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If x is a positive integer and 50!/30^x is a positive integer, what is
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25 Feb 2020, 00:14
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Competition Mode Question If x is a positive integer and \(\frac{50!}{30^x}\) is a positive integer, what is the greatest possible value of x ? A. 11 B. 12 C. 13 D. 14 E. 15 Are You Up For the Challenge: 700 Level Questions
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Re: If x is a positive integer and 50!/30^x is a positive integer, what is
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25 Feb 2020, 00:37
30=2*3*5 Our bottle neck is 5 so we need to know how many 5 are in 50! we have for every 5 numbers 1 and on 25 and 50 we have 2 fives thus 10+2=12 if we have 12 fives is 50! we can have 30^12 as the greatest value
Ans (b)



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Re: If x is a positive integer and 50!/30^x is a positive integer, what is
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25 Feb 2020, 00:58
We need to Prime factorizing for 30 > 2*3*5 So, the maximum number for 2 will be calculated by: \(\frac{50}{2}\) + \(\frac{50}{2^2}\) + \(\frac{50}{2^3}\) + \(\frac{50}{2^4}\) + \(\frac{50}{2^5}\) = 25+12+6+3+1= 47 So, the maximum number for 3 will be calculated by: \(\frac{50}{3}\) + \(\frac{50}{3^2}\) + \(\frac{50}{3^3}\) = 16+5+1= 22 So, the maximum number for 5 will be calculated by: \(\frac{50}{5}\) + \(\frac{50}{5^2}\) = 10+2 = 12 As 30 is the combination of 2, 3 and 5  We take the minimum value of them, i.e.  12. 'B' is the winner
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Re: If x is a positive integer and 50!/30^x is a positive integer, what is
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25 Feb 2020, 02:54
If x is a positive integer and \(\frac{50!}{30^{x} }\) is a positive integer, what is the greatest possible value of x ?
\(30^{x}=2^{x}*3^{x}*5^{x}\) > In order to get the greatest possible value of x, finding the number of \(5s\) in \(50!\) is enough:
\([\frac{50}{5}]+[\frac{50}{5^{2}}]+...= 10+2 =12\) > the number of \(5s\) in \(50!\) \(>x = 12\)
The answer is B



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Re: If x is a positive integer and 50!/30^x is a positive integer, what is
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25 Feb 2020, 04:44
\(50!/(2^x . 3^x. 5^x)\)
The greatest value of positive integer x can be determined by following: \(50/5 + 50/(5^2) + 50/(5^3) = 10 + 2 + 0 = 12 \)
FINAL ANSWER IS (B) 12



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Re: If x is a positive integer and 50!/30^x is a positive integer, what is
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25 Feb 2020, 06:31
30 = 2*3*5 Highest value is 5 So, 50!/5 = 10 & 10!/5 = 2 Hence, Answer must be 10 + 2 = 12, Answer must be (B) 12
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If x is a positive integer and 50!/30^x is a positive integer, what is
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Updated on: 26 Feb 2020, 00:05
If x is a positive integer and \(\frac{50!}{30^x}\) is a positive integer, what is the greatest possible value of x ? A. 11 B. 12 C. 13 D. 14 E. 15 \(\frac{50!}{30^x}\) = \(\frac{50!}{2^x*3^x*5^x}\) Here x would take highest value from \(5^x\) since \(2^x\) would give value of x that would falsify the statement. \(\frac{50}{5}\) = 10 (highest power of 5 in 50!) \(\frac{50}{25}\) = 2 (highest power of 25 in 50!) 10 + 2 = 12 Hence highest power of 5 = 12. Answer B.
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Originally posted by lnm87 on 25 Feb 2020, 07:24.
Last edited by lnm87 on 26 Feb 2020, 00:05, edited 1 time in total.



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Re: If x is a positive integer and 50!/30^x is a positive integer, what is
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25 Feb 2020, 07:47
30^x = 5*2*3 ; to get highest possible value divide 50!/5 ; 50!/5 + 50!/25= 10+2; 12 IMO B
If x is a positive integer and 50!/30^x is a positive integer, what is the greatest possible value of x ?
A. 11 B. 12 C. 13 D. 14 E. 15



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Re: If x is a positive integer and 50!/30^x is a positive integer, what is
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25 Feb 2020, 08:23
I guess the answer is D. I think that the exponent must comprise all the 3s that you can find from 1 to 30, which are progressively in the numbers 3,6(3x2),9(3^2),12(3x4),15(3x5),18(3^2x2),21(3x7),24(3x8),27(3^3) and finally 30(3x10). In total they are 14, hence D.



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Re: If x is a positive integer and 50!/30^x is a positive integer, what is
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25 Feb 2020, 16:17
50!/30^x
30=3*2*5.......so if we can get the no.of 5's in 50! Then that would be sufficient to find X....as 5 is the greatest prime factor of 5
50! Consists of 11 5's
So the max value of X is 11
OA:A



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Re: If x is a positive integer and 50!/30^x is a positive integer, what is
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25 Feb 2020, 17:10
Quote: If x is a positive integer and 50!/30^x is a positive integer, what is the greatest possible value of x ?
A. 11 B. 12 C. 13 D. 14 E. 15 primefactors(30)=2,3,5 multiples of 5 in 50!: sum quotients 50/5+50/25=10+2=12 Ans (B)



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Re: If x is a positive integer and 50!/30^x is a positive integer, what is
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25 Feb 2020, 23:55
30^x = (5*3*6)^x Greatest possible value of x = 50/5 + 50/25 = 10 + 2 = 12 Answer: B



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Re: If x is a positive integer and 50!/30^x is a positive integer, what is
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28 Mar 2020, 03:29
Bunuel wrote: Competition Mode Question If x is a positive integer and \(\frac{50!}{30^x}\) is a positive integer, what is the greatest possible value of x ? A. 11 B. 12 C. 13 D. 14 E. 15 Are You Up For the Challenge: 700 Level QuestionsAsked: If x is a positive integer and \(\frac{50!}{30^x}\) is a positive integer, what is the greatest possible value of x ? 30 = 2*3*5 Power of 30 will depend on maximum power of 5 in 50! Power of 5 in 50! = 10 + 2 = 12 IMO B




Re: If x is a positive integer and 50!/30^x is a positive integer, what is
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28 Mar 2020, 03:29






