The number of positive integers not greater than 100, which are not divisible by 2, 3 or 5 is: (CAT 1993)
The number of positive integers not greater than 100, which are not divisible by 2, 3 or 5 is: (CAT 1993)
The correct option is A 26
There are 50 odd numbers less than 100 which are not divisible by 2. Out of these 50 there are 17 numbers which are divisible by 3. Out of remaining there are 7 numbers which are divisible by 5. Hence numbers which are not divisible by 2, 3, or 5 = (50-17-7) = 26
Alternate Approach:
Taking the Euler's number approach -
If we take the prime factors of a number then we get all the numbers that are co-prime to that number, which means all the multiples of the prime factors are removed. Using the same formula we can find out the numbers that are not divisible by a particular set of numbers.
L.C.M. of 2, 3, 5 is 30. Number which is highest multiple of 30 and closest to 100 is 90. Euler's number for 90 is 24.
From 91 to 100, only 91 and 97 are not co-prime to 2, 3 or 5. Hence correct option will be 26.
There are 50 odd numbers less than 100 which are not divisible by 2. Out of these 50 there are 17 numbers which are divisible by 3. Out of remaining there are 7 numbers which are divisible by 5. Hence numbers which are not divisible by 2, 3, or 5 = (50-17-7) = 26
Alternate Approach:
Taking the Euler's number approach -
If we take the prime factors of a number then we get all the numbers that are co-prime to that number, which means all the multiples of the prime factors are removed. Using the same formula we can find out the numbers that are not divisible by a particular set of numbers.
L.C.M. of 2, 3, 5 is 30. Number which is highest multiple of 30 and closest to 100 is 90. Euler's number for 90 is 24.
From 91 to 100, only 91 and 97 are not co-prime to 2, 3 or 5. Hence correct option will be 26.
