Leonteq Interview Questions, Process, and Tips

600

time (dist covrd by husband) (dist covrd by wife)
0.5hr 20 miles 0 miles
1 hr 40 miles 25 miles
1.5 hr 60 miles 50 miles
2 hrs 80 miles 75 miles
2.5 hrs 100 miles 100 miles
Therefore wife catches up after 2.5 hrs..

Let the revolutins made by bigger wheel is: x
then revolution by smaller wheel will be: x+10
Now, the distance covered by both wheels will be same.
So,
7(x+10)=9x
7x+70=9x
70=2x
35=x
so distance travelled=9*35=315
or 7*45=315

523

Cousin

North-east

Maximum number of edges = 9. Start from one corner. Select any face including that corner. Complete a square (4 edges) around the face to reach at the starting corner point . Now, move to the opposite face through the edge joining them and passing through the starting point(1 edge). Now, complete the square of edges around this face(4 edges). Total = 4+1+4 = 9 edges

If a blue stone is thrown into a red sea, several things could happen depending on the context and the properties of the stone and the sea:

Symbolically: Since blue and red are contrasting colors, the interaction of a blue stone in a red sea could be seen as a visual or metaphorical contrast. It could represent a stark difference or an unexpected element introduced into an existing situation.

Scientifically: In reality, the color of the stone and the sea would not have a direct physical impact on each other. The stone would sink or float based on its density and the water’s buoyancy. The color of the water, whether red or any other color, does not change the fundamental principles of objects interacting with liquids.

It’s important to note that red seas, in the context of bodies of water, typically do not exist naturally. The phrase “red sea” is often used metaphorically or symbolically rather than referring to an actual body of water with a red color.

Let’s assume the length of each train is ‘L’ and the speeds of the two trains are ‘V₁’ and ‘V₂’ respectively.

When the trains are moving in the opposite direction, their relative speed is the sum of their individual speeds. The total distance they need to cover is the sum of their lengths. Since they cross each other completely in 5 seconds, we can set up the following equation:

(V₁ + V₂) × 5 = 2L

When the trains are moving in the same direction, their relative speed is the difference between their individual speeds. The total distance they need to cover is the difference between their lengths. Since they cross each other completely in 15 seconds, we can set up the following equation:

(V₁ – V₂) × 15 = 2L

Now, let’s solve these equations to find the ratio of their speeds.

From the first equation, we have:
(V₁ + V₂) × 5 = 2L
V₁ + V₂ = (2L) / 5

From the second equation, we have:
(V₁ – V₂) × 15 = 2L
V₁ – V₂ = (2L) / 15

Let’s add these two equations together:
V₁ + V₂ + V₁ – V₂ = (2L) / 5 + (2L) / 15
2V₁ = (6L + 2L) / 15
2V₁ = (8L) / 15
V₁ = (4L) / 15

So, the speed of the first train is (4L) / 15.

Now, let’s substitute this value back into the first equation to find V₂:
(4L) / 15 + V₂ = (2L) / 5
V₂ = (2L) / 5 – (4L) / 15
V₂ = (6L – 4L) / 15
V₂ = (2L) / 15

Therefore, the speed of the second train is (2L) / 15.

The ratio of their speeds is given by:
(V₁ / V₂) = ((4L) / 15) / ((2L) / 15)
(V₁ / V₂) = 4L / 2L
(V₁ / V₂) = 2

So, the ratio of their speeds is 2:1.

66.66%

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

Conclusion 1 follows

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

22

35 hours