In a science lab, a petri dish hosts a healthy colony of yeast for an experiment. Now every minute, all the yeast cells divide into two. At noon, there was just a single cell of yeast and at 1:22, the Petri dish was half full. Can you calculate when the dish will be full of yeast?
Since at every minute, the cells of yeast are multiplying into two and at 1:22, the dish was half full, it will become full the very next minute i.e. at 1:23.
Can you find out which triangle will have a bigger area among the following?
1. A triangle with sides 300, 400 and 500
2. A triangle with sides 300, 400 and 700
1st
The first option will have a bigger area. This is because the second triangle is not possible.
According to the formula:
Side 1^2 + Side 2^2 = Side 3^2
Three cars are driving on a track that forms a perfect circle and is wide enough that multiple cars can pass anytime. The car that is leading in the race right now is driving at 55 MPH and the car that is trailing at the last is going at 45 MPH. The car that is in the middle is somewhere between these two speeds.
Right now, you can assume that there is a distance of x miles between the leading car and the middle car and x miles between the middle car and the last car and also, x is not equal to 0 or 1.
The cars maintain their speed till the leading car catches up with the last car and then every car stops. In this scenario, do you think of any point when the distance between any two pairs will again be x miles i.e. the pairs will be x distance apart at the same time ?
Not Possible
As per the question, the middle car is running right now approximately at 50 MPH. Therefore, with time, the distance between them will keep increasing by x miles every hour for a certain time. After that, it will start decreasing between the leading car and the last car till they meet.
Therefore, you will find no point where the distance between the cars is x miles again.
I have thought of a number that is made up by using all the ten digits just once. Here are a few clues for you to guess my number:
First digits is divisible by 1.
First two digits are divisible by 2.
First three digits are divisible by 3.
First four digits are divisible by 4.
First five digits are divisible by 5.
First six digits are divisible by 6.
First seven digits are divisible by 7.
First eight digits are divisible by 8.
First nine digits are divisible by 9.
The number is divisible by 10.
Can you find out the number ?
The number is 3816547290
One night, I thought of ways that can be used for creating a palindrome. So I decided that I will turn into a larger number by adding the reversed digits to the original number and keep doing it till I finally obtained a palindrome.
I am not sure if this process will always result in a palindrome eventually but I was able to produce a four digit palindrome. Can you guess my starting number?
My starting number was 192.
192 + 291 = 483
483 + 384 = 867
867 + 768 = 1635
1635 + 5361 = 6996
Alex and Martin are planning on a vacation. Alex says, "It will be better if we take the train to the hotel. We will reach faster."
To this, Martin says, "No. You are wrong. The train stops at halfway to the hotel and then we will have to walk the rest of the way. We should take the bikes to the hotel directly."
Alex says, "You are wrong."
Now, Alex takes the train while Martin takes the bike. The train travels with four times the speed of bike. The bike travels at twice the speed of walking.
Who do you think will reach the hotel first?
Martin
S = total distance to the hotel.
V = walking speed.
2V = bike speed.
8V = train speed.
A = time taken by Alex
M = time taken by Martin
A = (S/2)/8V + (S/2)/V = S/16V + S/2V
M = S/2V
Now if you notice, A exceeds M by S/16V. Therefore, Martin will reach the hotel first.
Can you find a number that lies one third of the distance between 1/3 and 2/3?
Let us find a bigger multiple first. Lets multiply the numerator and denominator by 9 in both the numbers.
Now, 1/3 = 9/27
And, 2/3 = 18/27
Clearly, 12/27 lies one third on the distance between the two numbers now.
Below, you will find the mathematical proof that 10 equals 9.99999…. But is that possible or there is something wrong about it? Can you find the error?
x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10
No error is present in this proof and 10 is actually equal to 9.99999…. The proof is absolutely correct.
You have $100 with you and you have to buy 100 balls with it. 100 is the exact figure and you cant go below or above the numbers and you have to use the entire $100. If there is no kind of tax applied how many of each of the following balls will you be able to buy:
Green Balls costing $6
Yellow Balls costing $3
Black Balls costing $0.10
Now, how many of each must you buy to fulfill the condition given?
1 green ball = $6
29 yellow balls = $87
70 black balls = $7
Detailed Explanation :
Let us denote the number of balls to be brought with a variable
p = green sponges
q = yellow sponges
r = black sponges
Now using a simple expression:
p + q + r = 100
6p + 3q + 0.1r = 100
Multiplying the first equation by 6 then 3 and subtracting the two equations, we get:
6p + 6q + 6r = 600
3p + 3q + 3r = 300
3q = 500 - 5.9r
3p = 2.9r - 200
Usually, we have three equations to solve three variables. However, we will manage with just two here because we know that p and q are non-negative integers.
If 3q >/= 0, then 500 - 5.9r >/= 0.
Using this, r
Also, if 3p >/= 0, then 2.9r - 200 > 0. This implies that r >/= 68.97.
Now, the number of black balls must be an even dollar amount or we will land up with a fraction. Considering the expressions, you know that there can be just two integers that can satisfy the condition while lying in between 68.97 and 84.75.
If we take r as 80 and solve the equations (the last two equations), we will get p = 10.67 and q = 9.33. But p and q must be integer and not fraction. Thus you can cancel out 80.
If we take r as 70, we will get p = 1 and b = 29.
Therefore following are the number of balls that we must buy:
1 green ball = $6
29 yellow balls = $87
70 black balls = $7
I engaged in a strange activity. My birthday was approaching and I decided to collect money for my birthday bash. On the first day of the month, I kept a dollar in my piggy bank, on the second, I kept two dollars and on the third, I kept three and so on.
On my birthday, I had a total of 276 dollars in my piggy bank. Can you find out on which day of the month was my birthday?
23rd
The easiest way to find out without engaging in any formula would be to simply add them:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 = 276
Thus, the birthday falls on the 23rd day of the month.