What is the value of k^2 + k? (1) The value of k + 1 is 1. (2) The va

\(k^2+k=k(k+1)\) so we are looking for product of two consecutive integers, k and k+1...

(1) The value of k + 1 is 1.
=> k+1=1...k=0, so k(k+1)=0
Suff

(2) The value of k^2 is 0
=> k^2=0...k=0, so k(k+1)=0
Suff

D
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This is an easy question on Algebraic expressions and equations. To find out the value of the given expression viz., \(k^2\) + k, we will need the value of k. Any such information that gives us a unique value of k will be sufficient information.
Let us break down the given expression as k(k+1) (which is essentially the product of two consecutive numbers).

From statement I alone, k+1 = 1. This means that k = 0. If k=0, k (k+1) = 0. Statement I alone is sufficient. Answer options B, C and E can be eliminated.
Possible answer options are A or D.

From statement II alone, \(k^2\) = 0. Note that \(k^2\) is a term with an even power, therefore, \(k^2\) will always be non-negative. The smallest value of \(k^2\) will be zero when k=0.
So, since we know that \(k^2\)=0, we can conclude that k=0. If k=0, k(k+1) = 0. Statement II alone is sufficient. Answer option A can be eliminated.

The correct answer option is D.

Hope that helps!