Grupo orsa. Interview Questions, Process, and Tips

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

no

x (A to B by car) + y (B to A by cycle) is 7 hours

x (A to B by car) + x (B to A by car) is 7 minus 3 is 4 hours

2x is 4 and hence x is 2

2 + y is 7 and hence y is 5

y (A to B by cycle) + y (B to A by cycle) is 5 + 5 is 10 hours

72

15a=45

Let the total number of matches to played in the tournament be ‘x’.

Given that A county cricket team has won 10 matches and lost 4.

That means total number of matches played = 14.

So,

= > 70% of x = 14

= > (70/100) * x = 14

= > 70x = 1400

= > x = 20.

So, the number of matches to be played = 20.

They have a record of exactly 75% wins = 20 * 75/100

= > 15.

Therefore, the number of matches should the team win = 15 – 10 = 5.

Hope this helps!

I solve it as the 280m train being stationary… and the 120m train moving at (42+30) = 72kph…. or 20mps

The front of the train will have to go 280m to pass the stationary train plus another 120m for the backs to clear… that is 400m in all.

The time to travel 400m at 20mps is 20secs

1728

I have been teaching some students for 1 year.

b

Question is wrong i think