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Given that the sum of the odd integers from 1 to 49 is k, what is the

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Given that the sum of the odd integers from 1 to 49 is k, what is the [#permalink] New post   09 Dec 2021, 01:22
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This question is part of the GRE - Skill Builder Project for a Q170


Given that the sum of the odd integers from 1 to 49 is k, what is the sum of the even integers from 2 to 50 in terms of k?

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k+25
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Re: Given that the sum of the odd integers from 1 to 49 is k, what is the [#permalink] New post   09 Dec 2021, 02:24
answer is k + 50?
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Re: Given that the sum of the odd integers from 1 to 49 is k, what is the [#permalink] New post   09 Dec 2021, 02:28
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saptadas1809 wrote:
answer is k + 50?


k+25
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Re: Given that the sum of the odd integers from 1 to 49 is k, what is the [#permalink] New post   09 Dec 2021, 06:19
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This question is part of the GRE - Skill Builder Project for a Q170


Given that the sum of the odd integers from 1 to 49 is k, what is the sum of the even integers from 2 to 50 in terms of k?

Show: ::
k+25


Let 2 + 4 + 6 + 8 + . . . . . + 46 + 48 + 50 = x [notice that there are 25 terms in this sum]
Given: 1 + 3 + 5 + 7 + . . . . .+ 45 + 47 + 49 = k [notice that there are 25 terms in this sum as well]

Subtract the bottom equation from the top equation to get: 1 + 1 + 1 + 1 + . . . . . + 1 + 1 + 1 = x - k
Since the left side of both equations has 25 terms, the equation simplifies to get: 25 = x - k
Add k both sides of the equation: 25 + k = x

Answer: 25 + k

ASIDE: You would never see a Numeric Entry question like this on test day, Numeric Entry questions don't have non-numeric answers.
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