Rithvik's Blog 11+

2 packets of crisps and 2 drinks costs £1.50. 2 packets of crisps and 1 drink costs £1.10. What would it cost me if I buy 3 packets of crisps and 4 drinks?

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?

You are told that 56% of the pupils in a class are girls. What is the smallest number of pupils the class could contain?

It takes 2 men 3 days to build a wall. To answer these questions, assume that all men work at the same rate all the time and take no breaks! You may use fractions, where necessary. How long would it take one man to build the wall? How long would it take one man to build 6 such walls? How long would it take 3 men to build 6 such walls? How long would it take 10 men to build 6 such walls? 

100 aliens attended an inter-species meeting on Mars. 76 of them needed breathing apparatus, 52 needed shaded goggles, but 23 aliens didn’t need either. How many aliens needed breathing apparatus goggles?

Draw the three views of this new shape below. The diagrams do not have to be to scale. A rough free-hand sketch is all that is required Front View                                         Side View                                                   Plan View

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.

At a busy railway station trains leave from platform 5 every 6 minutes and from platform 8 every 10 minutes. Trains leave from both platforms at 15:57. When do trains next leave both platforms at the same time?

Determine how many two-digit numbers satisfy the following property: when the number is added to the number obtained by reversing its digits, the sum is 132

 What is the sum of the distinct prime integer divisors of 2016?

A rectangular room is twice as long as it is wide. The perimeter of the room is 36m. What is the length of the room?

Of the 26 boys in a class, 21 are right-handed. If 10 of the boys in the class wear glasses, what is the least number of boys in the class who are both right-handed and wear glasses?

A farmer has 364 ewes and each ewe has either one or two new born lambs. If there are 468 lambs in total, how many of the ewes have twin lambs?

1) The average number of runs scored by a cricket team in an innings is 17. What was the total number of runs scored by all eleven players? 2) In this innings the opening pair of batsmen scored an average of 39.5 runs. What was the average score of the remaining nine members of the team?

10 teachers can mark 180 exam papers in 3 hours. It takes each teacher the same amount of time to mark each exam paper.  a) How many teachers would it take to mark 90 exam papers in 3 hours? b) How long would it take 5 teachers to mark 180 exam papers? c) How many exam papers could 20 teachers mark in 1 hour?

If there are 5 Mondays, 5 Tuesdays and 5 Wednesdays in January, on what day of the week will February 1st fall? (There are 31 days in January)

When my age is divided by 2, 3, 4 or 6 there is always a remainder of 1. But when divided by 7 there is no remainder. How old am I?

This pattern of 20 tiles is arranged as 4 rows and 5 columns. The outer tiles around the edge are white and the inner tiles are black. When I change the number of rows and columns in my pattern I continue to keep the outer tiles around the edge white.  a) Complete the following table: b) I have 24 black tiles. What is the smallest number of white tiles I can use to make one of my patterns? Show workings to prove that your answer is the smallest possible solution.

An apple, 2 oranges and 3 pears cost £2.10 altogether. An orange and a pear cost 64 pence. How much more does an apple cost than an orange?

A running track has a perimeter of 400 metres. Roger trains every morning by running around the running track until he has run a distance of 6 kilometres. How many times around the track does Roger run each morning?

Frances writes down four whole numbers. The average (mean) of her numbers is six. The difference between the smallest and largest numbers is five. The smallest number is four. She did not write down the number 5. What numbers did she write down?

On my wall I want to put some stickers of my favourite pop star Singing Steve. The space I have available is 55cm by 60cm and the stickers are each 15cm by 5cm. What is the maximum number of stickers I can fit on the wall?

My friend Sanjay is making a scale model of the London Ear (a famous landmark in London). The London Ear is 80m tall and his model is 150cm tall. What is the scale of the model, in its simplest form?

Julia thinks of a number. She multiplies it by 5 and then subtracts 14. The answer she gets is 46. What number did she originally think of?

The minute hand on a clock points exactly to the number 7. It is then turned anticlockwise by 240°. What number does it now point to?

Ravi has two sisters, Harsha and Harpreet. He likes to share out his sweets unfairly. One day he gives Harsha twice as many as he gives himself, and he gives Harpreet half as many as he gives himself. If there are 42 sweets in total how many does Ravi get?

