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# If d is a positive integer and f is the product of the first

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Manager
Joined: 29 May 2017
Posts: 105
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability
Re: If d is a positive integer and f is the product of the first  [#permalink]

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30 Aug 2018, 15:22
Bunuel wrote:
If d is a positive integer and f is the product of the first 30 positive integers, what is the value of d?

(1) 10^d is a factor of f --> $$k*10^d=30!$$.

First we should find out how many zeros $$30!$$ has, it's called trailing zeros. It can be determined by the power of $$5$$ in the number $$30!$$ --> $$\frac{30}{5}+\frac{30}{25}=6+1=7$$ --> $$30!$$ has $$7$$ zeros.

$$k*10^d=n*10^7$$, (where $$n$$ is the product of other multiples of 30!) --> it tells us only that max possible value of $$d$$ is $$7$$. Not sufficient.

Side notes: 30! is some huge number with 7 trailing zeros (ending with 7 zeros). Statement (1) says that $$10^d$$ is factor of this number, but $$10^d$$ can be 10 (d=1) or 100 (d=2) ... or 10,000,000 (d=7). Basically $$d$$ can be any integer from 1 to 7, inclusive (if $$d>7$$ then $$10^d$$ won't be a factor of 30! as 30! has only 7 zeros in the end). So we cannot determine single numerical value of $$d$$ from this statement. Hence this statement is not sufficient.

(2) d>6 Not Sufficient.

(1)+(2) From (2) $$d>6$$ and from (1) $$d_{max}=7$$ --> $$d=7$$.

Hope it helps.

Since it did NOT say "what is the greatest value of d", that is the reason why 1 was not sufficient. correct?
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Joined: 02 Sep 2009
Posts: 50627
Re: If d is a positive integer and f is the product of the first  [#permalink]

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30 Aug 2018, 20:16
Mansoor50 wrote:
Bunuel wrote:
If d is a positive integer and f is the product of the first 30 positive integers, what is the value of d?

(1) 10^d is a factor of f --> $$k*10^d=30!$$.

First we should find out how many zeros $$30!$$ has, it's called trailing zeros. It can be determined by the power of $$5$$ in the number $$30!$$ --> $$\frac{30}{5}+\frac{30}{25}=6+1=7$$ --> $$30!$$ has $$7$$ zeros.

$$k*10^d=n*10^7$$, (where $$n$$ is the product of other multiples of 30!) --> it tells us only that max possible value of $$d$$ is $$7$$. Not sufficient.

Side notes: 30! is some huge number with 7 trailing zeros (ending with 7 zeros). Statement (1) says that $$10^d$$ is factor of this number, but $$10^d$$ can be 10 (d=1) or 100 (d=2) ... or 10,000,000 (d=7). Basically $$d$$ can be any integer from 1 to 7, inclusive (if $$d>7$$ then $$10^d$$ won't be a factor of 30! as 30! has only 7 zeros in the end). So we cannot determine single numerical value of $$d$$ from this statement. Hence this statement is not sufficient.

(2) d>6 Not Sufficient.

(1)+(2) From (2) $$d>6$$ and from (1) $$d_{max}=7$$ --> $$d=7$$.

Hope it helps.

Since it did NOT say "what is the greatest value of d", that is the reason why 1 was not sufficient. correct?

Yes. The question asks: WHAT is the value of d?
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Joined: 13 Sep 2018
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Re: If d is a positive integer and f is the product of the first  [#permalink]

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14 Sep 2018, 16:10
Bunuel wrote:
If d is a positive integer and f is the product of the first 30 positive integers, what is the value of d?

(1) 10^d is a factor of f --> $$k*10^d=30!$$.

First we should find out how many zeros $$30!$$ has, it's called trailing zeros. It can be determined by the power of $$5$$ in the number $$30!$$ --> $$\frac{30}{5}+\frac{30}{25}=6+1=7$$ --> $$30!$$ has $$7$$ zeros.

$$k*10^d=n*10^7$$, (where $$n$$ is the product of other multiples of 30!) --> it tells us only that max possible value of $$d$$ is $$7$$. Not sufficient.

Side notes: 30! is some huge number with 7 trailing zeros (ending with 7 zeros). Statement (1) says that $$10^d$$ is factor of this number, but $$10^d$$ can be 10 (d=1) or 100 (d=2) ... or 10,000,000 (d=7). Basically $$d$$ can be any integer from 1 to 7, inclusive (if $$d>7$$ then $$10^d$$ won't be a factor of 30! as 30! has only 7 zeros in the end). So we cannot determine single numerical value of $$d$$ from this statement. Hence this statement is not sufficient.

(2) d>6 Not Sufficient.

(1)+(2) From (2) $$d>6$$ and from (1) $$d_{max}=7$$ --> $$d=7$$.

Hope it helps.

Thanks a lot! That helps much
Re: If d is a positive integer and f is the product of the first &nbs [#permalink] 14 Sep 2018, 16:10

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