Playing with Numbers quiz

The general form of 39 is:

100 x 4 + 10 x 0 + 7 is equal to:

Which of the following numbers is divisible by 9?

The sum of a two-digit number and the number obtained by reversing its digits is always divisible by:

The difference between a two-digit number and the number formed by reversing its digits is always divisible by:

A number is divisible by 5 if its units digit is:

If 24x is divisible by 3, where x is a digit, then x can be:

The sum of a three-digit number and the two numbers formed by cycling its digits is always divisible by:

A number is divisible by 10 if its units digit is:

The difference between a three-digit number and the number formed by reversing its digits is always divisible by:

Write 94 and 765 in general form. (2 marks)

Using the general form, explain why every number whose units digit is 0 is divisible by 10. (2 marks)

Without actual division, check whether 5826 is divisible by 2, 3, 5 and 9. (2 marks)

Take the number 52. Reverse its digits and add the two numbers. Divide the sum by 11 and compare the quotient with the sum of the digits of 52. (2 marks)

If 24x is a multiple of 9, where x is a digit, find x. (2 marks)

If 31z5 is a multiple of 9, where z is a digit, find the possible values of z. (2 marks)

Find the difference between 825 and 528 and show that it is a multiple of 99. What is the quotient? (2 marks)

Using the general form of a two-digit number, explain why the number is divisible by 2 only when its units digit is even. (2 marks)

Solve the cryptarithm 2AB + AB1 = B18. (2 marks)

Minakshi chose 64, reversed its digits and added the two numbers, then divided the result by 11. Show her working and explain why the answer equals the sum of the digits. (2 marks)

Solve the cryptarithm AB + 37 = 6A, explaining how the carry helps you. (3 marks)

Solve the cryptarithms, where different letters stand for different digits: (i) 1A x A = 9A (ii) AB x 5 = CAB (find all possible solutions). (3 marks)

Find all two-digit numbers which, when added to the number formed by reversing their digits, give 121. (3 marks)

A three-digit number has digits a, 0 and c (in that order), with a greater than c. The number exceeds its reverse by 594, and the sum of its digits is 8. Find the number. (3 marks)

(i) Find the smallest four-digit number with all different digits that is divisible by 9. (ii) Find the largest three-digit number with all different digits that is divisible by 9. (iii) Find the digit x if 6x4 is divisible by 9. (3 marks)

Read the passage and answer the questions. Ravi shows a trick to his class: "Think of a three-digit number. Reverse its digits. Subtract the smaller number from the larger and divide the result by 99. Your answer is the difference between the first and last digits of your number." (i) Carry out the trick with the number 849. (ii) Using the general form, explain why the trick always works. (iii) What happens if the first and last digits of the chosen number are equal? (5 marks)

Read the passage and answer the questions. Meena chose the number 256 and wrote the numbers 562 and 625 by moving the digits in a cycle. She added the three numbers and divided the sum by 37. (i) Find the sum of the three numbers. (ii) Find the quotient when the sum is divided by 37, and compare it with the sum of the digits of 256. (iii) Explain, using the general form, why the sum is always divisible by 37. (5 marks)

Read the passage and answer the questions. A sweet shop has 2736 laddoos to pack. The owner wants to pack all of them in boxes with no laddoo left over, and is deciding between boxes holding 3, 5, 9 or 10 laddoos. (i) Using divisibility tests, decide which box sizes can be used. (ii) How many boxes of 9 laddoos will be needed? (iii) If boxes of 5 are used, how many laddoos will be left over? (5 marks)

Read the passage and answer the questions. In a puzzle club, the leader writes: "AB + BA = 132, where AB is a two-digit number with tens digit A and units digit B." (i) Using the general form, find A + B. (ii) List all the possible numbers AB with A greater than B. (iii) If it is also given that A - B = 2, find the number AB. (5 marks)

Read the passage and answer the questions. Rahul claims that the remainder when a number is divided by 9 is the same as the remainder when the sum of its digits is divided by 9. He tests his claim on the number 4567. (i) Find the sum of the digits of 4567 and its remainder on division by 9. (ii) Divide 4567 by 9 and check Rahul's claim. (iii) Explain the reason using the general form of a number. (5 marks)

Using the general form of a three-digit number, prove the tests of divisibility by 9 and by 3. Draw a flowchart for testing divisibility by 3 and by 9 together, and apply it to 729, 615 and 838. (6 marks)

Explain the two reversing games for two-digit numbers (sum and difference) and the reversing game for three-digit numbers, using general forms. Illustrate each game with one example, and state the divisor and the quotient in each case. (6 marks)

Draw a Venn diagram with three circles showing the numbers from 1 to 30 that are divisible by 2, by 3 and by 5. Use it to list the numbers divisible by both 2 and 3, by both 3 and 5, and by all three. What do you notice about the numbers divisible by both 2 and 3? (6 marks)

Solve the following cryptarithms, explaining each step: (i) A + A + A = BA (ii) 12A + 6AB = A09 (iii) AB x 3 = CAB. (6 marks)

Ask a friend to choose a two-digit number, double its tens digit, add 5, multiply the result by 5 and then add the units digit. If you subtract 25 from the final answer you get the original number. Draw a flowchart of the trick, try it with 47, and use algebra with the general form 10a + b to prove why it always works. (6 marks)