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OG 2016 #87 PS

This topic has 2 expert replies and 1 member reply
Azizakaria Senior | Next Rank: 100 Posts
Joined
29 Sep 2012
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OG 2016 #87 PS

Post Fri Oct 09, 2015 9:41 am
87. The sum of all the integers k such that -26 < k < 24 is
(A) 0
(B) -2
(C) -25
(D) -49
(E) -51

i don't understand why the answer is D

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Azizakaria Senior | Next Rank: 100 Posts
Joined
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Posted:
76 messages
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Post Sat Oct 10, 2015 2:44 am
now I understand, thanks for your help, the explanation in the OG is so unclear.

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GMAT/MBA Expert

Post Fri Oct 09, 2015 9:51 am
Azizakaria wrote:
87. The sum of all the integers k such that -26 < k < 24 is
(A) 0
(B) -2
(C) -25
(D) -49
(E) -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

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GMAT/MBA Expert

Post 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

GMAT assassins aren't born, they're made,
Rich

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