carpe_diem Posted August 17, 2006 Share Posted August 17, 2006 A positive integer k has exactly 2 positive prime factors, 3 and 7. If k has total of 6 positive factors, including 1 and k, what is the value of k ? 1. 3^2 is a factor of k 2. 7^2 is NOT a factor of k Ans: D please explain .... Quote Link to comment Share on other sites More sharing options...
GMAT-HELP Posted August 17, 2006 Share Posted August 17, 2006 k = 3^x*7^y => k has (x+1)*(y+1) factors => k has 6 factors => x = 1 and y = 2 or x = 2 and y =1 factors Stmt 1: 3^2 is a factor => x = 2 and y = 1 => k = 3^2*7^1 Sufficient Stmt 2: 7^2 is NOT a factor of k => x = 2 and y = 1 (as 7^2 is not a factor) => k = 3^2*7^1 Sufficient Ans D. Quote Link to comment Share on other sites More sharing options...
carpe_diem Posted August 17, 2006 Author Share Posted August 17, 2006 great explanation !! thanks GMAT help .. Quote Link to comment Share on other sites More sharing options...
prateek_goel Posted September 2, 2006 Share Posted September 2, 2006 Pardon me, if its a silly question. But could you please explain why "k = 3^x*7^y" implies k has (x+1)*(y+1) factors? Thanks, Prateek Quote Link to comment Share on other sites More sharing options...
kk_del Posted September 2, 2006 Share Posted September 2, 2006 Prateek Number of factors of any number K = (x+1) (y+1) ....and so on Where K = (p1 ^ x ) ( p2 ^ y ) ... Where p1 and p2 are prime factors of the number Quote Link to comment Share on other sites More sharing options...
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