Can you find out the value of x in the following equation?
(2^x) (30^3) = (2^3) (3^3) (4^3) (5^3)
(2^x)(30^3) = (2^3) (3^3) (4^3) (5^3)
(2^x)(30^3) = (120^3)
(2^x) = (120^3)/ (30^3)
(2^x) = (4^3)
(2^x) = 64
ln(2^x) = ln(64)
x ln(2) = ln(64)
x = ln(64)/ln(2)
x = 6
Thus x = 6.
You order chicken wings at KFC in the boxes of 6, 9 and 20. What is the largest number of wings that you cannot obtain by buying in any combination of the boxes?
43
You know that you can purchase any number of wings that is divisible by 3 but of course it should not be 3 itself. Thus, you should just try to purchase using the combinations of 9 and 6 boxes till the number is divisible by 3. If that number is not divisible by 3, then you have to use a box with 20. If the number that remains is divisible by 3, you are game. But if it is not divisible by 3, you can use a second box of 20. The number now will necessarily be divisible by 3.
Thus the largest number of wings that cannot be bought will come after buying two boxes of 20 and leaving a remainder that is divisible by 3:
3 + 20 + 20 = 43.
Suppose you drive to a picnic spot at 20 mph, then how fast you must go while returning back home on the same route such that your average speed becomes 40 mph?
infinite speed
Let us denote distance with d, time to get there by T, time to get back by t and the speed while travelling back with R.
Now by applying the simple time, distance and speed formula:
d = 20T
T = d/20
d = Rt
t = d/R
As you can see, we have the equations for both T and t now. We can now finally derive and equation for the round trip.
2d = 40(T + t)
2d = 40(d/20 + d/R)
2d = 40d(1/20 + 1/R)
1 = 20(R/20R + 20/20R)
20R = 20(R+20)
R = R + 20
You can clearly see that it is a paradox as to make the average speed 40 mph, you will have to travel back at an infinite speed. The faster you return, the quicker you can make it although your faster speed will offer a lesser impact on the average speed.
If you made the return trip instantly, it would be comparable to traveling double the distance in the same time that was taken on the one way trip.
Thus to reach the average speed of 40 mph, you must return with an infinite speed.
What does the following BrainBat signifies?
ABCDEFGHIJKLMNOPQRSTUVWYZ
QQQQQQQQQQQQQQQQQQQQQQQQQ.
No excuse.
It signifies that there is no X listed.
Before reading ahead, you must know the fact that only one of the person here is telling the truth.
A says that B is lying.
B says that C is lying.
C says both A and B are lying.
Can you find out who is speaking the truth?
B is speaking the truth.
A is lying when he says that B is lying. B is telling the truth when he says that C is lying. C is lying when he says that both A and B are lying since one of them is speaking the truth.
You are camping with your friends. You have a flashlight for any emergency and have brought 8 batteries along with you. Your brother calls to tell you that four of those batteries are already dead.
Your flashlight requires two working batteries to run. What is the least number of pairs you will need to test to guarantee that you can get the flashlight on ?
7
You must first divide the batteries in three groups: a group of two batteries and two groups of three batteries each. Now you have made sure that one of the group has two working batteries.
Now both the groups with three batteries can form three possible combinations and the group with two batteries has just one combination.
3 + 3 + 1 = 7.
There is a dressing drawer which contains the following colored socks in pairs: Purple, Magenta, Crimson, White, Yellow and Turquoise. Now, the socks are paired and each pair is together in the matching set. There is no light in the room and you open the drawer and pick up a pair. Then, without noticing any color, you keep them back and pick up again.
Can you calculate the probability that the pair of socks was Yellow both the times?
Whenever two events are independent, we calculate the probability of both occurring as:
P(A and B) = P(A) * P(B)
P(Yellow) = 1/6
P(Yellow and Yellow) = P(Yellow) * P(Yellow)
= 1/6*1/6
= 1/36
There was a blind beggar living on the footpath of a street. Suddenly on day, the beggars brother died. What was the relation of the blind beggar with the person who died ?
PS: Brother is not the answer.
The blind beggar was the sister of the person who died.
Can you find out a way through which you can make five squares out of the given figure by moving just six match sticks?
Many of you might have tried making five different squares but that was not asked in the question. See the figure for the explanation.