Question

Mrs. Brown is dividing 50 students into 3 groups for a class project. How many children are in the largest group?
(1) The total number of children in the two smaller groups is equal to the number of children in the largest group.
(2) The smallest group contains 6 children.

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• D. EACH statement ALONE is sufficient.
• E. Statements (1) and (2) TOGETHER are NOT sufficient

Hint:

In Data Sufficiency, "sufficient" means you can find a single, definitive answer to the question. If a statement leads to multiple possible answers, it is insufficient.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is a Data Sufficiency problem. We need to determine if the given statements, either alone or together, provide enough information to find a unique value for the number of children in the largest group.
Step 2: Key Formula or Approach:
Let the number of children in the three groups be \(G_1\), \(G_2\), and \(G_3\).
Let \(L\) be the largest group, and \(S_1\) and \(S_2\) be the two smaller groups.
Total students = 50, so \(S_1 + S_2 + L = 50\).
The question asks for the value of \(L\).
Step 3: Detailed Explanation:
Analyzing Statement (1):
"The total number of children in the two smaller groups is equal to the number of children in the largest group."
This translates to the equation: \(S_1 + S_2 = L\).
We can substitute this into our total student equation:
\[ (S_1 + S_2) + L = 50 \] \[ L + L = 50 \] \[ 2L = 50 \] \[ L = 25 \] This statement allows us to find a unique value for \(L\). Therefore, statement (1) alone is sufficient.
Analyzing Statement (2):
"The smallest group contains 6 children."
Let's say \(S_1 = 6\). Our total equation becomes:
\[ 6 + S_2 + L = 50 \] \[ S_2 + L = 44 \] This equation has two unknown variables, \(S_2\) and \(L\). We can find multiple possible solutions.
For example, if the groups are (6, 20, 24), then \(L=24\).
If the groups are (6, 10, 34), then \(L=34\).
Since we cannot find a unique value for \(L\), statement (2) alone is not sufficient.
Step 4: Final Answer:
Statement (1) alone is sufficient to answer the question, but statement (2) alone is not.