How many numbers from 1 to 1000 are there which are NOT divisible by any of the digits 2, 3 and 5 ?

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Submitted by examrobotsa on

Q: 102 (CAPF/2015)
How many numbers from 1 to 1000 are there which are NOT divisible by any of the digits 2, 3 and 5 ?

question_subject: 

Maths

question_exam: 

CAPF

stats: 

0,12,9,4,12,3,2

keywords: 

{'digits': [0, 0, 3, 2], 'many numbers': [0, 0, 2, 0]}

The correct answer is option 2: 266.

To find the number of numbers from 1 to 1000 that are not divisible by any of the digits 2, 3, and 5, we can use the principle of inclusion-exclusion.

First, we find the numbers that are divisible by 2. There are 1000/2 = 500 numbers divisible by 2 in the given range.

Next, we find the numbers that are divisible by 3. There are 1000/3 = 333 numbers divisible by 3 in the given range.

Similarly, we find the numbers that are divisible by 5. There are 1000/5 = 200 numbers divisible by 5 in the given range.

However, we have counted some numbers twice because they are divisible by more than one of the digits 2, 3, and 5. To correct this, we need to subtract the numbers that are divisible by both 2 and 3 (numbers divisible by 6), the numbers that are divisible by both 2 and 5 (numbers divisible by 10), and the numbers that are divisible by both 3 and 5 (numbers divisible by 15).

There are 1000/6