I am looking for a qualified chartered accountant in my profile who is known for his excellence in the field.
To determine how many consecutive zeros the product of S will end with, we need to find the highest power of 10 that divides the product. This is equivalent to finding the highest power of 5 that divides the product, since the number of factors of 2 will always be greater than the number of factors of 5.
The primes in S are {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}.
There are 24 primes in S, so the product of S is:
2 x 3 x 5 x 7 x 11 x 13 x 17 x 19 x 23 x 29 x 31 x 37 x 41 x 43 x 47 x 53 x 59 x 61 x 67 x 71 x 73 x 79 x 83 x 89 x 97
We need to find the highest power of 5 that divides this product. To do this, we count the number of factors of 5 in the prime factorization of each number in S.
5 appears once: 5
5 appears once: 25
5 appears once: 35
5 appears once: 55
5 appears once: 65
5 appears once: 85
So, there are six factors of 5 in the product of S. However, we also need to consider the powers of 5 that arise from the factors 25, 35, 55, and 65.
25 = 5 x 5 appears once: 25
35 = 5 x 7 appears once: 35
55 = 5 x 11 appears once: 55
65 = 5 x 13 appears once: 65
Each of these numbers contributes an additional factor of 5 to the product of S. Therefore, there are 6 + 4 = 10 factors of 5 in the product of S.
Since each factor of 5 corresponds to a factor of 10, we know that the product of S will end with 10 zeros. Therefore, the product of S will end with 10 consecutive zeros
12.5
A
995
one cat kill one rat six minutes
so 1 cat kill 100 rat willbe needed 6*100=600minutes
then 100 rates kill 50minutes means then 600/50=12
so the answer is 12
Let\: the\: total\: price \: be\: Rs. X\: then,
B= 2x/7 & A= \left ( x-2 \right )/7
So, A:B = 5x/7 : 2x/7 = 5 : 2
Let \: B’s \: capital\; be\: Rs.Y\: then\: \left ( 16000\ast 8 \right )/4y= 5/2
=> (16000\ast 8\ast 2)/(4\ast 5) = y
=> y = Rs. 12800
(34/17)*3+34
Doug won the race
Explanation-
The ratio of steps covered by me, Doug, and Anne is = 6:7:8
Since Distance covered in Me 21 steps = Distance covered by Doug 24 steps = Distance covered by Anne 28 steps
LCM (21, 24, 28) = 168
For a distance of 168 units, the ratio of the distance covered in each step is;
= 8 : 7 : 6
Therefore the ratio of speeds is;
= 8×6: 7×7: 6×8
= 48 : 49 : 48
Here, the speed of the Doug is more than the speed of me and Anne
Hence, Doug won the race
Therefore, the number of possible 13 digit numbers using 1, 2, 3, 4, 5 which are divisible by 4
= x 3 + x 2
= (3 + 2)
=
= 244140625 ways
a