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I am tutoring someone in preparation for the SAT. Below are two SAT questions that I find bothersome. I have the answers but disagree with the official answers and would appreciate understanding the SAT train of thought if anyone can conjure it up.

For problem #5, the SAT answer is C. I calculated using all points between $x=3$ and $x=4$ and found the percent increase to be around 6.4%.

For problem #7, the SAT answer is A. However, it appears the the greatest difference occurs right after $x=2$ - the beginning of month 3.enter image description here

Better2BLucky
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1 Answers1

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Let $x$ denote the number of months from the first class was offered and $y$ the number of people attending to the class. Also, let $\widehat{y}$ denote the estimated number of people attending to the class.

For problem $5$, observe that the predicted number of people attending to the class at month $4$ (that is to say, $x=4$) is slightly smaller than $800$, and the observed number of people who attented is $600$. Then, the percent greater that the actual number of people is $$\frac{\widehat{y}- y}{y} = \frac{800-600}{600}=33.33\%.$$ Since the predicted value was a bit lower than $800$, I would choose option $C$ to approximate it.

For problem $7$, you have to calculate, for each month $x=0,1,2,3,4,5$, what is the biggest difference $y - \widehat{y}$, which obviously occurs at $x=2$, that is to say, for month $2$.

user326159
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