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05 Mar 2016, 13:08
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D
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Difficulty:
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Question Stats:
75% (01:37) correct
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In the finite sequence of positive integers A1, A2, A3, ..., A11,
each term after the second is the product of the two terms
preceding it. If A4 = 18, what is the value of A11?
(1) A2 = 3
(2) A6 = 1,944
each term after the second is the product of the two terms
preceding it. If A4 = 18, what is the value of A11?
(1) A2 = 3
(2) A6 = 1,944
05 Mar 2016, 21:46
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RITU700
HI
INFO
each term after the second is the product of the two terms preceding it.
INFERENCE:-
all terms can be brought down to equation of \(A_1\) and \(A_2\)..
\(A_3=A_2*A_1\)..
\(A_4=A_3*A_2= A_2*A_2*A_1\)...
So if we know any TWO terms of the sequence, all numbers can be found
lets see the statements:-
(1) A2 = 3
\(A_4\) is already give..
With\(A_2\), it is SUFF
(2) A6 = 1,944
same as (1) above
Suff
D
General Discussion
07 Mar 2016, 17:11
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
In the finite sequence of positive integers A1, A2, A3, ..., A11,
each term after the second is the product of the two terms
preceding it. If A4 = 18, what is the value of A11?
(1) A2 = 3
(2) A6 = 1,944
In the original condition, A3 is variable. Since multiplication of the previous 2 terms defines the next term, A4=18. If you figure out A3, you can figure out the rest, which makes 1 variable. In order to match with the number of equations, you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), A3=6 is derived from (A2)(A3)=18, which is unique and sufficient.
For 2), A5 is derived from (A4)(A5)=1,944, which is unique and sufficient.
Therefore, the answer is D.
For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
In the finite sequence of positive integers A1, A2, A3, ..., A11,
each term after the second is the product of the two terms
preceding it. If A4 = 18, what is the value of A11?
(1) A2 = 3
(2) A6 = 1,944
In the original condition, A3 is variable. Since multiplication of the previous 2 terms defines the next term, A4=18. If you figure out A3, you can figure out the rest, which makes 1 variable. In order to match with the number of equations, you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), A3=6 is derived from (A2)(A3)=18, which is unique and sufficient.
For 2), A5 is derived from (A4)(A5)=1,944, which is unique and sufficient.
Therefore, the answer is D.
For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
