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Updated on: 31 Oct 2023, 04:10
Originally posted by quizicalindian on 26 Oct 2023, 22:46.
Last edited by quizicalindian on 31 Oct 2023, 04:10, edited 1 time in total.
Last edited by quizicalindian on 31 Oct 2023, 04:10, edited 1 time in total.
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
50% (02:39) correct
50%
(03:28)
wrong
based on 4
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If f(x) = f(x - 1) + f(x - 2) for all x > 2; is f(5) a perfect square ?
(1) f(2) = 2 f(1)
(2) The first two terms of the series, f(1) and f(2) are consecutive positive even numbers
(1) f(2) = 2 f(1)
(2) The first two terms of the series, f(1) and f(2) are consecutive positive even numbers
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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27 Oct 2023, 14:19
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quizicalindian
\(f(5) = f(4)+f(3).\)..(i)
\(f(4) = f(3)+f(2)...(ii)\)
\(f(3) = f(2)+ f(1)...(iii)\)
\(f(5) = f(2)+ f(1) +f(2) +f(2)+ f(1)...\) putting (ii) and (iii) in (i)
Thus \(f(5) = 3f(2) +2f(1)... (iv)\)
Thus if we can find \(f(2)\)mand \(f(1)\) we can answer the stem.
(1) f(2) = 2 f(1)
Using \((iv)\) we have \(6f(1)+2f(1) = 8f(1)\)
However we do not know \(f(1)\)
INSUFF.
(2) The first two terms of the series, f(1) and f(2) are consecutive even numbers.
We could have \(f(1)\) and \(f(2)\) with many possibilities such as:
\(2\) and \( 4 \)
\(0\) and \( 2 \)
\(0 \) and \(-2 \)
\(-2\) and \(-4 \)
etc.
As such we will get many values for \(f(5) = 3f(2) +2f(1)\)
INSUFF.
1+2
\(f(1)=-2 \) and \( f(2)=-4\) or:
\(f(1)=\hspace{1mm}2 \hspace{1mm}\)and \(\hspace{3mm} f(2)=\hspace{1mm}4 \)
Thus using eqn.(iv) we can get \(f(5)= 16\) or \(f(5)= -16 \)
Hence we can get both a YES and a NO.
IMO ans should be E
However if the author intended only +ve integers as consecutive even integers then \(f(1)=2 \) and \(f(2)=4\) then \(f(5) =16\) and ans would be C.
Hope it helps.
quizicalindian, please can you check with the author of the question, and clarify. Thanks.
31 Oct 2023, 04:09
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Quote:
You're right, it is positive. Modifying the question stem.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
