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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If (-20) + (-19) + (-18) + (-17) + . . . +
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15 May 2018, 06:09
15 May 2018, 06:09
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Question Stats:
71% (02:34) correct
28% (02:04) wrong based on 21 sessions
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If (-20) + (-19) + (-18) + (-17) + . . . + (-2x - 4) = 90, what is the value of x?
A) -24
B) -14
C) -10
D) 10
E) 14
A) -24
B) -14
C) -10
D) 10
E) 14
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If (-20) + (-19) + (-18) + (-17) + . . . +
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15 May 2018, 08:48
15 May 2018, 08:48
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GreenlightTestPrep wrote:
If (-20) + (-19) + (-18) + (-17) + . . . + (-2x - 4) = 90, what is the value of x?
A) -24
B) -14
C) -10
D) 10
E) 14
A) -24
B) -14
C) -10
D) 10
E) 14
First notice that (-20) + (-19) + (-18) + (-17) + . . . + 17 + 18 + 19 + 20 = 0 [because any pair of positive and negative numbers with the same magnitude must add to 0. For example, (-3) + 3 = 0, and (-11) + 11 = 0]
So, we have: (-20) + (-19) + (-18) + (-17) + . . . + 17 + 18 + 19 + 20 + 21 + 22 + ? + ? + ... + (-2x - 4) = 90
Simplify to get: -0 + 21 + 22 + ? + ? + ... + (-2x - 4) = 90
We can see that we won't need to add many consecutive integers (starting at 21) to get to a sum of 90
So, let's just keep adding integers until we reach 90
21 + 22 = 43
21 + 22 + 23 = 66
21 + 22 + 23 + 24 = 90 DONE!
So, it must be the case that -2x - 4 = 24
Add 4 to both sides to get: -2x = 28
Solve: x = -14
Answer: B
Cheers,
Brent
Re: If (-20) + (-19) + (-18) + (-17) + . . . +
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24 Aug 2022, 09:37
24 Aug 2022, 09:37
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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