shikha88 Wrote:hey!!
just wanted to know since statement no II of the question lacks the word "distinct" shouldnt we sum up all the factors including the one that is not distinct..
For example:the sum of factors of 9 should be 1+ 9+3+3=16 (even).
i think Statement II can be true only if the word "distinct" is mentioned there just like in statement I and III.
Please reply.
thanks.
The factors of 9 are 1, 3, and 9. Putting 3 on the list a second time is redundant.
Don't let the fact that 3 "pairs" with itself sucker you into thinking that it is somehow different from the other factors. A factor of 9 is any number that divides evenly into 9; it is irrelevant haw many times it does so! In other words, 9/1 = 9 and 9/3 = 3 don't imply that 1 and 3 are somehow different classes of factors because for the first the result is "distinct" and for the second the result is "non-distinct."
It's like this: Andy goes to a certain school in the morning, Billy goes in the morning and afternoon, and Chris goes to school in the afternoon. The students of the school are (Andy, Billy, and Chris) not (Andy, Billy, Billy, and Chris)!
It would be different if the question asked about the "prime factors" of 9.
9 has two prime factors: 3, 3 (Here you do need to repeat, because you need both to "build" 9.)
9 has one distinct prime factor: 3