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# M23-12

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Math Expert
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rananava wrote:
Can you explain how you know that n(n−1)=11∗12∗(11∗12−1) is divisible by 12?

Because it has 12 as a multiple.
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The explanation is good. This is a high quality question.
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My try is by doing with statement.
1. for being divisible by 11 let try with number 11. 11^2-11=110/12 which is not divisible. so first statement cannot be true.
2.for being divisible by 19 let try with number 19. 19^2-19=342/12 which is not divisible. so 2nd statement cannot be true.

now let combine both 11*19
for being divisible by 11*19 let try with LCM of both number 209. 209^2-209=209(209-1)/12= (209*208)/12 since none of these 208 and 209 is divisible by 3 thus t is not divisible by 12 too. so even combining these two wont solve problem.
so E is only ans left

LET ME KNOW IF I AM WRONG.
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aravsha wrote:
My try is by doing with statement.
1. for being divisible by 11 let try with number 11. 11^2-11=110/12 which is not divisible. so first statement cannot be true.
2.for being divisible by 19 let try with number 19. 19^2-19=342/12 which is not divisible. so 2nd statement cannot be true.

now let combine both 11*19
for being divisible by 11*19 let try with LCM of both number 209. 209^2-209=209(209-1)/12= (209*208)/12 since none of these 208 and 209 is divisible by 3 thus t is not divisible by 12 too. so even combining these two wont solve problem.
so E is only ans left

LET ME KNOW IF I AM WRONG.

You are wrong the way you have written..
in DS, a statement is sufficient if it can give a definite answer - definite YES or Definite NO
here you have just worked on getting a NO as the answer. you have to further check if it is true that there is some case where it will be div by 12 too
if there is a case , it is insufficient then only
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