Question

Find the maximum number of students among whom 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils.

• A. 91
• B. 910
• C. 1001
• D. 1911

Hint:

Finding the GCD of the quantities allows for equal distribution among the maximum number of recipients, ensuring each student gets the same quantity.

Answer 1

The Correct Option is A

Step 1: Determine the greatest common divisor (GCD) of the number of pens and pencils. To maximize the number of students that can receive an equal distribution of pens and pencils, we find the GCD of 1001 pens and 910 pencils: \[ \text{GCD of 1001 and 910} \] Calculation: Finding the GCD involves prime factorization: \[ 1001 = 7 \times 11 \times 13 \] \[ 910 = 2 \times 5 \times 7 \times 13 \] The common factors are \(7\) and \(13\), hence: \[ \text{GCD} = 7 \times 13 = 91 \]

Step 2: Conclusion. Thus, the maximum number of students among whom the pens and pencils can be equally distributed is 91, which is the GCD of the total number of pens and pencils.