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11 Nov 2022, 02:30
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C
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Difficulty:
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Question Stats:
64% (02:14) correct
36%
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wrong
based on 114
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The infinite sequence \(a_1\), \(a_2\),…, \(a_n\), … is such that \(a_{n} = a_{n-1} + a_{n - 2}\), for all n > 2. What is the value of \(a_1\) ?
(1) \(a_6 = 11\)
(2) \(a_9 = 17\)
(1) \(a_6 = 11\)
(2) \(a_9 = 17\)
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11 Nov 2022, 04:07
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Assume \(a_1\) = x; \(a_2\) = y
Starting \(a_3\) the value can be represented in terms of x and y
Ex. \(a_3\) = x + y; \(a_4\) = x + 2y and so on.
Question x = ?
Statement 1
\(a_6\) = 11
\(a_6\) will therefore be the sum of some coefficient * x and some coefficient * y. However, there will be two variables in the value.
As there are two unknowns and just one equation to deal with, this statement is not sufficient. We can eliminate A and D.
Statement 2
\(a_9\) = 17
Just as in statement 1, this statement is also not sufficient as \(a_9\) will still be dependent on x and y. The reasoning to eliminate this statement is same as that of St. 1.
Hence we can eliminate B
Combined
The two statements combined gives us two equations and we have two variable whose values we need to find.
Hence the statements combined are sufficient.
IMO C
Starting \(a_3\) the value can be represented in terms of x and y
Ex. \(a_3\) = x + y; \(a_4\) = x + 2y and so on.
Question x = ?
Statement 1
\(a_6\) = 11
\(a_6\) will therefore be the sum of some coefficient * x and some coefficient * y. However, there will be two variables in the value.
As there are two unknowns and just one equation to deal with, this statement is not sufficient. We can eliminate A and D.
Statement 2
\(a_9\) = 17
Just as in statement 1, this statement is also not sufficient as \(a_9\) will still be dependent on x and y. The reasoning to eliminate this statement is same as that of St. 1.
Hence we can eliminate B
Combined
The two statements combined gives us two equations and we have two variable whose values we need to find.
Hence the statements combined are sufficient.
IMO C
28 Feb 2023, 10:13
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Both of these statements are clearly not sufficient on their own.
Combined:
a7 = 11 + a5
a8 = 11 + a5 + 11 (which represents a6)
17 = 33 + 2*a5
a5 = -8.
Given the value of a6 and a5, you may easily find the values of items 4,3,2, and 1.
Combined:
a7 = 11 + a5
a8 = 11 + a5 + 11 (which represents a6)
17 = 33 + 2*a5
a5 = -8.
Given the value of a6 and a5, you may easily find the values of items 4,3,2, and 1.
