Arrange the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 above and below the division line in a manner that the thus formed fractions equals to 1/3.
You can use one number only once.
Hint:
The numerator will have four digits and the denominator will have five digits.
5832/17496
This fraction will result in 1/3.
A man had seven children. Upon receiving his salary, he called all of them. He had $100 with him to give to his children. He decided to start with the youngest child and then give $2 more than each younger child to his next elder child.
For example, if he gives $x to the youngest child, he will give $(x+2) to the next one, $[(x+2) + 2] to the next one and so on.
Can you find out how much did the youngest one receive?
The youngest child received $16.
There are four numbers given to you: 2, 3, 4 and 5. You are allowed to use only two mathematical symbols: + and = and come up with a mathematically true equation.
Can you do it?
PS- You can't repeat the symbols or numbers.
3^2 = 4 + 5
(^ is used for squaring the term, it is not a mathematical symbol.)
You are given a cube that is made with the help of 10x10x10 smaller cubes summing up to a total of 1000 smaller cubes. You are asked to take off one layer of the cubes.
How many remain now?
512
A layer will mean to remove from all sides of the cube. Thus it would reduce the dimension be two not one. In this way only a cube of 8x8x8 will remain. This totals to be 512.
While boarding a bus you notice that there are 7 girls in the bus already. All the girls have 7 bags each. In each bag there are 7 adult cats. Each of the adult cat have 7 little one. Each of the cat has 4 legs.
Can you calculate the number of legs in the bus?
Every girl has seven bags comprising of seven adult cats each with seven little cats per adult cat.
Thus for one girl:
1 girl + 49 adult cats + 343 little cats
Since there are 7 girls:
7 girls + 343 adult cats + 2410 little cats
Now calculating the legs:
14 legs of girls + 10976 legs of cats (There are total 2744 cats with 4 legs each).
Thus total legs = 10990
Now I climbed aboard the bus as well, thus total number of legs = 10990 + 2 = 10992 legs
If we add two legs of the driver as well,
Total legs = 10992 + 2 = 10994
In the figure given with this question, place the numbers from 1 to 19 in the circles in a manner that each side of the triangle sums up to 17.
There has been a house on fire. The fireman is now standing in the middle rung of the ladder and trying to extinguish the fire. He climbs 6 rungs more but the heat and deadly flames make him climb down 10 rungs. When the fire is settling gradually, he climbs 18 rungs and reaches the top of the ladder for better access to the house.
Calculate the number of rungs in the ladder ?
29 rungs
Suppose he is standing on m at first which is the middle rung.
He climbs 6 rungs which makes his position to be m+6.
He climbs down ten rungs which makes his position to be (m+6-10) = m-4
He climbs 18 rungs to reach the top t which makes his position (m-4+18) = m+14
Now, m+14 = t
Which means there are 14 rungs above the middle rung and 14 rungs below the middle rung. Counting the middle rung as well, it makes a total of 29 rungs.
A car M starts from point A and a car N starts from point B and move towards opposite sides at a constant speed. The cars meet 500 yards from A for the first time. After reaching the opposite points, each of the car returns back without any break and this time, they meet 300 yards from B.
What is the distance between the two points A and B and what is the relation between the speeds of the two boats?
When the cars first meet, they have traveled a combined distance equal to the 1 length of the distance. When they meet the second time, they have travelled 3 lengths.
The elapsed time and distance for each of the cars is three times. Now when they meet the second time, M has traveled 500x3 = 1500 yards and since, it is 300 yards longer than the total distance between both the points, the distance is 1200 yards.
The ratio of M’s speed to the ratio of N’s speed is equal to the distance that they traveled before they met for the first time.
i.e. 500/(1200 – 500) = 5/7
There is a jar in which there are two types of candies – 20 blueberry and 16 strawberry. You perform the following steps:
1) You take out two candies.
2) If the two candies are of same flavor, you add a blueberry one otherwise, you add the strawberry one.
You repeat these two steps till there is just one candy remaining in the jar. Which flavored candy will be left?
Also, if you began with 100 blueberry candies and 93 strawberry candies, which flavor would have been the last one to remain?
Let us suppose that there are x blueberry candies and y strawberry candies. While removing the candies, there can be three possibilities:
1) 2 blueberry candies. In this case, you will replace one blueberry candy and so the jar will have x+1 blueberry and y-2 strawberry candies.
2) 2 strawberry candies. In this case, you will replace 1 blueberry candy and so the jar will have x-1 blueberry candies and y strawberry candies.
3) 1 blueberry and 1 strawberry. In this case, you will replace a strawberry candy and so the jar will have x-1 blueberry candies and y strawberry candies.
In this way at each step, we are either removing a blueberry candy or replacing 2 strawberry candies by 1 blueberry candy irreversibly till there is only one candy left. Thus each strawberry candy is equivalent to 2 blueberry candies.
Therefore, if there are odd number of strawberry candies, the last candy will be strawberry and if there are even number of strawberry candies, the last one will be a blueberry one.
We know that the number 7 is the prime followed by a cube. Which next number is also a prime followed by a cube ?
There is no number other than 7 that is a prime followed by a cube.
To prove, let us assume that n3-1 is a prime for n.
N2-1 = (n^1)(n2+n+1)
Now, n-1 divides n3-1.
If n-1>1, then we are done as it is a contradiction to n3-1 being a prime.