What will be the best approach to finding all the prime numbers less than 75 that leave an odd reminder when we divide them with 5?

Our product and our sum always give the same answer. Who are we?

Two friends were stuck in a cottage. They had nothing to do and thus they started playing cards. Suddenly the power went off and Friend 1 inverted the position of 15 cards in the normal deck of 52 cards and shuffled it. Now he asked Friend 2 to divide the cards into two piles (need not be equal) with equal number of cards facing up. The room was quite dark and Friend 2 could not see the cards. He thinks for a while and then divides the cards in two piles.

On checking, the count of cards facing up is same in both the piles. How could Friend 2 have done it ?

What am I?

If it took eight men ten hours to build a wall, how long would it take four men to build it?

Can you solve the below algebraic mathematical equation?

(J+O+I+N+T)3 = JOINT

What is the largest amount of money that you can possess in change and still if someone asks you for a dollar, you won't be able to give?

There is a basket full of hats. Three are white and two are black. Three men, Tom, Tim, and Jim, each take a hat out of the basket and put it on their heads without seeing the hat they selected or the hats the other men selected. The men arrange themselves so Tom can see Tim and Jim’s hats, Tim can see Jim’s hat, and Jim can’t see anyone’s hat. Tom is asked what color his hat is and he says he doesn’t know. Tim is asked the same question, and he also doesn’t know. Finally, Jim is asked the question, and he does know. What colour is his hat?

They came out at night, without being called.
They lost at day, without being stolen.
Who are they?

Below is the sum of symbols in each row and column in the figure. Analyzing the figure, can you find out the value of the symbols?