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02 Nov 2021, 06:00
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
74% (01:43) correct
26%
(02:09)
wrong
based on 129
sessions
History
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Not Attempted Yet
The function f(n) for an integer n is defined as the number of positive integers that are factors of n. For example, f(6) = 4 because 6 has 4 factors: 1, 2, 3, 6. What is the value of f(f(24^2))?
A. 2
B. 4
C. 6
D. 8
E. 12
A. 2
B. 4
C. 6
D. 8
E. 12
02 Nov 2021, 06:10
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Bookmarks
24^2 = 2^2 x 2^2 x 2^2 x 3^2 = 2^6 x 3^2
Total factors = 7x3 = 21
Hence f(24^2) = 21
Now f(f(24^2)) = f(21)
21 = 3 x 7
f(21) = 2 x 2 = 4
Hence Option B
Total factors = 7x3 = 21
Hence f(24^2) = 21
Now f(f(24^2)) = f(21)
21 = 3 x 7
f(21) = 2 x 2 = 4
Hence Option B
Updated on: 09 Jun 2025, 19:49
Originally posted by BrushMyQuant on 01 Jul 2022, 00:21.
Last edited by BrushMyQuant on 09 Jun 2025, 19:49, edited 1 time in total.
Last edited by BrushMyQuant on 09 Jun 2025, 19:49, edited 1 time in total.
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Given that f(n) for an integer n is defined as the number of positive integers that are factors of n and we need to find the value of f(f(\(24^2\)))
To find f(f(\(24^2\))) we can start with finding the value of f(\(24^2\)) and then we can use that value to find the value of f(f(\(24^2\)))
To find the value of f(24^2) we need to compare what is inside the bracket in f(\(24^2\)) and f(n)
=> We need to substitute n with \(24^2\) in f(n) to get the value of f(\(24^2\))
=> f(\(24^2\)) = Number of positive integers that are factors of \(24^2\)
We can find the number of factors of \(24^2\) we can use the prime factorization method
\(24^2\) = 24*24 = \(2^3 * 3 * 2^3 * 3\) = \(2^6 * 3^2\)
=> Number of factors of \(24^2\) = (6+1)*(2+1) = 7*3 = 21
=> f(\(24^2\)) = 21
=> f(f(\(24^2\))) = f(21) = Number of positive integers that are factors of 21
21 = \(3^1 * 7^1\)
=> Number of factors of 21 = (1+1)*(1+1) = 2*2 = 4
=> f(\(24^2\)) = 4
So, Answer will be B
Hope it helps!
Watch the following video to MASTER Functions and Custom Characters
To find f(f(\(24^2\))) we can start with finding the value of f(\(24^2\)) and then we can use that value to find the value of f(f(\(24^2\)))
To find the value of f(24^2) we need to compare what is inside the bracket in f(\(24^2\)) and f(n)
=> We need to substitute n with \(24^2\) in f(n) to get the value of f(\(24^2\))
=> f(\(24^2\)) = Number of positive integers that are factors of \(24^2\)
We can find the number of factors of \(24^2\) we can use the prime factorization method
\(24^2\) = 24*24 = \(2^3 * 3 * 2^3 * 3\) = \(2^6 * 3^2\)
=> Number of factors of \(24^2\) = (6+1)*(2+1) = 7*3 = 21
=> f(\(24^2\)) = 21
=> f(f(\(24^2\))) = f(21) = Number of positive integers that are factors of 21
21 = \(3^1 * 7^1\)
=> Number of factors of 21 = (1+1)*(1+1) = 2*2 = 4
=> f(\(24^2\)) = 4
So, Answer will be B
Hope it helps!
Watch the following video to MASTER Functions and Custom Characters
