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If k is a positive integer and 5^k is a factor of

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ChandlerBong
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If k is a positive integer and 5^k is a factor of [#permalink] New post   07 Nov 2023, 08:45
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If k is a positive integer and \(5^k\) is a factor of the product of the odd integers from 99 to 199, inclusive, what is the greatest value of k?

A. 10

B. 13

C. 15

D. 20

E. 23
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gmatophobia
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If k is a positive integer and 5^k is a factor of [#permalink] New post   07 Nov 2023, 09:06
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ChandlerBong wrote:
If k is a positive integer and \(5^k\) is a factor of the product of the odd integers from 99 to 199, inclusive, what is the greatest value of k?

A. 10

B. 13

C. 15

D. 20

E. 23


As we are looking only at odd integers between 99 and 199, any number that has unit digit as \(5\) is divisible by 5.

105 → 5 * 21

115 → 5 * 23

125 → 25 * 5

135 → 5 * 27

145 → 5 * 29

155 → 5 * 31

165 → 5 * 33

175 → 25 * 7

185 → 5 * 37

195 → 5 * 39

Total number of 5s = 13

Option B
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Re: If k is a positive integer and 5^k is a factor of [#permalink] New post   02 Dec 2023, 01:41
gmatophobia - what is the formula for finding the product of odd/even numbers between y to z?
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Re: If k is a positive integer and 5^k is a factor of [#permalink] New post   19 Feb 2024, 23:47
Integers divisible by 5 but not 25: These contribute one factor of 5 each (e.g., 105, 115, 125, ..., 195). There are 10 such integers in the list.
Integers divisible by 25: These contribute two factors of 5 each (e.g., 125, 175). There are 2 such integers in the list.
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Re: If k is a positive integer and 5^k is a factor of [#permalink] New post   12 Mar 2024, 03:20
Why are the other odd #s like 1,3,7,9 not considered?
gmatophobia wrote:
ChandlerBong wrote:
If k is a positive integer and \(5^k\) is a factor of the product of the odd integers from 99 to 199, inclusive, what is the greatest value of k?

A. 10

B. 13

C. 15

D. 20

E. 23

As we are looking only at odd integers between 99 and 199, any number that has unit digit as \(5\) is divisible by 5.

105 → 5 * 21

115 → 5 * 23

125 → 25 * 5

135 → 5 * 27

145 → 5 * 29

155 → 5 * 31

165 → 5 * 33

175 → 25 * 7

185 → 5 * 37

195 → 5 * 39

Total number of 5s = 13

Option B

­
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Re: If k is a positive integer and 5^k is a factor of [#permalink] New post   20 Apr 2024, 15:15
unicornilove wrote:
Why are the other odd #s like 1,3,7,9 not considered?
gmatophobia wrote:
ChandlerBong wrote:
If k is a positive integer and \(5^k\) is a factor of the product of the odd integers from 99 to 199, inclusive, what is the greatest value of k?

A. 10

B. 13

C. 15

D. 20

E. 23

As we are looking only at odd integers between 99 and 199, any number that has unit digit as \(5\) is divisible by 5.

105 → 5 * 21

115 → 5 * 23

125 → 25 * 5

135 → 5 * 27

145 → 5 * 29

155 → 5 * 31

165 → 5 * 33

175 → 25 * 7

185 → 5 * 37

195 → 5 * 39

Total number of 5s = 13

Option B

­

­They arent divisible by 5
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Re: If k is a positive integer and 5^k is a factor of [#permalink] New post   22 Apr 2024, 21:58
unicornilove wrote:
Why are the other odd #s like 1,3,7,9 not considered?
gmatophobia wrote:
ChandlerBong wrote:
If k is a positive integer and \(5^k\) is a factor of the product of the odd integers from 99 to 199, inclusive, what is the greatest value of k?

A. 10

B. 13

C. 15

D. 20

E. 23

As we are looking only at odd integers between 99 and 199, any number that has unit digit as \(5\) is divisible by 5.

105 → 5 * 21

115 → 5 * 23

125 → 25 * 5

135 → 5 * 27

145 → 5 * 29

155 → 5 * 31

165 → 5 * 33

175 → 25 * 7

185 → 5 * 37

195 → 5 * 39

Total number of 5s = 13

Option B

­

­We need to find k which is the power of 5, hence we're looking for odd numbers divisible by 5. So odd numbers ending with 1,3,7,9 are not considered.
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Re: If k is a positive integer and 5^k is a factor of [#permalink]
22 Apr 2024, 21:58
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