From a group consisting of ballet dancers from Italy, Germany, and

Question

From a group consisting of ballet dancers from Italy, Germany, and France, including at least three ballet dancers from each country, how many same country pairs of ballet dancers can be selected?

(1) The group consists of 11 ballet dancers.

(2) The group consists of an equal number of Italian and French ballet dancers.

Source: Edvento Blog

eshan429 · Accepted Answer

OE Below:

This problem cannot be solved through formula. Given that the group consists of at least three ballet dancers of each country, we know that at least one same country pair of each country can be selected. From the first nine ballet dancers, we can therefore make three pairs, leaving three unpaired ballet dancers. To think through the problem, it is useful to conceptualize removing those nine ballet dancers from the group. We will need additional information about any ballet dancers left in the group to solve the problem.

Evaluating Statement (1) Alone:
Once those first nine ballet dancers have been removed, only two ballet dancers remain, but we do not have sufficient information about the country of the two ballet dancers to solve the problem. If the two remaining ballet dancers are from same country, we can add this final pair to the first three. This scenario results in four pairs and three ‘orphans’. However, if the final two ballet dancers are from different countries, each will make a new pair with one of the original three orphans, resulting in five pairs and one orphan. This is NOT sufficient. Eliminate choices A and D.

Evaluating Statement (2) Alone:

This statement gives no information about how many ballet dancers are in the group. This is NOT sufficient. Eliminate choice B.

Evaluating Statement (1) and Statement (2) Together:

Given that the group consists of 11 ballet dancers and that there are an equal number of Italian and French ballet dancers, there are two possible scenarios. Three Italian, three French, and five German ballet dancers would yield four pairs total. Four Italian, four French, and three German ballet dancers would yield five pairs total. This is NOT sufficient. Eliminate choice C.

The correct answer is E.

totosama · Answer

Hi,

how many same country pairs of ballet dancers can be selected? implies we need to know how many people of each country are in the group.
1) Gives us the total number of people => not sufficient.
2) Tells us the there is an equal number of people from each country.
Say the number of people per country is 2, since there are 3 countries that makes 3 pairs
Say the number of people per county is 1, that means there is no possible pair to select.

Let us use both: 1) and 2) are contradictory since it is not possible to have 11 people coming from 3 different countries (11 is not divisible by 3)

Hope this helps

eshan429 · Answer

The question stem specifically says there are at least 3 dancers from each country

Angry_Mallard · Answer

My method:

Numbers are small enough to brute force. Let each country's initial represent the number of dancers:

Given the problem:

I_>3
F_>3
G_>3

Given 1:

I + F +G = 11

Given 1: There are still multiple combinations that all add up to a total of 11, thus we can not determine the number of same-country pairs that exist.

Given 2:

I = F

We still have no information on the total number of dancers, thus it is impossible to determine the number of combinations. It could bet anywhere between 3 and infinity.

Given both:

Small quantities of numbers, easily broken in a manner of seconds via brute force. 3 Italian, 3 French, 5 German adds up to 11. 4 Italian, 4 French, 3 German, adds up to 11. Either combination yields a different answer.

Still insufficient. Answer E.

KarishmaB · Answer

Question stem: At least 3 from each country so there are at least 9 ballet dancers. 
How many same country pairs can be selected depends on exactly how many ballet dancers are from each country.

(1) The group consists of 11 ballet dancers.
Now the question is how the 11 are split among 3 countries: (3, 3, 5) or (3, 4, 4). The number of pairs of same country will be different in these two cases - 4 for (3, 3, 5) and 5 for (3, 4, 4). Not sufficient.

(2) The group consists of an equal number of Italian and French ballet dancers.
We don't know how many ballet dancers are actually there - all we know is that each country has at least 3. Not sufficient.

Using both statements, both cases are still valid. 
Italy and France could have 3 - 3 ballet dancers or they could have 4 - 4 ballet dancers. So we still don't know how many pairs we can form. Not sufficient.

Answer (E)

gmatPro88 · Answer

This problem can be solved with a simple diagram

mvictor · Answer

1.
we can have 
I=3 - 1 pair 
G=3 - 1 pair
F=5 - 2 pairs

or:
I=4 - 2 pairs
G=4 - 2 pairs
F=3 - 1 pair.

not sufficient.

2.
I=3 - 1 pair
F=3 - 1 pair
G=4 - 2 pairs

or
I=3 - 1 pair
F=3 - 1 pair
G=90 - 45 pairs

not sufficient.

1+2
I=3 - 1 pair 
G=3 - 1 pair
F=5 - 2 pairs

or:
I=4 - 2 pairs
G=4 - 2 pairs
F=3 - 1 pair.

not sufficient
answer is E.

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From a group consisting of ballet dancers from Italy, Germany, and

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