OG 2016 #87 PS

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Azizakaria: Senior | Next Rank: 100 Posts; Posts: 76; Joined: Sat Sep 29, 2012 11:19 am; Thanked: 3 times

OG 2016 #87 PS

by Azizakaria » Fri Oct 09, 2015 9:41 am

87. The sum of all the integers k such that âˆ’26 < k < 24 is
(A) 0
(B) âˆ’2
(C) âˆ’25
(D) âˆ’49
(E) âˆ’51

i don't understand why the answer is D

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Source: Beat The GMAT — Problem Solving | Fri Oct 09, 2015 9:41 am

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by [email protected] » Fri Oct 09, 2015 9:47 am

Hi Azizakaria,

We're limited to the INTEGERS that fall in the range -26 < K < 24....so that would be....

-25, -24, -23.....0.....22, 23

Each of the positive integers form 1 to 23 (inclusive) would be 'cancelled out' by the negative integers from -1 to -23 (inclusive). The sum of ALL of those terms would be 0. But then you have to consider the other remaining integers: -24 and -25. Adding those two numbers gets us -49.

Final Answer: D

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Rich

Contact Rich at [email protected]

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by Brent@GMATPrepNow » Fri Oct 09, 2015 9:51 am

Azizakaria wrote:87. The sum of all the integers k such that âˆ’26 < k < 24 is
(A) 0
(B) âˆ’2
(C) âˆ’25
(D) âˆ’49
(E) âˆ’51

i don't understand why the answer is D

(-25) + (-24) + (-23) + (-22) + (-21) + . . . . .+ 21 + 22 + 23

Notice that the blue values all cancel out, because for each positive value, there's a negative value with the same magnitude (e.g., -23 + 23 = 0, and -22 + 22 = 0, etc)

So, we're left with (-25) + (-24), which equals -49

Brent Hanneson - Creator of GMATPrepNow.com