M4maths Previous Puzzles

08 Apr 2014 Solve

Upto how many integers we should take the product 1*2*3*4*5.......... to make 31 zeros at last of the number.

OPtion

1) 140
2) 130
3) 125
4) 110
5) 100
6) 105
7) 135
8) 115
9) 145
10)None of these

Solution

For obtaining 31 zeros at last of the number, 31 powers of 5 is necessary. Product 1*2*3*4*5……………upto 125
contain 5, 10 ,15………. 125. These 25 numbers are multiple of 5, besides it 25, 50, 75, 100, 125 contain a second 5 and 125 contains a third 5 hence total number of 5 = 25+5+1 = 31

Option 3)

Correct Option: 3 Best Solution (24)

Dr.Dipin Singh   10 years AGO

No of zeros at last of product 1*2*3*4*5.......n = n/5 +n/25+n/125 =31
n(25+5+1)=31*125
31*n=31*125
n=125 .... option 3

Like? Yes (10) | No (3)  

Aman   10 years AGO

As
125/5 +125/25 +125/125= 25+5+1=31
hence we should take 125 integers for the product 1*2*3*4*5.......... to make 31 zeros at last of the number.

Like? Yes (9) | No (3)  

Saranjit Singh   10 years AGO

zeros at last of number in n!= n/5 +n/25+n/125+n/625
when n=125,
no. of zeros= 125/5+125/25+125/125=31

Like? Yes (7) | No (2)  

Pargat Pal Singh   10 years AGO

1*2*3*4*5.....n = n!
no of zeros at end of n! is given by
n/5 +n/25+n/125.
so n/5 +n/25+n/125 = 31
n=125

Like? Yes (7) | No (3)  

llamar   10 years AGO

1-10 you get 2 zero
10-20 u get 2 as well
...............upto 100 u get 21 zeros then after
100-110=>4 zero
110-120=>4 zeros
125 u get 2 zeros

Like? Yes (1) | No   

vishnuvardhan   10 years AGO

125!=
[125/5]+[125/25]+[125/125]=25+5+1=31

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Vaishali Dhiman   10 years AGO

ans is 125

Like? Yes (1) | No   

AMAN   10 years AGO

125/5=25,125/25=5,125/125=1,add them 31

Like? Yes (1) | No (2)  

ashish kumar   10 years AGO

for this the rule is
(N/5)+(N/5^2)+(N/5^3)+(N/5^4)+.......
take N =125 from option u will dirtectly able to tel l that this is answer.
(125/5)+(125/5^2)+(125/5^3)+.....
25+5+1=31
take only integers

Like? Yes (3) | No (4)  

MD SOHAIL AKHTER   10 years AGO

To calculate no. of zeroes let the no. be 125 then
125/5=25
25/5=5
5/5=1
now, adding all the quotient-25+5+1=31
total no. of zeroes =31
ans- 125

Like? Yes (3) | No (6)  

Md Shahid Akhter   10 years AGO

To calculate no. of zeroes let the no. be 125 then
125/5=25
25/5=5
5/5=1
now, adding all the quotient-25+5+1=31
total no. no. of zeroes =31
the no. will be 125

Like? Yes (2) | No (5)  

ASHISH MITTAL   10 years AGO

125/5=25
25/5=5
5/5=1
25+5+1=31

Like? Yes (1) | No (4)  

Ann Theressa   10 years AGO

For finding the number of trailing zeros at the end of a factorial(let it be n!), the equation is,

number of trailing zeros
= n/5 + n/5^2 + n/5^3+....+n/5^k
where 5^(k+1) > n

Here number of trailing zeros = 31

n/5 + n/25 + n/125+ ... = 31

Solving n = 125

Like? Yes (1) | No (4)  

AVIJIT   10 years AGO

125/5=25
125/25=5
125/125=1
25+5+1=31

Like? Yes (1) | No (4)  

ABY   10 years AGO

125/5=25
125/25=5
125/125=1
25+5+1=31

Like? Yes (1) | No (4)  

ABYSUP   10 years AGO

125/5=25
125/25=5
125/125=1
25+5+1=31

Like? Yes (1) | No (4)  

mohit gupta   10 years AGO

125!= to calculate zero in product we formula divide 125/5=25
125/25=5
125/125=1
total 25+5+1=31
hence c option

Like? Yes (1) | No (4)  

Mukesh Nayal   10 years AGO

the method is like this
125/5+125/5*5+125/5*5*5=31
no of zeroes are found by calculating the number of 5 for the factorial of a number.

Like? Yes (3) | No (6)  

VIKASH RAY   10 years AGO

We know to find out the zeros last in the number we should divide the number by 5
here the number of zeroes is 31 ....
so the last in the required sequence is---
31*5=125
so option 3 is correct.

Like? Yes (1) | No (4)  

Surya Narayana K   10 years AGO

Ans is 125 (option 3).
The formula for number of zeros in n! is n/5+(n/5^2)+(n/5^3)+....

Consider 140 = 140/5+140/25+140/125=28+5+1=34
130=130/5+130/25+130/125=26+5+1=32
125=125/5+125/25+125/125=25+5+1=31.

So answer is 125.

Like? Yes (1) | No (4)  

Sivanjali   10 years AGO

The formula for number of zeros in n! is n/5+(n/5^2)+(n/5^3)+....

Consider
125=125/5+125/25+125/125=25+5+1=31.

So answer is 125.

Like? Yes (1) | No (4)  

AJAY KUMAR   10 years AGO

ans=125
125/5-quotient 25
25/5-quotient 5
5/5-quotient 1
total no of zeros=25+5+1=31

Like? Yes (1) | No (4)  

shree   10 years AGO

because 4 multi give the 0 up to 10

Like? Yes (1) | No (6)  

Rajat Goyal   10 years AGO

Best Option

Like? Yes (1) | No (6)