Rithvik's Blog 11+

For each of the prime numbers in the table below: (a) Find the remainder when the prime number is divided by 4; and (b) Find whether the prime number can be expressed as the sum of two square numbers. If the prime number can be expressed as the sum of two square numbers, state the two square numbers. If the prime number cannot be expressed as the sum of two square numbers state “Not possible”. Complete the table below. The first two rows have been completed for you.

A perfect number is one in which all its factors (except the number itself) total to the number. For example 6 = 1 + 2 + 3 is a perfect number since the proper factors of 6 are 1, 2 and 3 and they total to 6. 12 is not a perfect number as its proper factors are 1, 2, 3, 4, 6 and they total 16. (a) Find one other perfect number between 20 and 30.

This mystery number has 4 digits. Every digit is an odd number. None of the digits is a 9. Every digit in the number is different. The smallest digit is in the thousands place. The greatest digit is in the ones place. This describes two possible numbers. The mystery number is the greater of those two numbers. What is the mystery number?

It takes a team of four people six hours to paint my fence. How long would a team of eight people have taken? One of my neighbours has a similar fence which is twice as long as mine.  She would like the work to be completed in less than five hours. What is the minimum number of people that she should employ?

We say that there is an even chance of getting a head when a coin is thrown. Which one of the following statements is definitely true?   A: There is an even chance that England will win the next football World Cup.  B: There is an even chance that I get one head and one tail when I toss a coin twice.  C: There is a greater than even chance that I get a 5 when I roll a single dice.  D: There is a less than even chance of picking a blue ball from a bag containing 3 blue and 2 red balls.  E: There is a less than even chance that a baby will be born somewhere in the world in the next minute

John came home from his vacation at his grandmother’s with 5 books. While he was away he bought 2 books at the bookshop and got 1 book as a present from his grandmother. During his stay at his grandmother’s, he also gave his cousin 4 books that he had finished. How many books did he take with him when he left for his holiday?

In an orchestra there are 60 children. If 1 5 play the recorder and 40% play the triangle, how many children play something else?

There are three islands close together near Australia:  Azure, Bounty, and Coconut  On the three islands live three types of guinea pig:  Pongos, Quangos and Ringos  The following are all true facts well known to sailors in this part of the world.  1. There are no Pongos on Bounty Island.  2. All the guinea pigs on Coconut Island are Ringos.  3. Pongos and Quangos are the only type of guinea pig on Azure Island.  A shipwrecked sailor lands on one of the islands. She sees a guinea pig which she thinks is a Ringo 1) Which island does the sailor think she is definitely not on? Later on she sees another guinea pig. She is not sure what it is but it is certainly different from the first kind of guinea pig 2) Which island is she definitely not on?