After increasing a number by 1, its square and cube are added in it. If this expression is 5220,

M4maths Previous Puzzles

27 Oct 2009 fine the number

After increasing a number by 1, its square and cube are added in it. If this expression is 5220,
then the number is

OPtion

1) 14
2) 19
3) 20
4) 17
5) 16
6) 15
7) 18
8) 13
9) 21
10) 22

Solution

According to given condition (x+1)+ x^2+ x^3 = 5220
On solving we get x = 17

Correct Option: 4 Best Solution (2)

Tijo Jose   15 years AGO

Let the number be x.

Given, (x+1) + x^2 + x^3 = 5220
i.e., x^3 + x^2 + x + 1 = 5220.

Solve it.
We get, x=17, (by the following approximation, it is really fast!).

18^3 = 5832 (Too large for 5220)
16^3 = 4096 (Too small to reach 5220)

17^3 = 4913 (Almost there!)
17^2 = 289
4913+289+17+1 = 5220.

Like? Yes (2) | No   

Pargat Pal Singh   15 years AGO

n^3+n^2+n+1= 5220
n^3+n^2+n=5219
checking given options, only 17 is such that
sq ends with 9.
cube ends with 3
17 ends with 7.
so 17.. option 4.

Like? Yes (1) | No