If D is a positive Integer and f is the product of the 1st 30 positive integers, what is the value of D?
1) 10^d is a factor of f
2)d>6
D=? - GMAT Prep
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This question can be easily done if we know the no of tens in f.
we know that f = 30!
if we want to know the no of tens in a factorial here is the method
lets say we want to know the no of tens in 30!
it will be [30/5] +[30/5^2] + [30/5^3] + ... so on till the division produces 0.
here the no of tens is 6 +1 + 0 = 7.
Now using d>6 we easily approach the answer
we know that f = 30!
if we want to know the no of tens in a factorial here is the method
lets say we want to know the no of tens in 30!
it will be [30/5] +[30/5^2] + [30/5^3] + ... so on till the division produces 0.
here the no of tens is 6 +1 + 0 = 7.
Now using d>6 we easily approach the answer
saurabh, can you please explain this a lil more.. how did you decide to divide by 5[email protected] wrote:[30/5] +[30/5^2] + [30/5^3] + ... so on till the division produces 0.
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if I want to know the no of tens I need to find 5*2 in a number, rite?
now if a number has 3 5s and 6 2s.
How many tens will it make .obviously it will be 3 as no of five is only 3.
So i have divided the number(factorial) by 5 to know the no of tens in a number.
I read this method in a book long ago and hence thought of applyin here too
Please let me know if you need further explanation
now if a number has 3 5s and 6 2s.
How many tens will it make .obviously it will be 3 as no of five is only 3.
So i have divided the number(factorial) by 5 to know the no of tens in a number.
I read this method in a book long ago and hence thought of applyin here too
Please let me know if you need further explanation
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I Agree the ans should be C
now the nos that we are considering here is 30!
so highest value of d would be the nos of trailing 0's in the nos 30!
now 30! is
1X2X3X4.........X29X30
now in this product a trailing 0 would be produced in two cases
1) when an even nos is multiplied by 5
2) when any nos is multiplied by 10
now in this product we have the nos
5,10,15,20,25,30
which would lead to trailing 0's
e.g. 4X5 or 5X6 will give u a trailing 0, take any ways
i.e product upto 6!= 4! X (5X6)
or think of this as product upto 5! is 3!X (4X5)
However 25 = 5X5 so we can visualise prodcut upto 25! as
23! X (24X5) X (5X26)
here 24X5 as well as 5X26 would produce trailing 0's so this would add 2 0's
hence total nos of 0's =7 (d>6)
so C is SUFF
now the nos that we are considering here is 30!
so highest value of d would be the nos of trailing 0's in the nos 30!
now 30! is
1X2X3X4.........X29X30
now in this product a trailing 0 would be produced in two cases
1) when an even nos is multiplied by 5
2) when any nos is multiplied by 10
now in this product we have the nos
5,10,15,20,25,30
which would lead to trailing 0's
e.g. 4X5 or 5X6 will give u a trailing 0, take any ways
i.e product upto 6!= 4! X (5X6)
or think of this as product upto 5! is 3!X (4X5)
However 25 = 5X5 so we can visualise prodcut upto 25! as
23! X (24X5) X (5X26)
here 24X5 as well as 5X26 would produce trailing 0's so this would add 2 0's
hence total nos of 0's =7 (d>6)
so C is SUFF
Regards
Samir
Samir