Problem Solving

31. Does the integer k have a factor p such that 1<p<k?

1). k>4!

2). 13!+2<= k<=13!+13

IMO B
the question is basically asking whether the number k is prime or not
1) INSUFF
36- has lot of factors >1 and <36
37-None

2)13!+2<= k<=13!+13
13! has numbers upto 13 as factors
now you add any number>=2 to 13! it will have a factor between 2 and 13 inclusive, so k is not prime.
SUFFICIENT

good job posting these questions man, definitely 700+ level

tohellandback wrote:IMO B
the question is basically asking whether the number k is prime or not
1) INSUFF
36- has lot of factors >1 and <36
37-None

2)13!+2<= k<=13!+13
13! has numbers upto 13 as factors
now you add any number>=2 to 13! it will have a factor between 2 and 13 inclusive, so k is not prime.
SUFFICIENT

good job posting these questions man, definitely 700+ level

I don't understand how do you find that the integer formed by adding add an integer (greater than equal 2 but less than equal 13) to 13! is not prime number?

pl. explain

real2008 wrote:

tohellandback wrote:IMO B
the question is basically asking whether the number k is prime or not
1) INSUFF
36- has lot of factors >1 and <36
37-None

2)13!+2<= k<=13!+13
13! has numbers upto 13 as factors
now you add any number>=2 to 13! it will have a factor between 2 and 13 inclusive, so k is not prime.
SUFFICIENT

good job posting these questions man, definitely 700+ level

I don't understand how do you find that the integer formed by adding add an integer (greater than equal 2 but less than equal 13) to 13! is not prime number?

pl. explain

will give you an example
let's say 4! i.e. 1*2*3*4 so 2, 3 and 4 are factors
now if you add 4! + 3, it will not be prime because 4! is of the form 3K(because 3 is a factor)
so 4!+3 is 3k+3 =3(k+1) so 3 is a factor and thas why 4!+3 can't be prime

now lets take a bigger number. for ex 100!
factors are 1,2,3,4,....100
we have to see if 100! +59 is prime or not
No because 100! is of the form 59K
so 100!+ 59 is 59K+59=59(k+1), so 59 is a factor and the number cannot be prime

Going to basiscs.. definition of prime says any its divisble by itself and 1.
So in general lets say for any integer k such that k! is yet another integer which is divisble by all integers > 1 upto k! .. as k! = 2*3*..*k

Now coming to the point if you add 1 to K! and get K! + 1 , it means its the reverse of earlier situation . Now k! + 1 is not divisble by any integer > 1 upto k! ...

In question here , 13! + 2<= k <13! + 13 is divisble by 2 , 13! + 3 is divisbvle by 3 , similaryly its divisble by all till 13 ( 13! + 11 , is divisble by 11 , 13! + 13 is divisible by 13 , etc ) ..its only 13! + 1 which is divisible by none other than 1.
So it can be ascertained that the given inequality mentioned avoids being prime

tohellandback wrote:

real2008 wrote:

tohellandback wrote:IMO B
the question is basically asking whether the number k is prime or not
1) INSUFF
36- has lot of factors >1 and <36
37-None

2)13!+2<= k<=13!+13
13! has numbers upto 13 as factors
now you add any number>=2 to 13! it will have a factor between 2 and 13 inclusive, so k is not prime.
SUFFICIENT

good job posting these questions man, definitely 700+ level

I don't understand how do you find that the integer formed by adding add an integer (greater than equal 2 but less than equal 13) to 13! is not prime number?

pl. explain

will give you an example
let's say 4! i.e. 1*2*3*4 so 2, 3 and 4 are factors
now if you add 4! + 3, it will not be prime because 4! is of the form 3K(because 3 is a factor)
so 4!+3 is 3k+3 =3(k+1) so 3 is a factor and thas why 4!+3 can't be prime

now lets take a bigger number. for ex 100!
factors are 1,2,3,4,....100
we have to see if 100! +59 is prime or not
No because 100! is of the form 59K
so 100!+ 59 is 59K+59=59(k+1), so 59 is a factor and the number cannot be prime

Thanks! Oh it was so simple that I should have done myself...