Bunuel wrote:

In a sequence of consecutive numbers the sum of the first half of the numbers is 196. If there are 14 numbers in the set, what is the sum of the second half of the numbers?

A. 201

B. 206

C. 210

D. 245

E. 266

With 14 consecutive integers, the first half of the numbers are terms 1 through 7. Sum of these first seven = 196

For consecutive integers,

First term = n

Seventh term = n + 6

Sum of first half of numbers:

(Average)(# of terms) = Sum

Average = \(\frac{(First Term+LastTerm)}{2}\)

\(\frac{(n + n + 6)}{2} * 7 = 196\)

\((2n + 6)(7) = 392\)

\(14n + 42 = 392\)

\(14n = 350\)

\(n = 25\)

Second half of numbers = terms 8 to 14

8th term: (n+7) = (25+7) = 32

14th term: (n+13)=(25+13) = 38

Sum of second half of numbers, from 32 to 38:

\(\frac{32 + 38}{2}*(7)=(35*7)=245\)

Answer D

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"