The diagram below shows a road network connecting the villages A to H. The numbers between the letters show how far apart the villages are in miles. A route connects two villages by travelling along the straight lines. An example of a route from E to D is EF – FC – CD.

A football competition was held between five Year 6 teams. Each team played every other team once. How many games did the teams play in total?

In a scrabble tournament, players score 5 points for a win, 3 points for a draw and get 0 points if they lose. Part way through the tournament four of the players taking part, players, A, B, C and D, have played different numbers of games and have all lost at least one game. Note that there are other players playing in the tournament whose results are not listed here.

If 2⁴ x 3¹ = 2 x 2 x 2 x 2 x 3 = 48 and 2⁰ x 3² = 3 x 3 = 9 Using this method to set out your work and solve: 2² x 3³

There are twenty gifts stacked up into four piles.  The first pile has 3 less than the second pile.  The second pile has two more than the third pile.  The fourth pile has twice as many as the second pile.  How many gifts are in each pile?

When my age is divided by 2, 3, 4 or 6 there is always a remainder of 1. But when divided by 7 there is no remainder. How When my age is divided by 2, 3, 4 or 6 the multiple is always one higher. But when divided by 7 there is no remainder. How old am I?

One angle of an isosceles triangle is 80°. What are the other angles?  There are two possible solutions to this question.

 Snow White and the seven dwarves work in a mining company. As Chief Executive, Snow White earns as much as all the dwarves put together. Sneezy gets 24 gold galleons a day. Sleepy earns 50% more than Happy. Bashful earns twice as much as Grumpy who earns one more galleon than Sneezy. Doc gets 24 galleons a day more than Dopey and between them they get four times that of Sneezy. Sleepy earns seven-eighths of Sneezy’s salary.   Complete the table below to work out how much Snow White earns in a day

A top international bowler playing in a cricket match bowls a cricket ball at 90 miles per hour.  (a) How many miles would the ball travel in one minute?  (b) If a mile is 1760 yards, how many yards would the ball travel in one minute?  (c) How many yards does the ball travel in one second?  (d) If the distance the ball travels through the air from the point where the bowler bowls the ball to the point where it is hit by the batsman is 22 yards, how long is the ball travelling for? [8 marks] 7a 7b 7c 7d

A train leaves London and travels at a steady speed of 120mph to Edinburgh. Before reaching Edinburgh, the train stops in Leeds after travelling for one and a half hours. The distance from London to Edinburgh is 420 miles. Use this information to answer the following:  (a) How long does the train take to travel from London to Edinburgh? (b) How far is Leeds from London?

Jeff goes to the cinema. He buys a ticket for £5.75, popcorn for £1.50 and a drink for 76p. His return train fare is £3.80. If he leaves home with a £20 note how much change does he return with?

 When asked how many chickens and cows he had on his farm Mr Brown refused to answer directly, but he did say that the total number of heads 30 was and the total number of legs was 100. How many of each was there?

Bill sold his motor scooter to Tom for £120. After driving it for a few days, Tom discovered it was in such a broken-down condition that he sold it back to Bill for 30% less than he paid. The next day Bill sold it to Jack for £90. What is Bill’s profit on the final sale?

There are 27 students in Mrs Din’s class. Mrs Din buys 4 boxes of chocolates. There are 36 chocolates in each box. She shares out the chocolates equally amongst her 27 students.  (a) Work out the number of chocolates each student receives. (b) Work out the number of chocolates left over

 Sorry for the lack of posting. I have been busy with joining a new school I will try to start posting again ASAP

 At a railway station there are two platforms. At one platform, trains leave every 24 minutes and at the other every 30 minutes. If trains leave both platforms at 9 a.m., what time is it when trains next leave both platforms at the same time?

A twelve inch ruler is approximately 30 cm long. Use this fact to estimate each of the following:  The number of centimetres in 4 inches.  The number of inches in 5 centimetres.  The number of centimetres in 9 feet 10 inches.

