Question : How many natural numbers less than 1000 are divisible by 5 or 7 but not by 35?
Option 1: 243
Option 2: 341
Option 3: 285
Option 4: 313
Correct Answer: 285
Solution : The number of natural numbers less than 1000 that are divisible by 5. $⇒\left\lfloor\frac{999}{5}\right\rfloor = 199$ The number of natural numbers less than 1000 that are divisible by 7. $⇒\left\lfloor\frac{1000}{7}\right\rfloor = 142$ However, we've double-counted numbers that are divisible by both 5 and 7, i.e., numbers that are divisible by 35. There are $\left\lfloor\frac{1000}{35}\right\rfloor = 28$ such numbers. The total number of natural numbers less than 1000 that are divisible by 5 or 7 but not by 35 is $199+ 142 - 2\times28 = 285$ Hence, the correct answer is 285.
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Question : How many natural numbers up to 2001 are divisible by 3 or 4 but NOT by 5?
Option 1: 768
Option 2: 801
Option 3: 934
Option 4: 1067
Question : How many numbers between 400 and 700 are divisible by 5, 6 and 7?
Option 1: 20
Option 2: 10
Option 3: 2
Option 4: 5
Question : The number 1563241234351 is:
Option 1: divisible by 11 but not by 3
Option 2: neither divisible by 3 nor by 11
Option 3: divisible by both 3 and 11
Option 4: divisible by 3 but not by 11
Question : Ramu had to select a list of numbers between 1 and 1000 (including both), which are divisible by both 2 and 7. How many such numbers are there?
Option 1: 142
Option 2: 71
Option 3: 97
Option 4: 642
Question : How many numbers between 300 and 700 are divisible by 5, 6, and 8?
Option 1: 3
Option 2: 2
Option 3: 5
Option 4: 20
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