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# Difficult PSLE Math Questions For Practice

The Primary School Leaving Examination (PSLE) is a mandatory exam for students who complete Grade 6. The PSLE Math tests in basic concepts and applying logical problem-solving skills across all important mathematical topics such as Geometry, Fraction, Percentages, and more.

### PSLE Math Questions

Question 1:

Mrs Wong wanted to divide 72 girls and 60 boys equally into as many teams as possible. Each team had the same number of children. The number of boys in each team was the same. How many boys were there in each team?

• 12
• 2
• 5
• 6

Question 2:

Gopal had 3 identical tins of paint that were filled. He poured 760 ml out of each tin. The total amount of paint left in the 3 tins after pouring was equal to the amount of paint in each tin at first. What was the amount of paint in each tin at first?

Question 3:

FIve identical circles are placed as shown below.

Find the diameter of the circle.

Question 4:

There are 85 plates of fried noodles for 80 people. Each adult eats 2 plates of fried noodles and every 3 children share 1 plate of fried noodles. How many adults and how many children are there?

Question 5:

A bakery and a library are 120m apart. They’re located between Hong’s house and Jeya’s house, as shown below. The bakery is exactly halfway between the two houses.

One day, Hong and Jeya started cycling from their houses at the same time and they arrived at the library together. Jeya cycled at 70m per min while Hong cycled at a speed 15m per min faster than Jeya.

a) How much further did Hong cycle than Jeya?

b) How far is Jeya’s house from the library?

### PSLE Math Solutions

Since there are 72 boys and 60 girls, the total is 132.

Factorize 132 to understand how many maximum teams we can have.

132 -> 11 x 3 x 2 x 2   ->  11 x 12

We can start with either 12 teams with 11 each. 72 boys can be distributed equally in each team as 6 each and 60 girls can be distributed as 5 each (totalling to 11 members per team).

So, the number of boys is 5. Option C.

Assume each tin originally has ‘X’ ml of paint. Since, 760 ml of paint was taken out from all the cans ,the new amount of paint present in the cans are:

X – 760

X – 760

X – 760

The total amount of paint in the three tins after pouring is the same as the amount of paint in each tin at first. This means the below

(Sum of the paint remaining in all three tins) 3X – 2280 = X (amount of paint in the tin originally)

2X = 2280

X =1140

1140 ml is the original amount of paint present in the tin.

Step 1: Mark the two unknowns as ‘x’ and ‘y’

This means:

Diameter = 22 + x

Also, diameter = x + 12 + y

Therefore, 22 + x  = x + 12 + y

This gives us, y = 10

Now, because the right top circle has 22 measured, the remaining part of the diameter has to be ‘x’ and correspondingly the other unknown has to be ‘y’.

This means the diameter is 2y + 16 = 20 +16 = 36

Let the number of adults be ‘X’

Let the number of children be ‘Y’

X + Y = 80 (total people)

Since each adult eats two plates and three children share one plate, it has to be

2X + Y/3 = 85 (total plates)

Solving both these equations will give you Y = 45 and X = 35

So, adults are 35 and children are 45.

Let’s assume the total distance between Hong’s house and Jeya’s house be ‘d’

Since the time taken is the same for both to travel until the library, we equate distance/speed of both.

So, (d/2  + 120 ) / 85 = (d/2 – 120) / 70

=> d/170 + 120/85 = d/140 – 120/70

=> d= 2480 m

Therefore, distance from Bakery to Jeya’s house will be d/2 = 1240 m.

A).

Hong cycled d/2 + 120 = 1240 + 120 = 1360 m

Jeya cycled d/2 – 120 = 1240 -120 = 1120 m

Hong cycled 1360 – 1120 = 240m more than Jeya.

B). Since 120 m is the distance between Bakery and Library, the distance between Jeya’s house and Library will be 1240 – 120 = 1120 m.

Hope you find this useful, thank you.

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