A student has test scores of 85, 90, and 78 on the first three tests. What score is needed on the fourth test for the student's average to…

For an average of $85$ over four tests, the total must be $4\cdot85=340$. The first three scores sum to $85+90+78=253$. The fourth score must make up the difference: $340-253=87$, choice C. Check: $\frac{253+87}{4}=\frac{340}{4}=85$. Choice B ($85$) assumes the fourth score should equal the target average, but the first three scores average only $84.33$, which is below $85$. Choice D ($92$) would give an average of $86.25$. Choice A ($82$) would give $83.75$.