Latest TCS Aptitude Question SOLUTION: How many of the 1st 1200 natural nums r either prime to 6 or to 15

1 to 1200
no. of primes of 6=1200/6=200
no. of primes of 15=1200/15=80
LCM of 6,15=30
no. of primes of 30=1200/30=40
reqd no.=200+80-40=240

The number of primes to 6 cannot be found directly. If a number is co-prime to 6, it should not be a multiple of either 2 as well as 3.
For example, 4 cannot be co-prime to 6, as it is a multiple of 2, same is the case with 9.
Similarly, if a number is prime to 15, it should not be multiple of 3 or 15.

So, in the final answer we should consider the numbers which are not multiples of each of 2, 3 and 5.

So, we have to solve this in terms of venn-diagrams, a three variable venn diagram
In the diagram one circle denotes the multiples of 2, the other one multiples of 6 and the third one multiples of 5.

Multiples of 2 = n(A) = 1200/2 = 600
Multiples of 3 = n(B) = 1200/3 = 400
Multiples of 5 = n(C)= 1200/5 = 240
Multiples of 2 and 3 = n(A n B) = 1200/6 = 200
Multiples of 2 and 5 = n(A n C) = 1200/10=120
Multiples of 3 and 5 = n(B n C) = 1200/15 = 80
Multiples of 2, 3 and 5 = 1200/30 = 40

So, n( A U B U C) n(A) + n(B) + n(C) - n(AnB)-n(AnC)-n(BnC) + n(AnBnC)= 600+400+240-200-120-80+40 = 880

So, all these numbers ar either multiple of 2, 3 or 5.

So, the remaining numbers that is 1200-880 = 320 are primes with respect to 6 and 15

Some of these numbers in the list are all the primes and composite numbers like 77, 91 and so on

Answer is 320

Pls tell me which one is right.. !!!

numbers prime to 6 are=1200(1-(1/2))(1-(1/3))=400
numbers prime to 15 =1200(1-(1/3))(1-(1/5))=640
numbers prime to both=1200(1-(1/2))(1-(1/3))(1-(1/5))=320
therefore total= 400+640-2*320=400.
This is the correct answer

It depends on the actual question.
If it is about co-primes, 320 is the correct answer. As I have seen a similar problem before, i assumed it as co-primes.
If the question is about multiples of either 6 or 15, then 240 is the right answer.

I agree with the Kavi Priya on the values except the final answer, it should be
640+400-320 = 720

So, if we are considering primes of either 6 or 15, which means we are considering a number like 25 in the list because though 25 is not a prime of 15, it is prime to 6, in this case 720 is the answer.

720 is the answer

i am so confused wd so many asnwers

i think 400 is the right answer

400 is the exact answer

1 to 1200
no. of primes of 6=1200/6=200
no. of primes of 15=1200/15=80
LCM of 6,15=30
no. of primes of 30=1200/30=40
reqd no.=200+80-40=24

now total no which are prime to 6 or 15 are=1200-240 =960
am correct ?

please explain which one is the correct answer..??