Explanation:

Let's calculate how many numbers from 500 to 650 are neither divisible by 3 nor by 7.

- Total numbers from 500 to 650: 650 - 500 + 1 = 151

- Numbers divisible by 3:

- First number: 501 (since 500 is not divisible by 3)

- Last number: 648

- Total numbers = (648 - 501) / 3 + 1 = 50

- Numbers divisible by 7:

- First number: 504

- Last number: 644

- Total numbers = (644 - 504) / 7 + 1 = 21

- Numbers divisible by both 3 and 7 (i.e., divisible by 21):

- First number: 504

- Last number: 630

- Total numbers = (630 - 504) / 21 + 1 = 7

Applying the principle of inclusion-exclusion:

- Total divisible by 3 or 7 = 50 + 21 - 7 = 64

- Therefore, numbers neither divisible by 3 nor 7 = 151 - 64 = 87

Option 3: 87 is the correct answer.