Raj wants to buy 7 floors in an 68 storied building whose numbering stars from 1 upto 68.but it has to follow certain rules which are as follows

1)none of the floor should be a prime number

2)none of the digit of the floor should be a prime number

3)Raj cannot buy the 1st floor as it is being assigned to the architect.

SO how many options are left with Raj to buy the floor

option)
1). 11
2). 13
3). 15
4). 17

• eliminate the numbers from 1 to 68 based on given conditions
  1)should not be a prime number
  -->There are 19 prime numbers from 1 to 68. So, we are left with 68-19=49 floors
  2)digit of the floor should not be a prime number
  -->There are 31 numbers like that (excluding prime numbers). So, we have 49-31=18 floors to choose
  Again, in this 18 floors we have to take out 1st floor because we are not allowed to select
  Finally, we have 18-1=17 options left
• 8 years agoHelpfull: Yes(33) No(1)
• Since floor starts form the 1 therefore 2 will be the 1st floor.
  Form 1 to 10 only 4,6,8,9,10 are not prime.
  Form 11 to 20 only 14 ,16,18 are not prime also non of their digits are prime.
  From 21 to 30 each number has a prime number so it must no be consider.
  In between 40 to 49 we have to consider only 40,44,46,48,49.
  50 to 59 follow either of the condition so we have too neglect it.
  In between 60 to 68 60,64,66,68.
  total option =17.
• 8 years agoHelpfull: Yes(26) No(3)
• Ans is 17
  4,6,8,9,10,14,16,18,40,44,46,48,49,60,64,68,66
• 8 years agoHelpfull: Yes(6) No(1)
• 13 as there will be 6 non primes between 0-9 6c2=15 ,raj cant stay in 1st floor and 0th floor so 15-2=13
• 8 years agoHelpfull: Yes(3) No(11)
• 15
  4,6,8,9,10,14,16,18,44,46,48,49,64,66,68
• 8 years agoHelpfull: Yes(1) No(10)
• the ans is 17
• 8 years agoHelpfull: Yes(1) No(1)
• 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67 these are total prime numbers btw 1 to 68 so there are 11 ways how raj can buy 7 floors
• 8 years agoHelpfull: Yes(1) No(1)
• 17
  This problem is permutation problem
  0,1,2, 3,4,5,6,7,8,9 =D digits
  No digit can be prime D-{2,3,5,7}
  Now how many ways we can make max
  two digit number less than 70 excluding 0 and 69
  _ _=4(including 0,1,4,6 digits)×6(including 0,1,4,6,8,9)=24-2(00,69)=22
  Now no no can be prime and can't be 1 floor
  =22-(prime no b/w 1 to 68)4-1=17
• 7 years agoHelpfull: Yes(1) No(0)
• 4.) the required numbers can be 4,6,8,9,10,14,16,18,40,41,44,46,48,49,60,64,66,68.So total number=17.
• 8 years agoHelpfull: Yes(0) No(0)
• from 1 to 68 number that not to be consider are 1(according condition 3),2,3,5,7,11,13,17,19,23,29,31,37,43,47,53,59,61,67.
  68 - 19 = 49.
  now imposing second condition by removing all number from digit 1,2,3,5,7 even if they are not prime(condition2).
  4,6,8,10,14,16,18,40,44,46,48,49,64,66,68
  so total is 15.
  
• 8 years agoHelpfull: Yes(0) No(0)
• 17 is the answer.
• 8 years agoHelpfull: Yes(0) No(0)
• 17 options left by eliminating all the conditions
• 8 years agoHelpfull: Yes(0) No(0)
• option 4 17 is correct
• 8 years agoHelpfull: Yes(0) No(0)
• eliminate the numbers from 1 to 68 based on given conditions
  A) ........ Should not be a prime number ?
  There are 19 prime numbers from 1 to 68. So, we are left with 68-19=49 floors
  B) ....... Digit of the floor should not be a prime number ?
  There are 31 numbers like that (excluding prime numbers).
  So, we have 49-31=18 floors to choose
  Again, in this 18 floors we have to take out 1st floor because we are not allowed to select
  Finally, we have 18-1=17 options left
• 7 years agoHelpfull: Yes(0) No(0)
• eliminate the numbers from 1 to 68 based on given conditions
  1)should not be a prime number
  -->There are 19 prime numbers from 1 to 68. So, we are left with 68-19=49 floors
  2)digit of the floor should not be a prime number
  -->There are 31 numbers like that (excluding prime numbers). So, we have 49-31=18 floors to choose
  Again, in this 18 floors we have to take out 1st floor because we are not allowed to select
  Finally, we have 18-1=17 options left
• 7 years agoHelpfull: Yes(0) No(1)
• Form 1 to 10 only 4,6,8,9,10 are not prime.
  Form 11 to 20 only 14 ,16,18 are not prime also none of its digits are prime.
  From 21 to 30 each number has a prime number so must no need to consider.
  In between 40 to 49 we consider only 40,44,46,48,49.
  50 to 59 has none.
  In between 60 to 68 their are 4 numbers: 60,64,66,68.
  total option =17.
• 7 years agoHelpfull: Yes(0) No(0)
• Ans 13).
  
  acc. to rules 1)none of the floor should be a prime number
  
  2)none of the digit of the floor should be a prime number
  
  3)Raj cannot buy the 1st floor as it is being assigned to the architect.
  
  
  set of options will be (4,6,8,9,40,44,46,48,49,60,64,66,68) 13 options
• 4 years agoHelpfull: Yes(0) No(0)