Question

3. The prouct of three consecutive numbers cannot

be:
A. 210
B. 336
C. 560
D. 1716

Answer 1

C. 560

Explanation:

let x be the number

then x+1 , x+2 will be the next consecutive numbers.

product of three consecutive numbers will be

`x(x+1)(x+2)= (x^(2) +x )(x+2)\\ =x^(3)+3x^(2) +2x`

now one way is to check is putting the values of given option in place of Z in the following formula and check the roots.

`x^(3)+3x^(2) +2x=Z`

so for option A , put Z=560

`x^(3)+3x^(2) +2x=560`

when you check the roots

you will get two complex root and on root in decimal form(not integer)

so 560 is number which cannot be written as a product of three consecutive numbers.