Solution:

Step 5 is invalid, because we are dividing by (x-y), and since x=y, we are thus dividing by 0. This is an invalid mathematical operation (division by 0), and so by not following basic mathematical rules

Solution:

Very large hands.

Solution:

Day 1:
Alibaba Give 1kg gold bar.

Day2:
Now Alibaba gives 2kg gold bar and takes back 1kg gold bar back.

Day3:
Alibaba gives 1kg gold bar.

Day4:
Alibaba gives 4kg gold bar and take back 1kg gold bar back

Day5:
Alibaba gives 1kg gold bar.

Day6:
Alibaba gives 2kg gold bar and takes back 1kg gold bar back.

Day7:
Alibaba gives 1kg gold bar.

Solution:

You just need to check $150 bag.

Explanation:
Note: All bags labels are incorrect.
Case 1: If it contains $100 bill, then
A) Current bag contains $200 bills
B) $100 bag contains $150 bills
C) $200 bag contains $100 bills

Case 2: If it contains $50 bill, then
A) Current bag contains $100 bills.
B) $100 bag contains $200 bills
C) $200 bag contains $150 bills

Solution:

63.984375

Explanation:
This question is hypothetical because you cannot transact in fractions in bank account. The following is the solution:

Year Amount Interest and Deduction
Start 63.984375
Y1 End 62.968750 63.984375 * 2 - 65
Y2 End 60.937500 62.96875* 2 - 65
Y3 End 56.875000 60.9375 * 2 - 65
Y4 End 48.750000 56.875 * 2 - 65
Y5 End 32.500000 48.75 * 2 - 65
Y6 End 0.000000 32.5 * 2 - 65 = 0

Solution:

As shown in the picture below.
Cut 1 : Cut the cake across the diameter.
Cut 2 : Cut horizontally and you will get 4 equal pieces of cake
Cut 3 : Cut horizontally from other side and you will get 8 equal pieces of cake

Solution:

1/3

Explanation
Assuming T1 is the Toy for brother1, T2 is the toy for brother2 and T3 is the toy for brother3.

Following are the possible cases for toys distribution:

Boy1 Boy2 Boy3
T1 T2 T3
T1 T3 T2
T2 T1 T3
T2 T3 T1 .... (A)
T3 T1 T2 .... (B)
T3 T2 T1

In both steps (A) & (B), no one gets the correct toy.
Therefore probability that none brother can get the own toy is 2/6 = 1/3

Solution:

Mr. Orange is wearing a Green shirt.
Mr. Pink is wearing an Orange shirt.
Mr. Green is wearing a Pink shirt.

One should notice that the person wearing Green shirt agreed to Mr. Pink's statement which implies that Mr. Pink is not wearing Green. Obviously, he cannot be wearing a Pink shirt which is why he must be wearing an Orange shirt.

Now, we can easily deduce that the Green shirt is being worn by Mr. Orange and the Pink shirt by Mr. Green since they must be wearing a color different than their names.

Solution:

A) Fill 5 ml gallon ( 5mlGallon - 5, 3mlGallon - 0)
B) Transfer to 3 ml gallon (5mlGallon - 2, 3mlGallon - 3)
C) Empty 3 ml gallon ( 5mlGallon - 2, 3mlGallon - 0)
D) Transfer 2 ml from 5 ml gallon to 3 ml gallon (5mlGallon - 0, 3mlGallon - 2)
E) Fill 5 ml gallon(5mlGallon - 5, 3mlGallon - 2)
F) Transfer 1 ml from 5 ml gallon to 3 ml gallons(5mlGallon - 4, 3mlGallon - 3)

Solution:

18

Explanation:
More minutes implies more tea.
More women implies more tea.

The time become twice (3 minutes / 1.5 minutes).
women become six times (9 / 1.5).

Number of tea = 2 * 6 * Original(1.5)
= 18