NTSE Stage 2 SAT 2019 Exam Question Paper

Question : 41 of 100

Marks: +1, -0

m=n^2-n

where n is an integer, then

m^2-2m

is divisible by

Solution:

∵m=n^{2}-n=n(n-1)

Now

m^{2}-2m=m(m-2)

=n(n-1)(n^{2}-n-2)

=n(n-1)(n-2)(n+1)

Since we know that product of any four consecutive integers is always divisible by 24.
∴

m^2-2m

is divisible by 24.

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