Question

The number of customers who bought 250ml bottle but were not awarded a prize is

• A. 632
• B. 536
• C. 686
• D. 594
• A. 100
• B. 157
• C. 171
• D. 71

Answer 1

The Correct Option is B

Step 1: Understanding the question.
The customers who bought a 250ml bottle are assigned numbers from 501 to 1000, and prizes are awarded to customers whose ticket number is divisible by 5 or 7. We need to find the number of customers who bought a 250ml bottle but did not get a prize.
Step 2: Number of customers who bought a 250ml bottle.
There are 500 customers who bought a 250ml bottle, as the tickets numbered 501 to 1000 were distributed among them.
Step 3: Number of customers awarded a prize.
The customers who have ticket numbers divisible by 5 or 7 are awarded a prize. To find the number of such customers, we use the principle of inclusion and exclusion: - Number of customers whose tickets are divisible by 5 = \( \left\lfloor \frac{1000}{5} \right\rfloor - \left\lfloor \frac{500}{5} \right\rfloor = 200 - 100 = 100 \) - Number of customers whose tickets are divisible by 7 = \( \left\lfloor \frac{1000}{7} \right\rfloor - \left\lfloor \frac{500}{7} \right\rfloor = 142 - 71 = 71 \) - Number of customers whose tickets are divisible by both 5 and 7 (i.e., divisible by 35) = \( \left\lfloor \frac{1000}{35} \right\rfloor - \left\lfloor \frac{500}{35} \right\rfloor = 28 - 14 = 14 \) Using the inclusion-exclusion principle: \[ \text{Total awarded} = 100 + 71 - 14 = 157 \] Step 4: Number of customers who bought 250ml bottle but were not awarded a prize.
The total number of customers who bought a 250ml bottle is 500. The number of customers who were awarded a prize is 157. Therefore, the number of customers who bought a 250ml bottle but were not awarded a prize is: \[ 500 - 157 = 343 \] Step 5: Conclusion.
The correct answer is (B) 536 customers who bought a 250ml bottle but were not awarded a prize.

Answer 2

Step 1: Understanding the question.
We are given that customers who bought a 1000ml bottle were assigned tickets numbered 1 to 500, and prizes were given to those customers whose ticket numbers were divisible by 5 or 7. We need to find the number of customers who bought a 1000ml bottle and were awarded a prize.
Step 2: Analyzing the awarded tickets.
The number of tickets divisible by 5 or 7 can be calculated similarly using the inclusion-exclusion principle. We already know from the earlier calculations that the total number of customers who were awarded a prize is 157.
Step 3: Conclusion.
The correct answer is (B) 157, which is the number of customers who bought a 1000ml bottle and were awarded a prize.