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
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Source: Beat The GMAT — Problem Solving |
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?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
pl. explain
will give you an examplereal2008 wrote: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?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
pl. explain
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
The powers of two are bloody impolite!!
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
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
Thanks! Oh it was so simple that I should have done myself...tohellandback wrote:will give you an examplereal2008 wrote: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?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
pl. explain
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
