I am a prime number.
The double of myself is equal to the square of me.

which number am I?

Find the mistake in the below maths equations

A = 2
A(A-1) = 2(A-1)
A2-A = 2A-2
A2-2A = A-2
A(A-2) = A-2
A = 1

A boy and a girl are sitting on the porch.
"I'm a boy," says the child with black hair.
"I'm a girl," says the child with red hair.
If at least one of them is lying, who is which?

Two friends Smith and Andrew were talking about the bravery of their families. Smith told great stories about his courageous grandfather who fought for Britain in "World War I". Andrew told that his grandfather was so brave that in 1919 just after the war he was honoured with a bravery medal with the words "For our Courageous Soldiers In World War I" embedded into it. Smith knows that his friend is lying. How?

A Monkey, a squirrel, and an Eagle are racing to the top of the mango tree. Assuming all these animals are in perfect shape, Which animal will reach to Banana first?

Fate has decided that you will only be pleased to meet me when you need me

Maybe that is why, when I am working, I start working

However annoying I may be to the regulars, the little ones are always inspired

I will always be waiting if you try to reach me

How many of you can guess my name, let me see

John left on a horse on Thursday , was gone for two days, and came back on Thursday after completing his work. How did that happen?

Get total of 120 by using five zeros 0,0,0,0,0 and any one mathematical operator.
Do you ?

Outside a massage parlour, there is a board that reads
"I only massage those who do not massage themselves."

Reading the above statement, does the masseur massage himself?

A quarter is one-fourth of a dollar but Mr. John has changed the equation as below :

DOLLAR * 4 = QUARTER

Can you replace each letter with a digit to make the above solution correct?