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The first and second numbers in a sequence of numbers are pl

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The first and second numbers in a sequence of numbers are pl [#permalink] New post 16 Sep 2013, 21:56
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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.
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Last edited by mau5 on 03 Nov 2013, 00:21, edited 3 times in total.
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Re: The first and second numbers in a sequence of numbers are pl [#permalink] New post 16 Sep 2013, 22:10
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honchos wrote:
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.


From F.S 1, we have the series as x,2x-1,4x-3,8x-7 .. etc

Now, as per the question stem, the two co-ordinates will be : (x,2x-1) and (4x-3,8x-7) --> The slope of the line : \frac{(8x-7)-(2x-1)}{(4x-3)-x} = \frac{6(x-1)}{3(x-1)}

The slope will be 2, if x\neq{1} and undefined if x = 1. However, we don't know that. Insufficient.

From F.S 2, all we know is the first term, clearly Insufficient.

Taking both statements together, we know that x\neq{1} and hence, the slope is 2. Sufficient.

C.
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Re: The first and second numbers in a sequence of numbers are pl [#permalink] New post 16 Sep 2013, 22:13
mau5 wrote:
honchos wrote:
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.


From F.S 1, we have the series as x,2x-1,4x-3,8x-7 .. etc

Now, as per the question stem, the two co-ordinates will be : (x,2x-1) and (4x-3,8x-7) --> The slope of the line : \frac{(8x-7)-(2x-1)}{(4x-3)-x} = \frac{6(x-1)}{3(x-1)}

The slope will be 2, if x\neq{1} and undefined if x = 1. However, we don't know that. Insufficient.

From F.S 2, all we know is the first term, clearly Insufficient.

Taking both statements together, we know that x\neq{1} and hence, the slope is 2. Sufficient.

C.


Boss Your solution is amazing.

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Re: The first and second numbers in a sequence of numbers are pl [#permalink] New post 16 Sep 2013, 22:56
mau5 wrote:
honchos wrote:
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.


From F.S 1, we have the series as x,2x-1,4x-3,8x-7 .. etc

Now, as per the question stem, the two co-ordinates will be : (x,2x-1) and (4x-3,8x-7) --> The slope of the line : \frac{(8x-7)-(2x-1)}{(4x-3)-x} = \frac{6(x-1)}{3(x-1)}

The slope will be 2, if x\neq{1} and undefined if x = 1. However, we don't know that. Insufficient.

From F.S 2, all we know is the first term, clearly Insufficient.

Taking both statements together, we know that x\neq{1} and hence, the slope is 2. Sufficient.

C.




The mistake in your solution is that you assumed that there are just 4 points. But the question does not say this. It says " and all subsequent pairs in the sequence" which means there are more than 4 terms in the sequence. In case of 2 points you will a straight line. But if the number of points is more than 2, you wont get a straight line. So both statements are not sufficient.

So E.
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Re: The first and second numbers in a sequence of numbers are pl [#permalink] New post 16 Sep 2013, 22:57
nspatel wrote:
mau5 wrote:
honchos wrote:
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.


From F.S 1, we have the series as x,2x-1,4x-3,8x-7 .. etc

Now, as per the question stem, the two co-ordinates will be : (x,2x-1) and (4x-3,8x-7) --> The slope of the line : \frac{(8x-7)-(2x-1)}{(4x-3)-x} = \frac{6(x-1)}{3(x-1)}

The slope will be 2, if x\neq{1} and undefined if x = 1. However, we don't know that. Insufficient.

From F.S 2, all we know is the first term, clearly Insufficient.

Taking both statements together, we know that x\neq{1} and hence, the slope is 2. Sufficient.

C.




The mistake in your solution is that you assumed that there are just 4 points. But the question does not say this. It says " and all subsequent pairs in the sequence" which means there are more than 4 terms in the sequence. In case of 2 points you will a straight line. But if the number of points is more than 2, you wont get a straight line. So both statements are not sufficient.

So E.


By evening I will give the official answer, I dont have it Now.
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Re: The first and second numbers in a sequence of numbers are pl [#permalink] New post 16 Sep 2013, 23:22
Expert's post
nspatel wrote:
mau5 wrote:
honchos wrote:
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.


From F.S 1, we have the series as x,2x-1,4x-3,8x-7 .. etc

Now, as per the question stem, the two co-ordinates will be : (x,2x-1) and (4x-3,8x-7) --> The slope of the line : \frac{(8x-7)-(2x-1)}{(4x-3)-x} = \frac{6(x-1)}{3(x-1)}

The slope will be 2, if x\neq{1} and undefined if x = 1. However, we don't know that. Insufficient.

From F.S 2, all we know is the first term, clearly Insufficient.

Taking both statements together, we know that x\neq{1} and hence, the slope is 2. Sufficient.

C.




The mistake in your solution is that you assumed that there are just 4 points. But the question does not say this. It says " and all subsequent pairs in the sequence" which means there are more than 4 terms in the sequence. In case of 2 points you will a straight line. But if the number of points is more than 2, you wont get a straight line. So both statements are not sufficient.

So E.


I have assumed no such thing.Make a list of all the terms you keep getting based on F.S 1, you will get the same expression for slope, and hence it is a part of the straight line.

For eg: x,2x-1,4x-3,8x-7,16x-15,32x-31,64x-63,128x-127,etc..
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Re: The first and second numbers in a sequence of numbers are pl [#permalink] New post 16 Sep 2013, 23:26
It is not giving the same slope..


I have assumed no such thing.Make a list of all the terms you keep getting based on F.S 1, you will get the same expression for slope, and hence it is a part of the straight line.

For eg: x,2x-1,4x-3,8x-7,16x-15,32x-31,64x-63,128x-127,etc..[/quote]
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Re: The first and second numbers in a sequence of numbers are pl [#permalink] New post 16 Sep 2013, 23:31
Expert's post
honchos wrote:
It is not giving the same slope..



Please re-check your calculations
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Re: The first and second numbers in a sequence of numbers are pl [#permalink] New post 17 Sep 2013, 00:35
mau5 wrote:
honchos wrote:
It is not giving the same slope..



Please re-check your calculations



Yes, C is correct. My mistake.
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Re: The first and second numbers in a sequence of numbers are pl [#permalink] New post 14 Oct 2013, 21:30
GREAT solution mau5. GOOD JOB!!!!
Re: The first and second numbers in a sequence of numbers are pl   [#permalink] 14 Oct 2013, 21:30
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