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The first and second numbers in a sequence of numbers are plotted as the \(x\) and \(y\) coordinates, respectively, of a

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by VJesus12 » Thu Jul 30, 2020 8:48 am

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The first and second numbers in a sequence of numbers are plotted as the \(x\) and \(y\) coordinates, respectively, of a point on the coordinate plane, as are the third and fourth numbers, and all subsequent pairs in the sequence and a line is formed by connecting these points, what would be the slope of the line?

(1) Except for the first number, the sequence of numbers is formed by doubling the previous number and then subtracting 1.
(2) The first number in the sequence is 3.

[spoiler]OA=A[/spoiler]

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Source: — Data Sufficiency |
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Re: The first and second numbers in a sequence of numbers are plotted as the \(x\) and \(y\) coordinates, respectively,

by deloitte247 » Sat Aug 01, 2020 12:04 pm
Let the first number = x, then we have (x, x+1) coordinate, (x+2, x+3) coordinates.
Target question=> A line is formed by connecting the coordinate, what would be the slope of the line?
$$Slope=\frac{\triangle y}{\triangle x}=\frac{y2-y1}{x2-x1}$$
Statement 1: Except for the first number, the sequence of numbers is formed by doubling the previous number and then subtracting 1.
Therefore, considering the first 4 numbers for (x1,y1) and (x2,y2) coordinates.
[x, (2x-1)] and [(4x-3), (8x-7)]
x1=x, x2=4x-3, y1=2x-1, y2=8x-7
$$Therefore,\ slope\ \left(m\right)=\frac{\left(8x-7\right)-\left(2x-1\right)}{\left(4x-3\right)-x}$$ $$=\frac{8x-7-2x+1}{4x-3-x}=\frac{6x-6}{3x-3}$$
$$=\frac{2\left(3x-3\right)}{3x-3}=2$$
Statement 1 is SUFFICIENT

Statement 2: The first number in the sequence is 3.
This does not tell us how the sequence is formed and we do not know if it is consecutive or not. Statement 2 is NOT SUFFICIENT.
Since only statement 1 is SUFFICIENT, then the correct answer is option A.
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