jloock524 wrote:attached is an IR Two Part Analysis question; sequencing is the topic. Please explain how to complete this problem. I am having trouble understanding the explanation the OG gives.
Thank you
Hi jloock524,
The question asks for the jointly compatible values of S1 and S4. It does not simply ask for their values.
Let's understand the difference between Unique values and Jointly compatible values.
Say, for example, a linear equation is 2x + 3y = 12. Since there are two variables x and y, we cannot get the unique values of x and y; we need another equation in x and y such that upon dealing with the two linear equations, we get the unique values of x and y.
However, this does not mean that we cannot get the jointly compatible values of x and y.
For the equation 2x + 3y = 12, x = 3 and y = 2 is one of the many jointly compatible values of x and y.
Few others can be x = 1, y =10/3; x = 2, y = 8/3, ...
Let's switch to the problem.
We are given that S(n+2) = (Sn)^2 - S(n+1), S2 = 1, where n = any psotive integer
Since we have to get the jointly compatible values of S1 and S4, we must ensure that with the use of the relationship S(n+2) = (Sn)^2 - S(n+1), we reach them.
@ n = 1, S(n+2) = (Sn)^2 - S(n+1) => S3 = (S1)^2 - S2 => S3 = (S1)^2 - 1
We see that S3 is unwanted here while S4 is missing. If we put n = 2, in S(n+2) = (Sn)^2 - S(n+1), we can reach S4. So let's do it.
@ n = 2, S(n+2) = (Sn)^2 - S(n+1) => S4 = (S2)^2 - S3 => S4 = (1)^2 - S3 => S4 = 1 - S3
We again see that S3 is unwanted here while S1 is missing; by dealing with both the derived equations, we can get rid of S3. Let's see how.
We have,
S3 = (S1)^2 - 1 ---(1)
S4 = 1 - S3 ---(2)
By plugging in the value of S3 from eqn (1) in eqn (2), we get,
S4 = 1 - [(S1)^2 - 1 ]
S4 = 1 - (S1)^2 + 1
S4 = 2 - (S1)^2
The equation S4 = 2 - (S1)^2 is a two variable equation, and we cannot get the unique values of S1 and S4; however, we can get their jointly compatible values.
We see that there are there are five values given in the answer table; they all are eligible for S1 and S4; however only one pair of values would be jointly compatible and we have to find out that.
Say, S1 = -12, then S4 = 2 - (-12)^2 = 2 - 144 = -142. There is no value as -142 in the table.
Since -142 is a very small value, let's try with larger values.
Say, S1 = 0, then S4 = 2 - (0)^2 = 2 . There is no value as 2 in the table.
Let's try with another value.
Say, S1 = -1, then S4 = 2 - (-1)^2 = 2 - 1 = 1 . There is no value as 1 in the table.
Let's try with another value.
Say, S1 = -3, then S4 = 2 - (-3)^2 = 2 - 9 = -7 . There is a value as -7 in the table, thus we got the answer.
=> S1 = -3 and S4 = -7.
Be cautious to mark the answers correctly. The correct answers are C (in the S1 column) and B (in the S4 column); marking B and C is incorrect.
The correct answer: [spoiler]C/B[/spoiler]
Hope this helps!
Relevant book:
Manhattan Review GMAT Integrated Reasoning Guide
-Jay
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