Good question. Just need some careful calculations.
S1:
(1/7)^4y >(1/7)^(8y+14)
Now this can not be directly equated. You will need to write it like this.
(7)^-4y>(7)^-(8y+14)
or
-4y>-(8y+14)
hence y>-3.5
Sufficient
S2:
4y^2 +12y <0
This will give you -3<y<0
hence y >-4
Sufficient
Answer is D
S1:
(1/7)^4y >(1/7)^(8y+14)
Now this can not be directly equated. You will need to write it like this.
(7)^-4y>(7)^-(8y+14)
or
-4y>-(8y+14)
hence y>-3.5
Sufficient
S2:
4y^2 +12y <0
This will give you -3<y<0
hence y >-4
Sufficient
Answer is D
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