In the list $p, q, r, s, t, u, v$, each letter represents a positive integer. The sum of the values of each group of three consecutive letters in the list is 35. If $q+u=15$, then $p+q+r+s+t+u+v$ is
(A) 85
(B) 70
(C) 80
(D) 90
(E) 75

Grade 8
The sum of the values of each group of three consecutive letters is 35 .

Thus, $r+s+t=35$ and $s+t+u=35$.

Since each of these equations is equal to 35 , then the left sides of the two equations are equal to each other.

That is, $r+s+t=s+t+u$ and since $s+t$ is common to both sides of this equation, then $r=u$.

Since $q+u=15$ and $r=u$, then $q+r=15$.

Since $p+q+r=35$ and $q+r=15$, then $p=35-15=20$.

Finally, we get

$$
p+q+r+s+t+u+v=p+(q+r+s)+(t+u+v)=20+35+35=90
$$

ANSWER: (D)