Question

The $2007$ AMC $10$ will be scored by awarding $6$ points for each correct response, $0$ points for each incorrect response, and $1.5$ points for each problem left unanswered. After looking over the $25$ problems, Sarah has decided to attempt the first $22$ and leave only the last $3$ unanswered. How many of the first $22$ problems must she solve correctly in order to score at least $100$ points?

$13$

$14$

$15$

$16$

$17$

Answer: D

Concepts:inequality linear equation

Difficulty rating: 1120

Small Hint:

The unanswered problems still contribute points

Big Hint:

Subtract the points from the $3$ blanks, then divide the remaining needed points by $6$

Solution:

The three blank problems give $3\cdot 1.5 = 4.5$ points, so Sarah needs $100-4.5=95.5$ points from the first $22.$

Since $\frac{95.5}{6}$ lies between $15$ and $16,$ she must answer at least $16$ correctly, which would give a score of $100.5.$

Thus, the correct answer is D.

2007 AMC 10B Problem 6

Answer: D

Difficulty rating: 1120

Small Hint:

Big Hint:

Solution:

Problem 6 in Other Years