f(x) = (f(x-2))(f(x-1))(x) for x>0 & f(x) = 1 for all x<1
What is the largest prime number that divides f(50)?
The answer is 47 but need help understanding how?
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largest prime that divides f(50)
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Hi binaras,
This question is really about 'mapping out' the information and not about 'doing math'
We're told that f(x) = (f(x-2))(f(x-1))(x) for x>0
So when the question asks for the f(50), we can map that out...
f(50) = (f(48) x (f(49) x 50
Unfortunately, that calculation requires that we deal with f(48) and f(49), but we can write down what those mean too:
f(48) = (f(46) x (f(47) x 48
f(49) = (f(47) x (f(48) x 49
Now, each of THOSE calculations would have two more calculations. This pattern would go on and on UNTIL we got to the other piece of information that we've been given:
f(x) = 1 for all x<1
This tells us that eventually, all of the calculations would end up getting multiplied by 1.
So, we'd have a GIGANTIC string of integers multiplied together (and it's all of the integers from 1 to 50, inclusive, with some duplicates). The question asks for the largest PRIME number that divides into that calculation. The largest prime that is between 1 and 50, inclusive is 47.
GMAT assassins aren't born, they're made,
Rich
This question is really about 'mapping out' the information and not about 'doing math'
We're told that f(x) = (f(x-2))(f(x-1))(x) for x>0
So when the question asks for the f(50), we can map that out...
f(50) = (f(48) x (f(49) x 50
Unfortunately, that calculation requires that we deal with f(48) and f(49), but we can write down what those mean too:
f(48) = (f(46) x (f(47) x 48
f(49) = (f(47) x (f(48) x 49
Now, each of THOSE calculations would have two more calculations. This pattern would go on and on UNTIL we got to the other piece of information that we've been given:
f(x) = 1 for all x<1
This tells us that eventually, all of the calculations would end up getting multiplied by 1.
So, we'd have a GIGANTIC string of integers multiplied together (and it's all of the integers from 1 to 50, inclusive, with some duplicates). The question asks for the largest PRIME number that divides into that calculation. The largest prime that is between 1 and 50, inclusive is 47.
GMAT assassins aren't born, they're made,
Rich
