algebra - 1 (SNAP-2008)

The inequality of p²+5 < 5p + 14 can be satisfied if :

(A)  p <= 6, p = -1

(B)   p = 6, p=-2

(C)   p <= 6, p <= -1

(D)  p >= 6, p = 1
Solution follows here:

Solution:

This can be done quickly by eliminating options by substitution method:

All the options centre around 6.

Check out for p=6,  6²+5 < 5(6)+14 => 41 < 44 True

Check out for p=5<6, 5²+5<5(5)+14 => 30<39 True

Check out for p=7>6, 7²+5<5(7)+14 => 54<49 False hence option D is out

Check out for p=-2<-1, (-2)²+5<5(-2)+14 => 9<4 False hence options B and C are out

The only left out option is A

Answer is (A)