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Point C is the midpoint of AB

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Carcass
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Point C is the midpoint of AB [#permalink] New post   18 Sep 2020, 10:23
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Point C is the midpoint of \(\overline {AB}\) and n is a positive integer.

Quantity A
Quantity B
k
14



A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
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C
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Re: Point C is the midpoint of AB [#permalink] New post   18 Sep 2020, 19:34
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if C is a midpoint of AB, it is true that:

\(k*3^n = \frac{(3^n + 3^{n+3})}{2}\)

doing some math:

\(2*k-1 = \frac{(3^{n+3})}{3^n}\)

\(2*k-1 = 3^3\)

\(k= 14\)
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Re: Point C is the midpoint of AB [#permalink] New post   18 Sep 2020, 10:24
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Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!

For more theory and practice see our GRE - Math Book
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Re: Point C is the midpoint of AB [#permalink] New post   19 Sep 2020, 02:04
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If C is the midpoint of AB, then we can write:

\(k.3^n-3^n=3^{n+3}-k.3^n\)

\(2*k*3^n=3^n+3^{n+3}\)

\(2*k*3^n=3^n(1+3^3)\)

\(2*k=1+3^3\)

k=14


C

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Re: Point C is the midpoint of AB [#permalink] New post   07 Oct 2021, 14:39
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3^n+3 -3^n
3^n(27-1)
k=26/2
k=13
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Re: Point C is the midpoint of AB [#permalink] New post   18 Sep 2023, 01:40
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k*3^n=3^n-k*3^n
3^n (k-1)=3^n (3^3-k)
k-1=27-1--→k=14
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Re: Point C is the midpoint of AB [#permalink] New post   02 Dec 2024, 07:24
Carcass pls provide an explanation for this question, I am not getting the solutions above
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Point C is the midpoint of AB [#permalink] New post   02 Dec 2024, 09:25
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The midpoint means that the segment AC=CB

Therefore our midpoint that is \(k*3^n\) is equal to AC and CB divided by two because is the midpoint we need to find out

\(k*3^n = \frac{(3^n + 3^{n+3})}{2}\)

At this point is just a matter of computation

K is = to 14

C is the answer
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Point C is the midpoint of AB [#permalink]
02 Dec 2024, 09:25
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