Question

Alan purchased pen and pencil at a certain shop, where each pen costs 3 dollars and each pencil cost 2 dollars. What is the total number of pen and pencils Alan purchased?
(1) Alan bought pen and pencils for the total cost of 10 dollars.
(2) Total cost of the pens which Allan bought is less than 10 dollars.

• A. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
• B. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
• C. Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.
• D. Each statement alone is sufficient to answer the question.
• E. Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.

Hint:

When solving equations with two variables, ensure the given information forms a complete equation to solve for both variables.

Answer 1

The Correct Option is A

Step 1: Analyze Statement 1.
Let the number of pens be \( x \) and the number of pencils be \( y \). From statement 1, we know: \[ 3x + 2y = 10 \] This equation alone is sufficient to solve for the values of \( x \) and \( y \) (the number of pens and pencils). Hence, statement 1 alone is sufficient.
Step 2: Analyze Statement 2.
Statement 2 only gives us information about the cost of pens being less than 10 dollars, but it doesn't provide a relationship between the number of pens and pencils. Hence, statement 2 alone is insufficient.
Step 3: Conclusion.
The correct answer is (A).