Children’s Ages

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The ages of all children in Group A are the same, and the ages of all children in Group B are the same. Is the age of a child in Group A less than the age of a child in Group B?

(1) The sum of the ages of 3 children in Group A and 2 children in Group B is less than the sum of ages of 2 children in Group A and 4 children in Group B.

(2) The sum of the ages of 4 children in Group A and 3 children in Group B is less than the sum of ages of 3 children in Group A and 4 children in Group B.

Review: Children's Ages




Explanation

We can understand the question to state that children in Group A are all a years old, and children in Group B are all b years old, and we want to know whether . On to the statements, separately first.

Statement (1) tells us that . Subtracting 2a and 2b from both sides of this inequality yields , which is close to what we are looking for, but different. Statement (1) would allow a case in which b was huge and therefore , and it would allow a case in which a was actually greater than b but less than 2b. So we don't have a consistent answer for all cases. Statement (1) is insufficient.

Statement (2) is similar but has the potential to work out differently. It says that . Subtracting 3a and 3b from both sides gives , exactly what we are looking for. So Statement (2) gives a fact that makes the answer to the question "yes" in every case; it's therefore sufficient.

The correct answer is (B).


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