statement 1 is NOT SUFFICIENT.

Statement 2: If Spain were to give France half 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.
I.e (Total France medals) = (Total Spain medals) - 22
gf= gf + 0.5gs
sf= 0.5sf (0.5sf given to Spain)
gs= 0.5gs (0.5gs guven to France)
ss= ss + 0.5sf
Therefore, (gf + 0.5gs + 0.5sf) = (0.5gs + ss + 0.5sf) - 22
gf - ss = -22
Also, we cannot get the value of total France medals from this expression.
Hence, statement 2 is NOT SUFFICIENT.

Combining both statements together;
From the question stem, we are looking for;
Total France medals - Total Spain medals
So, (gf + sf) - (gs + ss)
gf + sf - gs - ss
(gf - ss) + (sf - gs)
From statement 1; sf - gs = 26
From statement 2; gf - ss = -22
If we substitute these values; (-22) + (26) = 4

Therefore, France received 4 more medals than Spain, hence, both statements combined together are SUFFICIENT.

Answer = OPTION C

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