Bunuel wrote:

If x ? y is defined for all x and y as the sum of all integers from x to y, inclusive, what is the value of 5 ? 150?

A. 22,630

B. 22,475

C. 11,315

D. 11,238

E. 5,658

The

? strange symbol just gives the rule that, in this problem, the task is to find the sum of an arithmetic series of integers, from 5 to 150 inclusive.

Sum = (Average) * (Number of terms)

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

Average = \(\frac{150 + 5}{2}\) = \(\frac{155}{2}\) Leave it.*

Number of terms = (Last Term - First term + 1)

Number of terms = (150 - 5) + 1 = 146

Sum of series: \(\frac{155}{2}\) * (146) = 155 * 73

If you do the arithmetic fully, 155 * 73 = 11,315

ANSWER C

To simplify the arithmetic:

Three answers, A, D,and E, can be eliminated immediately because the units' digit of the answer must be five (3*5 = 15).

Between B and C: Answers B and C are far enough apart that you can round numbers to speed the arithmetic.

150 * 70 = 10,500. That's close to C. To get close to Answer B, the number of terms would have to double.

Either way:

Answer C

*If the average of consecutive integers is not an integer because the sum of the first and last terms is odd (odd/2 = not integer), the number of terms will be even, and the 2 in the denominator will be factored out. So write the two factors, average and number of terms, before calculating; that way it is clear that dividing by 2 will lead to an integer.

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