Tori's mathematics test had 75 problems: 10 arithmetic, 30 algebra, and 35 geometry problems. Although she answered 70% of the arithmetic, 40% of the algebra, and 60% of the geometry problems correctly, she did not pass the test because she got less than 60% of the problems right. How many more problems would she have needed to answer correctly to earn a 60% passing grade?
$\text{(A)}\ 1 \qquad \text{(B)}\ 5 \qquad \text{(C)}\ 7 \qquad \text{(D)}\ 9 \qquad \text{(E)}\ 11$
First, calculate how many of each type of problem she got right:
Arithmetic:  $70\% \cdot 10 = 0.70 \cdot 10 = 7$
Algebra:  $40\% \cdot 30 = 0.40 \cdot 30 = 12$
Geometry:  $60\% \cdot 35 = 0.60 \cdot 35 =  21$
Altogether, Tori answered $7 + 12 + 21 = 40$ questions correct.
To get a $60\%$ on her test overall, she needed to get $60\% \cdot 75 = 0.60 \cdot 75 = 45$ questions right.
Therefore, she needed to answer $45 - 40 = 5$ more questions to pass, so the correct answer is $\boxed{(B) 5}$