rainbownlife Posted June 13, 2008 Share Posted June 13, 2008 If k=m(m+4)(m+5) k and m are positive integers. Which of the following could divide k evenly? I.3 II.4 III.6 I think all three could divide k evenly. OA posted is 3,6 only. Not sure about the correctness of the OA.... if m=3 , 4 cud divide the expression? I would understand ans =3,6 , if question asked MUST divide. Any thoughts...? Quote Link to comment Share on other sites More sharing options...
abhijit_sen Posted June 14, 2008 Share Posted June 14, 2008 If m = 1 then (m+4) = 5 and (m+5) = 6. Thereby it is not divisible by 4. Quote Link to comment Share on other sites More sharing options...
saege Posted June 14, 2008 Share Posted June 14, 2008 Yes its is 3 and 6 Test as many values as possible 1. m= 1 then k = 1*5*6 2. m=2 then k = 2*6*5 3. m= 3 then k = 3*7*8 4. m= 4 then k = 4*8*9 5. m=5 then k = 5*9*10 What the Q is asking is to check if K is divisible by 3,4 or 6 Check 1 to 5 we see that K is indeed divisible by 3 then not divisible by 4 in step 1 so it fails again divisible by 6 in steps 1 to 5 since for it to be divisible by 6 it should be divisible by 2 and 3 together hence that is true Ans is 3 & 6 Quote Link to comment Share on other sites More sharing options...
rainbownlife Posted June 14, 2008 Author Share Posted June 14, 2008 still not clear guys... @saege the question asks Which of the following could divide k evenly? 4 could divide k evenly as well . It does not ask for nos that "must" divide k evenly then why is 4 not included? Quote Link to comment Share on other sites More sharing options...
Makumajon Posted June 15, 2008 Share Posted June 15, 2008 k=m(m+4)(m+5) =m(m^2+9m+20) =m^3+9m^2+20m Depending on the value of m, all 3, 4, and 6 can evenly divide k. Typical values of m can be 3, 4 or 5 to be divided by 3, 4, and 5 respectively. Quote Link to comment Share on other sites More sharing options...
saege Posted June 16, 2008 Share Posted June 16, 2008 Hai Divide K evenly means divide it without leaving a remainder and it should divide it for all values of m. It fails for m= 1 & 5. But 3 and 6 can evenly divide for any value of m. Thats why 3 & 6 are the ans choices is it clear now? still not clear guys... @saege the question asks Which of the following could divide k evenly? 4 could divide k evenly as well . It does not ask for nos that "must" divide k evenly then why is 4 not included? Quote Link to comment Share on other sites More sharing options...
Makumajon Posted June 17, 2008 Share Posted June 17, 2008 But saege, the question talks about COULD, not MUST. So, if we can show one case in which 4 can divide k evenly, then II must be true. Now suppose m=8 (a positive integer) k=8*12*13. Now 4 could divide k. Quote Link to comment Share on other sites More sharing options...
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