Value of m

[deepesh.gupta]

If p is an integer and m = -p + (-2)^p, is m^3> 1?
1) p is even
2) p^3≤-1

[thephoenix]

imo e

[neoreaves]

IMO C

m = -p + (-2)^p

1) p = even ...so p can be ...-100.....-2 , 0, 2, ....100

when p is negative

m = positive Even + positive Even fraction (as -2^p will be positive as p is even )
--> m > 1

if p = 0

m = 0 + 1 = 1 ( so m >1 doesnt hold here )

if p > 0

lets say p = 2

m = -2 + 4 = 2 and for other values (-2)^p is even bigger so m >1

Insufficient as m=1 or m>1

2) p^3 <= -1

if p = -1
m = 1 + (-2)^-1 = 1/2 thus m > 1 is not true

if p = -2
m = 2 + (-2)^-2 thus m >1 is true

c) m > 1 from 1) and 2 so its sufficient

[ansumania]

OA pl.

[deepesh.gupta]

OA is C

OA pl.