pradeepspanchal wrote:For positive integers k , the function g is defined by g(k) = C^k+ 2, where C is a constant.What is the value of g(2)?
(1) g(4) = 18
(2) g(5) = -30


I am not clear whether we will have a negative & a positive value or only a positive value as the constant raised to the power of 4 in option (1) . Which is making my response incorrect.

Please help .

IMO B

solving for C
st(1) C^4=16 => C {-2;2} Not sufficient
st(2) C^5=-32 => C=-2 Sufficient

g(2)=(-2)^2 +2= 6

g(k) = C^k+ 2, where C is a constant

(1) g(4) = 18

Thus, g(4) = C^4 + 2 => C = +2 or -2

Take C = +2 then g(2) = (+2)^2 + 2 = 6
Take C = -2 then g(2) = (-2)^2 + 2 = 6

Sufficient.

(2) g(5) = -30

Thus, g(5) = C^5 + 2 => C = -2

Take C = -2 then g(2) = (-2)^2 + 2 = 6

Sufficient.

IMO D

pradeepspanchal wrote:For positive integers k , the function g is defined by g(k) = C^k+ 2, where C is a constant.What is the value of g(2)?
(1) g(4) = 18
(2) g(5) = -30


I am not clear whether we will have a negative & a positive value or only a positive value as the constant raised to the power of 4 in option (1) . Which is making my response incorrect.

Please help .

g(4) is equal to C^4+2. If this is equal to 18, we get
C^4=16

when we have an equation with an even power, both positive and negative values should be considered, as both 2 and -2 are valid values for C here: (2)^4 is equal to (-2)^4 and they're both equal to 16.

However, since the question stem also uses g(2) - an even power, it doesn't really matter here:
g(2) = c^2 + 2.
Plug in C=2 or -2 into C^2+2, and you'll get the same result of 6, for the same reasoning as above. Stat (1) is sufficient, because it limits the value of g(2) to a single number, regardless of whether C=2 or -2.

Stat. (2)
C^5+2 = -30
C^5 = -32
C mus equal -2, which leads to a single value for g(2).

ah yes g(2) cancels -ve, so it's D

Thanks everyone ..