A theme park wants to make more money. The director thinks that if she reduces the ticket price by one-third, the number of people who come to the theme park will double.  a. In 2016, the park made £360 from ticket sales. Tickets were £4.50. How much money does the director think the theme park will make in 2017?  b. In fact, the theme park makes £390. How many more people went to the theme park in 2017 compared to 2016?

Amy, Bella and Cara have twenty sweets altogether.  Amy says she has ten of the sweets. Bella says that Cara has one more sweet than Amy. Cara says that she has the most sweets.  Exactly one of them is lying. Who is lying? Explain briefly how you know

A bag contains 49 red balls and 1 blue ball. How many red balls should be removed for the bag to contain 90% red balls?

 I am keeping the last unanswered questions free for you to answer. Try and answer as many as you can!

The numbers 34 and 55 are two examples of two-digit numbers which are made up using the digits 3, 4 and 5. How many two-digit numbers in total can be made using some or all of the digits 3, 4 and 5? 

Four friends, Alex, Ben, Cory and Dani have lunch together. Although each eats a differently priced snack, they share the bill equally. Yesterday, this resulted in Alex paying £1 less than the cost of his snack, Ben paying £3 more, Cory £4 less and Dani paid £4. What was the actual price of the snack that each friend ordered?

Of the 26 boys in a class, 21 are right-handed. If 10 of the boys in the class wear glasses, what is the least number of boys in the class who are both right-handed and wear glasses?

How many ODD three digit numbers is it possible to make using the numbers 4, 5 and 7 if you are allowed to use each of the numbers more than once in a particular three digit number?

This is a question which needs you to be organised, and to work in a logical manner. Set your answers out clearly. Write down all the 3-digit numbers which can be made by using each of the digits 1, 2, and 3 once only

A ball is dropped and bounces up to a height that is 75% of the height from which it was dropped. It then bounces again to a height that is 75% of the previous height and so on. How many bounces does it make before it bounces to a height that is less than 25% of the original height?

Fazal has £2.60 and Gareth has £5.30. Gareth gives Fazal some 5p coins. Each boy now has the same amount of money. How many 5p coins did Gareth give Fazal?

The perimeter of a rectangle is 22cm. One of the sides has length 8cm. Calculate the lengths of the other three sides.

Jerry puts a cube against the floor and the walls in the corner of his room, as in diagram 1, then paints the faces that he can see. He therefore paints three faces. In the second corner he puts four cubes in a square on the floor in the corner and then puts one cube on top in the corner too as shown in diagram 2. If he paints all the faces he can see now, how many faces does he paint on the cubes in this corner?

This is not a question but a note for you. As exams are on their way, for the next five days, I will be posting three questions a day.  Afterwards, posting will be continued as normal with 1 question a day. Please contact rithvikmu@gmail.com for further questions

In Sydney Australia the time is 11 hours ahead of the UK. John decides to phone his Great Aunt Matilda at 2300 hours UK time on the 30th January. What is the time and date in Sydney when Matilda receives the call? John’s sister Penny goes one better and decides to visit Great Aunt Matilda. She leaves the UK at the same time that John makes his phone call. Given that the total journey time is 27 hours, what is the Sydney time and date when Penny arrives?

2 packets of crisps and 2 drinks costs £1.50. 2 packets of crisps and 1 drink costs £1.10. What would it cost me if I buy 3 packets of crisps and 4 drinks?

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?

How many different 3 digit numbers can you make from the digits 1, 1 and 3. You can use each digit as many times as you like.

10 teachers can mark 180 exam papers in 3 hours. It takes each teacher the same amount of time to mark each exam paper. (a) How many teachers would it take to mark 90 exam papers in 3 hours? (b) How long would it take 5 teachers to mark 180 exam papers? (c) How many exam papers could 20 teachers mark in 1 hour?

Alison, Bhavini and Catherine share a bag of sweets. Alison gets 5 more sweets than Bhavini and Catherine gets twice as many sweets as Alison. Catherine gets 22 sweets. How many sweets are there in the bag?

Jeff goes to the cinema. He buys a ticket for £5.75, popcorn for £1.50 and a drink for 76p. His return train fare is £3.80. If he leaves home with a £20 note how much change does he return with?

