Find m if the sum of the consecutive integers from -16 to m, inclusive is 74.


A) 17
B) 18
C) 19
D) 20
E) 21

Sum of all consecutive integers from -16 to +16 = 0

Now sum of 17+18+19+20=74

Hence m= 20

Answer option D

Bunuel please increase one option here to make it a GMAT like question .

Add an option E)21
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Imo D
Can be calculated from sum formula of a sequence

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We can use the following formula:

sum = average x quantity

Since we have a set of evenly spaced integers, the average is (-16 + m)/2.

We can also calculate the quantity as m - (-16) + 1 = m + 17.

Thus:

74 = (-16 + m)/2 x (m + 17)

148 = (m - 16)(m + 17)

148 = m^2 + m - 272

m^2 + m - 420 = 0

(m + 21)(m - 20) = 0

m = -21 or m = 20

Since m > -16, m must be 20.

Alternate Solution:

The integers in the sum will be -16, -15, -14, …, -2, -1, 0, +1, +2, …, m. Notice that all the negative integers from -16 to -1 inclusive will be offset by the positive integers from +1 to +16, yielding a net sum of 0. So now, starting with the integer +17, we need to add consecutive integers until we get a sum of 74. We see that 17 + 18 + 19 + 20 = 74, and thus m = 20, the largest integer in the set.

Answer: D
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