Try some past year questions?

Primary 6 - Find the greatest 4-digit number which when decreased by 1 is exactly divisible by 2, 3, 4, 5, 6 and 7

To keep this order, where should plate D be placed? Choose one of the following:

A) Before A        B) Between A and B          C) Between B and C           D) After C

Primary 6 - If all the numbers in the number pattern, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, … n, n, n, n add up to 1860, what is n?

Primary 6 - Three plates of fruits A, B, and C are arranged in increasing order of their total mass.

Primary 6 - Ten boys played Rock-Paper-Scissors to determine who was the smartest. Every boy played against each of the other boys once.                      In each game, the winner received 3 points, the loser received 0 points, and in case of a draw, each of the two boys received 1                      point each. The total number of points given was 125. How many games ended with a draw?

Answer:

 LCM of 2, 3, 4, 5, 6 and 7 = 420 Largest 4-digit multiple of 420 = 420 × 23 = 9660 The required number is 9660 + 1 = 9661

Answer:

Let the mass of a pumpkin, a pineapple and a pomelo be x, y and z respectively. To simplify the problem, remove 1 pumpkin from each plate.


We then have: Since 2y is less than 2z, so y is less than z. Since 2z is less than x + y, and y is less than z, then x has to be more than z. Hence, y is less than z, which is less than x. Therefore, y + z is less than 2z but more than 2y, so D should be placed between A and B.

Answer:

1860 ÷ 4 = 465

1 + 2 + 3 + … + n = 465,

((1+ n) x n)/2 = 465

(1 + n) × n = 930

n = 30

Answer:

Ten boys played a total of 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45 games.

3 points were given for a win-lost outcome and 2 points were given for a draw.

45 × 3 = 135 points would have been given out if there were no draws.

135 – 125 = 10 points

10 games were draws.

Primary 5 - Bobo always tells the truth on Mondays, Tuesdays, Wednesdays, and Thursdays. Qiqi always tells the truth on Mondays,                     Fridays, Saturdays, and Sundays. On the rest of the days, they may tell the truth or they may lie.

                    One day last week, Bobo and Qiqi both said, "I lied yesterday."                      

                    On which day of the week did that happen?

Answer:

Bobo could only say that on Mon, Fri, Sat, Sun. Qiqi could only say that on Tue, Wed, Thu and Fri. Only on Friday can both of them say that.

Primary 5 - John had $15 more than James for his weekly allowance. They each spent $60 weekly and saved the rest. John saved $315                     and James saved $210 after a few weeks. How many weeks did it take John to save the $315?

Answer:

In 1 week, John is able to save $15 more than James

315 – 210 = 105    John saved $105 more than James.

105 ÷ 15 = 7     It took John 7 weeks to save $315.

Primary 5 - Following the arrows given in the diagram, how many different routes are there                     from X to Y passing through P?

Answer: 30

Primary 4 - Amir, Bala, and Chandra each has a different favourite food which are satay, pizza, and nasi lemak.

                     Amir does not like pizza or nasi lemak. Bala does not like pizza.

                     Name the favourite food of each person.

Answer:

Since Amir likes neither pizza nor nasi lemak, then satay must be his favourite food. Since Bala does not like pizza and it’s not satay (Amir’s favourite food), then nasi lemak must be Bala’s favourite, and so Chandra’s favourite food must be pizza.

Primary 4 - There were seven friends. Each person shook hands with each of the other six friends. How many handshakes were there                     altogether?

Answer:

The least number of pupils who answered all 4 questions correctly happens when different pupils could not answer different questions. Since 13 pupils got Q1 wrong, 8 got Q2 wrong, 9 got Q3 wrong and 4 got Q4 wrong, then 42 – (13 + 8 + 9 + 4) = 8.

At least 8 pupils answered all 4 questions correctly.

Primary 4 - Three ladies Anne, Betty and Carol made the following statements:

                     Anne: I am 22 years old. I am 2 years younger than Betty. I am 1 year older than Carol.

                     Betty: I am not the youngest. Carol and I are 3 years apart. Carol is 25 years old.

                     Carol: I am younger than Anne. Anne is 23 years old. Betty is 3 years older than Anne.

                     If only two of the three statements made by each lady are true, find the age of Anne.

Answer:

Suppose Anne is 22 years old:

Then Carol’s 1st and 3rd statements must be true.

That makes Betty’s 2nd and 3rd statements false.

Since two of three statements must be true, we conclude that Anne is not 22 years old, and Anne’s 2nd and 3rd statements must be true.

This makes Carol’s 3rd statement false and Carol’s 1st and 2nd statements true.

Therefore, Anne is 23 years old.

Primary 3 - Petrus pasted 4 dot stickers along two sides of a square as shown below.

 








                     Show where he should paste 5 more stickers so that there are 3 stickers on each side of the square.

Answer:

Primary 3 - The total number of storybooks that John and Ken have is 25.

                     The total number of storybooks that John and Lionel have is 20.

                     The total number of storybooks that Ken and Lionel have is 31.

                     Who has the most number of books? How many does he have?

Answer:

Total number that John, Ken and Lionel have = (25 + 20 + 31) ÷ 2 = 38

Number of books Lionel has = 38 – 25 = 13

Number of books Ken has = 38 – 20 = 18

Number of books John has = 38 – 31 = 7

Ken has the most number of books. He has 18 books.

Primary 3 - Five friends wanted to know the number of balloons in a bunch,

                     Kara guessed 25, Kegan guessed 31, Calida guessed 29, Eugene guessed 24 and David guessed 27.

                     Two guesses were wrong by 2; one guess was wrong by 3 and one guess was wrong by 4. Only one guess was correct.

                     Who guessed the correct number of balloons?

Answer:

Arrange the guesses in ascending order: 24 - 25 - 27 - 29 - 31

The answer is 27 since 25 and 29 are wrong by 2; and 24 is wrong by 3; and 31 is wrong by 4.

Therefore, it was David who guessed correctly.

2018

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