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3^q is a factor of (300!/100!) where q is a positive integer. What is

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3^q is a factor of (300!/100!) where q is a positive integer. What is  [#permalink]

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New post 31 Mar 2018, 04:30
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Question Stats:

54% (02:25) correct 46% (02:37) wrong based on 49 sessions

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3^q is a factor of (300!/100!) where q is a positive integer. What is the highest possible value of q?

A) 67
B) 89
C) 100
D) 114
E) 148

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3^q is a factor of (300!/100!) where q is a positive integer. What is  [#permalink]

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New post Updated on: 01 Apr 2018, 04:31
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sandysilva wrote:
3^q is a factor of (300!/100!) where q is a positive integer. What is the highest possible value of q?

A) 67
B) 89
C) 100
D) 114
E) 148


Total number of factors of 3 in 300!=148
Total number of factors of 3 in 100!=48

3^q=(3^148)/(3^48)=3^100

option c

Originally posted by kunalcvrce on 31 Mar 2018, 04:36.
Last edited by kunalcvrce on 01 Apr 2018, 04:31, edited 1 time in total.
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Re: 3^q is a factor of (300!/100!) where q is a positive integer. What is  [#permalink]

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New post 31 Mar 2018, 05:07
kunalcvrce wrote:
sandysilva wrote:
3^q is a factor of (300!/100!) where q is a positive integer. What is the highest possible value of q?

A) 67
B) 89
C) 100
D) 114
E) 148


Total number of factors of 3 in 300!=157
Total number of factors of 3 in 100!=57

3^q=(3^157)/(3^57)=3^100

option c
How did you calculate it?

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Re: 3^q is a factor of (300!/100!) where q is a positive integer. What is  [#permalink]

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New post 31 Mar 2018, 05:17
aghosh54 wrote:
kunalcvrce wrote:
sandysilva wrote:
3^q is a factor of (300!/100!) where q is a positive integer. What is the highest possible value of q?

A) 67
B) 89
C) 100
D) 114
E) 148


Total number of factors of 3 in 300!=157
Total number of factors of 3 in 100!=57

3^q=(3^157)/(3^57)=3^100

option c
How did you calculate it?

Sent from my Redmi 4 using GMAT Club Forum mobile app



the number of factors for 3 in 300!
[300/3]+[300/3^2]+[300/3^3]+[300/3^4]+[300/3^5]+[300/3^6]=157

formula is summation of [number/factor(increase the factor)]
you can do similarly for 100!

Hope u get it..
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Re: 3^q is a factor of (300!/100!) where q is a positive integer. What is  [#permalink]

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New post 01 Apr 2018, 03:00
1
Further explanations for the rule can be found here:
/forum/everything-about-factorials-on-the-gmat-85592.html (cant link because not 5 posts yet)
The principle of calculation done by kunalcvrce is correct, however, the divident and divisor should be 148/48, as 100/3 + 100/3^2 ... etc is 48
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Re: 3^q is a factor of (300!/100!) where q is a positive integer. What is  [#permalink]

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New post 01 Apr 2018, 04:20
kunalcvrce wrote:

Total number of factors of 3 in 300!=157
Total number of factors of 3 in 100!=57

[300/3]+[300/3^2]+[300/3^3]+[300/3^4]+[300/3^5]+[300/3^6]=157

formula is summation of [number/factor(increase the factor)]
you can do similarly for 100!

Hope u get it..


Still not sure how you calculated 157... If I calculate it, the number of factor 3 in 300! is 148 and in 100! it's 48 (still the same result though.

I think you went one step too far, 3^6 is already 729, and you "can't divide" 300 by 729.

Best,
T
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Re: 3^q is a factor of (300!/100!) where q is a positive integer. What is  [#permalink]

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New post 01 Apr 2018, 04:30
Tommy87HG wrote:
kunalcvrce wrote:

Total number of factors of 3 in 300!=157
Total number of factors of 3 in 100!=57

[300/3]+[300/3^2]+[300/3^3]+[300/3^4]+[300/3^5]+[300/3^6]=157

formula is summation of [number/factor(increase the factor)]
you can do similarly for 100!

Hope u get it..


Still not sure how you calculated 157... If I calculate it, the number of factor 3 in 300! is 148 and in 100! it's 48 (still the same result though.

I think you went one step too far, 3^6 is already 729, and you "can't divide" 300 by 729.

Best,
T


Hi Tommy,

Thanks for correcting it 148 and 48 only..
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Re: 3^q is a factor of (300!/100!) where q is a positive integer. What is &nbs [#permalink] 01 Apr 2018, 04:30
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