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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

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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 was 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 was 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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AAPL wrote:
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 was 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 was to give Spain half of its silver medals, then Spain would have a total of 22 more medals than France.

OA C
Say

The number of gold received by France = x;
The number of silver received by France = y;

The number of gold received by Spain = a;
The number of silver received by Spain = b

Thus,
total medals received by France = x + y; and
total medals received by Spain = a + b

We have to get the value of (x + y) - (a + b).

Let's take each statement one by one.

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.

=> (x/2 + y + b/2) - (a + x/2 + b/2) = 26
=> y - a = 26 ---(1)

Insufficient.

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

=> (a/2 + y/2 + b) - (x + a/2 + y/2) = 22
=> x - b = -22 ---(2)

Adding (1) and (2), we get

(x + y) - (a + b) = 26 - 22 = 4. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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