enigma123 wrote:
What is the positive integer n?
(1) For every positive integer m, the product m(m + 1)(m + 2) ... (m + n) is divisible by 16
(2) n^2 - 9n + 20 = 0
Guys - the OA is C. But can someone please let me know what does statement 1 implies over here?
For me it says that the product of consecutive integers is divisible by 16. But how its used in this question?
I understand statement 2 though.
Usually, when approaching a DS question, you start with statement (1), then go to statement (2)...
If you don't know how to attack statement (1), go directly to (2), especially if it looks "friendlier", as in this case.
(2) The given quadratic equation has two solutions: \(n=4\) and \(n=5\).
Not sufficient. So, the answer is certainly not B.
Now go back to (1) and start by checking the two values for \(n\) you obtained in (2).
Take \(m=1\). Obviously, \(1\cdot2\cdot3\cdot4\cdot5\) is not divisible by 16, but \(1\cdot2\cdot3\cdot4\cdot5\cdot6\) is.
The answer can be C, if without the condition in statement (2), there can be more than one value of \(n\) which fulfills the condition.
You don't have to look for the smallest \(n\). Obviously, if \(n=15\), we have \(16\) consecutive numbers, so their product is definitely divisible by 16.
Therefore, the answer cannot be A.
In conclusion, answer is C.
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