Billy is given some toffees by his father. He eats one and then shares the rest out equally between himself and Emily. He then eats another and then shares the rest out equally between himself and Detti. He eats one more and gives the last one to Sean. How many toffees did Detti get? How many toffees did Emily get? How many toffees did Billy have at the start?

At the end of 2011, there were 1234 members of Feel Fit Gym. During the year, 167 members had joined the gym and 38 had left. How many members were there at the start of 2011?

To find the digital root of a number, you add the digits repeatedly until you reach a single digit number. For example, the digital root of 169 is 7 because 1 6 9 16, and 1 6 7 The digital roots of the first 9 square numbers are given in the table below: (a) Complete the table of digital roots of the next nine square numbers.

In a money-bag there are an equal number of 2 pence and 5 pence pieces and no other coins. How many coins are in the bag altogether if the total amount of money is £1.26

When asked how many chickens and cows he had on his farm Mr Brown refused to answer directly, but he did say that the total number of heads was 30 and the total number of legs was 100. How many of each was there?

Each day a shoal of small fish increases in number by 50% but each night a shark eats 300 of them. So if there are 1000 fish on Monday morning, then there will be 1500 by Monday evening but only 1200 left by Tuesday morning! Complete the following tables showing the number of fish each morning.

8. A class of students is set a test with 20 questions. A correct answer scores 5 marks, but a wrong answer loses 3 marks. An answer space left blank scores 0 marks.  (a) Adil answers all of the questions, leaving no blank answer spaces and gets 12 right.  What is his score?   (b) Brett answers 6 out of the 20 questions correctly but leaves 8 answers spaces blank.  What is his score?

 What is the area of this triangle?

In a barn there are only horses and people. If there are 12 heads and 34 legs how many horses and how many people are there?

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?

 Can you find a four digit number which is reversed when multiplied by 9?

When each diagram below is complete the number in the middle of each group of 3 adjoining cells is the average of its two neighbours. Fill in the missing numbers.

 Compute: 1) 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 ....... + 99 + 100 2) 5 + 10 + 15 + 20 + 25 + ...... + 495 + 500

  How many different squares are there in total, taking into account all sizes and positions?

Ten runners, numbered 5 to 14 inclusive, take part in a race. There were no tied positions. Winston watched the race but forgot to write down the positions of the runners. Fortunately Winston is a mathematician and he remembered one fact about the number of each competitor. List all possible numbers of the competitors in the spaces below. Hence complete the table showing the final positions in the race. 1st Prime number 2nd Factor of 24  3rd Cube number 4th Multiple of 5  5th Factor of 187  6th Two-digit even number in which the first digit is smaller than the second 7th Two-digit number in which both digits are square numbers  8th Number which has exactly four factors 9th A square number 10th A number which is greater than 10

Ravi has two sisters, Harsha and Harpreet. He likes to share out his sweets unfairly. One day he gives Harsha twice as many as he gives himself, and he gives Harpreet half as many as he gives himself. If there are 42 sweets in total how many does Ravi get?

A new mobile phone app is sold for 79 pence per download and proves to be very popular so that 150 people are downloading the app every day. The person who created the app gets 44 pence every time it is downloaded and she gets paid at the end of each week. How many weeks will it take for her to have £2,000?

A large crate holds twelve cartons of milk whereas a small crate holds only four cartons. I have five large crates and twenty small crates available. What is the smallest number of crates in total that I could use to store 110 cartons of milk?

Pembury Youth centre held a Judo club on Tuesday evenings. At the beginning of the year the children’s heights were recorded on a chart. (The last 6 names are the girls names.)  Complete the chart for the four missing children using the information below.  1. Tina is the same height as Mark.  2. Faye is 20cm shorter than the tallest boy.  3. If Barry grew another 1 cm he would be the same height as the tallest girl.  4. Steven is 20cm taller than the shortest boy.  

It takes 2 men 3 days to build a wall. To answer these questions, assume that all men work at the same rate all the time and take no breaks! You may use fractions, where necessary. 1) How long would it take one man to build the wall? 2) How long would it take one man to build 6 such walls? 3) How long would it take 3 men to build 6 such walls? 4) How long would it take 10 men to build 6 such walls? 5) How long would it take 10 men to build x such walls? 6) How long would it take y men to build x such walls?

