Brian is dividing 50 marbles into 3 groups. How many marbles are in the…

Concept: In a Data Sufficiency question, a statement is "sufficient" only when it lets you pin down exactly one numeric value for the quantity asked, here the size of the largest group. When a statement expresses a relationship between the parts of a total that is already known, that relationship can be combined algebraically with the known total to solve for the unknown directly.

Applying this to the question:

1. Let the three group sizes be a (largest), b, and c, with a + b + c = 50 (the known total).

2. Statement (1) says the two smaller groups together equal the largest group: b + c = a.

3. Substituting b + c = a into the total gives a + a = 50, so 2a = 50, which means a = 25.

4. Statement (1) alone therefore fixes the largest group at exactly 25 marbles, it is sufficient by itself.

5. Statement (2) says only that the smallest group c = 6, leaving a + b = 44 with no other constraint tying a and b together.

6. With c = 6, a 38-6-6 split gives a = 38, while a 22-22-6 split gives a = 22, both satisfy "smallest group = 6" yet produce different largest-group values.

7. Since more than one value of a remains possible, statement (2) alone is not sufficient.

Cross-check: Substituting a = 25 back into statement (1): if the largest group is 25, then b + c = 25, and the total is 25 + 25 = 50, which checks out, confirming that statement (1) alone already fixes the largest group without needing statement (2).

Result: So statement (1) alone is sufficient, while statement (2) alone is not.