acutetrader Posted July 21, 2005 Share Posted July 21, 2005 1. If n is the greatest positive integer for which 10n is a factor of 24! , then n =? 2. A ball was dropped from a certain height. On each bounce it rose straight up exactly 3/4 of the height of the previous fall. When it reached the ground at the third times, it had travelled 2146 cm. What is the origin height (approximately)? 3. K(n+1)=2Kn+1, K1=1, K4=? Try it first, I'll post OA later. Quote Link to comment Share on other sites More sharing options...
gmat0805 Posted July 21, 2005 Share Posted July 21, 2005 2. reqd. distance = h + 2*(3/4h) + 2*(3/4)^2 *h = 2146 h(1+1.5+1.125) = 2146 h = 2146/3.625 = 592 cm. 3. K(4) = 2K(3) + 1 = 2( 2K(2) + 1) + 1 = 4K(2) + 3 = 4( 2K(1) + 1) + 3 = 8K(1) + 7 = 15. For 1. you meant 10^n (not 10n) ? Quote Link to comment Share on other sites More sharing options...
adcambridge Posted July 21, 2005 Share Posted July 21, 2005 for 1 ans n=1000 ? there are 4 5s i.e 5^4 and 17 2s i.e 2^17 in 24! multiples of 10 will be 5^4 * 2^4 =10n (if the question is 10^n then n=3) n =1000 Quote Link to comment Share on other sites More sharing options...
fensterkreuz Posted July 21, 2005 Share Posted July 21, 2005 1) 24! = 24 * 23 * 22 ... * 2 - There are no very much multiples of 10 in this, just 10 and 20. - n should be the biggest of which 10 is a factor of 24! so n=2 because n*10 = 20 which is the biggest mulitiple of 10 in 24! But don't hit me, if I'm wrong. 2) same as gmat0805 has .. 592cm. 3) don't understand the question Quote Link to comment Share on other sites More sharing options...
800needed Posted July 21, 2005 Share Posted July 21, 2005 I think your number 2 is wrong. How can a ball that was dropped from 592 cm bounce higher on it's first bounce? I think the solution (which is long math work) should be: X*(3/4)^3=2,146 X=2146*64/27=137344/27= (about) 5,086 cm. Correct me if I am wrong though cause I am extremely tired today.:sleepy: Quote Link to comment Share on other sites More sharing options...
gmat0805 Posted July 22, 2005 Share Posted July 22, 2005 How can a ball that was dropped from 592 cm bounce higher on it's first bounce? 800needed, 2146 is the total distance travelled by the ball after 3 bounces. NOT the height it rose after the 3 bounces. Quote Link to comment Share on other sites More sharing options...
800needed Posted July 22, 2005 Share Posted July 22, 2005 Yup, completely missread. I need some rest. Quote Link to comment Share on other sites More sharing options...
Dimas Posted July 22, 2005 Share Posted July 22, 2005 Q1: If 10n is a factor of 24! then: 24! / 10n = integer if n = 23! then 24, which is the remainder, is not divisible by 10. The problem is in the number 5 which is not avilable except for 20. Accordingly, 24! / 19! = 24*23*......*20 this last number is divisible by 10. The biggest n is 19! Q2: 592 cm Q3: 15 Quote Link to comment Share on other sites More sharing options...
gmat0805 Posted July 22, 2005 Share Posted July 22, 2005 Q1: If 10n is a factor of 24! then: 24! / 10n = integer if n = 23! then 24, which is the remainder, is not divisible by 10. The problem is in the number 5 which is not avilable except for 20. Accordingly, 24! / 19! = 24*23*......*20 this last number is divisible by 10. The biggest n is 19! Q2: 592 cm Q3: 15 If 10n is a factor of 24! then: I think the biggest n will be simply 24!/10. Quote Link to comment Share on other sites More sharing options...
andyecon Posted July 22, 2005 Share Posted July 22, 2005 I agree with gmat0805 on part 1. We have: 24! = 10n*k for n, k integers. It would seem then, to maximize n, we should take k = 1. Thus we have 24! = 10n, where n should be the maximum n possible. We would then get simply n = 24!/10. Quote Link to comment Share on other sites More sharing options...
800Bob Posted July 22, 2005 Share Posted July 22, 2005 I'm sure that question 1 is supposed to read: 1. If n is the greatest positive integer for which 10^n is a factor of 24! , then n = ? And question 3 should be: 3. K[sub(n+1)]=2K[subn]+1, K[sub1]=1, K[sub4]=? Quote Link to comment Share on other sites More sharing options...
fmku Posted July 22, 2005 Share Posted July 22, 2005 1. If n is the greatest positive integer for which 10n is a factor of 24! , then n =? Greatest possible integer which is a factor of 24! = 24!. Therefore 10n = 24! n = 24! / 10. Quote Link to comment Share on other sites More sharing options...
acutetrader Posted July 22, 2005 Author Share Posted July 22, 2005 1. We need to find the no. of 10's in 24!. A 10 is obtained either in the form of a no. ending in zero or with the multiplication of a term ending in 5 & and an even no. With these, we get only 4 zero's in 24! => n=4 2. 582cm 3. K(n+1)=2kn+1,k1=1,k4=? K1 = 1 K2 = 2(1)+1 = 3 K3 = 2(3)+1 = 7 K4 = 2(7)+1 = 15 **The 1st question is not OA!, please advice if it's wrong** 1. If n is the greatest positive integer for which 10n is a factor of 24! , then n =? 2. A ball was dropped from a certain height. On each bounce it rose straight up exactly 3/4 of the height of the previous fall. When it reached the ground at the third times, it had travelled 2146 cm. What is the origin height (approximately)? 3. K(n+1)=2Kn+1, K1=1, K4=? Try it first, I'll post OA later. Quote Link to comment Share on other sites More sharing options...
daipayan_b Posted July 22, 2005 Share Posted July 22, 2005 I'm sure that question 1 is supposed to read: 1. If n is the greatest positive integer for which 10^n is a factor of 24! , then n = ? So how do we solve it...considering its 10^n. Quote Link to comment Share on other sites More sharing options...
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