jdhar Posted October 2, 2006 Share Posted October 2, 2006 How many different prime factors does N have? (1) 2N has 4 different prime factors. (2) N ^2 has 4 different prime factors. Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient. Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient. BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. Each statement ALONE is sufficient to answer the question. Statements 1 and 2 TOGETHER are NOT sufficient to answer the question Quote Link to comment Share on other sites More sharing options...
homer_74 Posted October 2, 2006 Share Posted October 2, 2006 Let N = 3X5X7;N has 3 prime factors 2N will have 4 prime factors Let N=2X3X5X7; N has 4 prime factors 2N also has 4 prime factors Hence 1) not sufficient If any number x has N prime factors, x^2 will also have N prime factors Hence B Quote Link to comment Share on other sites More sharing options...
jdhar Posted October 3, 2006 Author Share Posted October 3, 2006 Is " If any number x has N prime factors, x^2 will also have N prime factors" a number property? What if x= 3, it has two prime factors 1 and 3. But x^2=9 has 3 prime factors 1,3,9. Please explain. Quote Link to comment Share on other sites More sharing options...
homer_74 Posted October 3, 2006 Share Posted October 3, 2006 jdhar, 9 is not a prime factor. I don't think 1 is considered a prime factor either. Any other takers for this please? Quote Link to comment Share on other sites More sharing options...
_GMAT_ Posted October 3, 2006 Share Posted October 3, 2006 Is " If any number x has N prime factors, x^2 will also have N prime factors" a number property? What if x= 3, it has two prime factors 1 and 3. But x^2=9 has 3 prime factors 1,3,9. Please explain. Well Jdhar neither 1 nor 9 is considered as prime. Quote Link to comment Share on other sites More sharing options...
GREMAT Posted October 3, 2006 Share Posted October 3, 2006 Is " If any number x has N prime factors, x^2 will also have N prime factors" a number property? What if x= 3, it has two prime factors 1 and 3. But x^2=9 has 3 prime factors 1,3,9. Please explain. jdhar, every positive integer greater than 1 may be represented as a product of prime factors. For instance, 14=2*7 36=2*2*3*3 and so on Let`s look at a number 30 30=2*3*5 30^2=30*30=2*3*5*2*3*5 Therefore, by squaring a number with n prime factors, the squared number will also have n prime factors, only in pairs. The same is valid for 30^3, 30^4 and so on, note that the factors will come in groups of three, four, etc. Quote Link to comment Share on other sites More sharing options...
jdhar Posted October 3, 2006 Author Share Posted October 3, 2006 Can you please mention N^2 which has 4 primary factors. My understanding is that perfect square always has odd number of primary factors eg 4 has 2 as primary factor, 9 has 3 has primary factor, 16 has 2,4,8 has primary factor, 25 had 5 has primary factor. Is there anything which i m missing? it says "N ^2 has 4 different prime factors" Quote Link to comment Share on other sites More sharing options...
GREMAT Posted October 3, 2006 Share Posted October 3, 2006 A Prime number is a number which has only two divisors: 1 and itself Prime numbers are 2,3,5,7,11,13,17,19,etc a number with 4 prime factors is for example 24=2*2*2*3 a number with 4 DIFFERENT prime factors is 210=2*3*5*7 so, 210^2=210*210=2*3*5*7*2*3*5*7, also 4 DIFFERENT prime factors Quote Link to comment Share on other sites More sharing options...
jdhar Posted October 3, 2006 Author Share Posted October 3, 2006 got it now..Thanks! i didn't know that "prime factors" are factors which are prime number. I thought it as all the factors of that number. Thanks for the explanation! Quote Link to comment Share on other sites More sharing options...
cicerone Posted October 5, 2006 Share Posted October 5, 2006 It is B Quote Link to comment Share on other sites More sharing options...
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.