Amar (form captain), Brian (vice captain), Charles and Daniel are best friends in the same class at school.  They always like to stand next to each other in the lunch queue.  On Mondays it is a school rule that the form captain is at the front of the queue followed by the vice captain.  There are two ways in which these boys can queue up on a Monday: ABCD and ABDC.  On Tuesdays, the form captain must again queue up first but the remaining three boys can follow in any order.  There are six ways in which these boys can queue up on a Tuesday.  Four of these ways are listed below. Write down the remaining two: ABCD, ABDC, ACBD, ACDB, _______, _________  On Wednesdays there are no restrictions and all four boys can queue up together in any order.  In how many ways can this be done?

The average of a set of numbers is worked out by adding the numbers together and then dividing by the number of numbers. The average number of runs scored by a cricket player in a cricket team in an innings is 17. What was the total number of runs scored by all eleven players?

  If the number 40,505 is divided by 25 and then multiplied by 5, what is the final answer?

The new TV channel, Lazy Living, broadcasts for 98 hours a week. If two-sevenths of its output is devoted to make-over programmes and the rest to celebrity gossip, for how many hours each week does the channel broadcast programmes on celebrity gossip?

A person’s Body Mass Index (BMI) is worked out by dividing their weight (in kilograms) by the square of their height (in metres). A person is then classified as “underweight”, “normal”, “overweight” or “obese” according to the following table: For example, Jill weighs 72 kg and is 1.82 m tall. Her body mass index is worked out as follows: If Jack weighs 84 kg and is 1.71 m tall, calculate his BMI.                                      

 Find the largest value of n for which 2 0  x 3 ⁿ  is less than 100.

Amy, Bella and Cara have twenty sweets altogether.  Amy says she has ten of the sweets. Bella says that Cara has one more sweet than Amy. Cara says that she has the most sweets.  Exactly one of them is lying.  Who is lying?  Explain briefly how you know.

 Write down two numbers which differ by 2 and multiply to 168.

The Eiffel tower in Paris was built in 1889 and is 1051 feet tall. In 1931 New York’s Empire State Building was completed which is 1472 feet tall.   How many years elapsed between the building of the Eiffel tower and the Empire State?

A train leaves London and travels at a steady speed of 120mph to Edinburgh. Before reaching Edinburgh, the train stops in Leeds after travelling for one and a half hours. The distance from London to Edinburgh is 420 miles. Use this information to answer the following: (a) How long does the train take to travel from London to Edinburgh?

In the triangles shown below each number is the sum of the two numbers directly underneath it. For example, 26 = 12 + 14 and 5 = 1 + 4. Complete the triangle of numbers.

Class 6A go on a Geography trip to Eastbourne and investigate the size of pebbles on the beach. Jonnie picks up seven small pebbles and measures their lengths in millimetres.  The lengths of the first six pebbles are:  1, 1, 1, 4, 7, 13  Assuming that the pattern that you observed above continues to hold, work out the length of Jonnie’s seventh pebble.

Four bells ring at intervals of 2, 8, 7 and 11 seconds.  If they are all rung at the same time, how many seconds will pass before they all ring at the same time again?

 Three bicycles are priced at £79, £80 and £84. If the shopkeeper decided to sell them for the same total amount, but made the three prices equal, what would each cost?

In the grid below, each symbol represents a number. The total of each row and column is shown.  Work out which number each symbols represent.

The notation 4! is used as an abbreviation for the product 4 * 3 * 2 * 1 so that 4! = 24.  Similarly, 9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 * =  362880. Work out: 3! 10! 100!/98!

The symbol ϕ represents a mathematical rule.  The rule for ϕ is “add the two numbers and then multiply their sum by the second number”.  For example, 2 ϕ 3 = (2 + 3) × 3 = 5 × 3 = 15  Work out: 1) 2 ϕ 6 2) 1/2 ϕ 3

2 packets of crisps and 2 drinks costs £1.50. 2 packets of crisps and 1 drink costs £1.10. What would it cost me if I buy 3 packets of crisps and 4 drinks?

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?