The issue with (C) is that it doesn't strengthen the conclusion.
Remember, the conclusion is: if United States children are to do well in mathematics, they must watch less television.
Answer choice (C) discusses children WHO WANT TO DO WELL. We are not discussing what children who want to do well do as opposed to those who do not want to do well. Regardless of what these children want, we are looking to fid out whether watching less television is necessary in order to get children in the United States to do well in mathematics.
Answer choice (D) is there to trick you. Think about the conclusion we are looking to strengthen: if U.S. children are to do well in math, then they must watch less tv:
Conclusion: USCWM ==> LTV not LTV ==> not USCWM
Answer choice (D) states: if children watch less TV, then they will do well in math.
(D): LTV ==> USCWM not USCWM ==> not LTV
This does not help strengthen our conclusion. This is merely an incorrect contrapositive of our conclusion. Just because watching less TV is sufficient to do well in math concepts such as advanced measurement and geometry, that does not mean that watching less TV is NECESSARY to doing well in these areas, which is what the conclusion is purporting.
Thus, answer choices (C) and (D) do not strengthen the conclusion. Meaning, they are incorrect.
Hope that helps! Please let us know if you have any other questions.
