Singapore Chinese Girls Sch 2008 PSLE Math Prelim Q42

In the diagram below, 75% of square Z is not shaded. The ratio of the area of square X to the area of square Y is 9:4. The ratio of the area of square Y to the area of square Z is 4:1.
a) What is the ratio of the area of square X to the area of square Z?
b) Find the ratio of the unshaded area of square Y to the unshaded area of square Z.



Solution

a)
X : Y : Z
9 : 4 : 1

X : Z
9 : 1 (Answer)


b)
Total Area
Y : Z
4 : 1
16 : 4

Unshaded Area
Y : Z
15 : 3 * (see explanatory notes below)
5 : 1 (Answer)

* Total Area (ratio) Y:Z is 4:1. 75% of Z is unshaded, hence for Z, 3 units out of 4. This means 1 unit is shaded. For Y, 16 units total less 1 unit shaded = 15 units unshaded. Hence, unshaded area is Y:Z ---- 15:3.

Singapore Chinese Girls Sch 2008 PSLE Math Prelim Q40

The number of girls who registered for art class was 20% of the number of boys. On the actual day, 3 more girls and 3 more boys turned up for the class. As a result, there were 1/3 as many girls as boys at the art class. What was the total number of children who came to art class?

Solution

Girls 20% of boys, hence, girls 1/5 of boys

Before

Girls 1 unit
Boys 5 units

After 3 more boys and 3 more girls turned up, there were 1/3 as many girls as boys:

Girls 1 unit + 3 ----- 1 part (x3)
Boys 5 units + 3 ----- 3 parts

Girls 3 units + 9 ----- 3 parts
Boys 5 units + 3 ----- 3 parts

(Boys) 5 units + 3 ----- 3 units + 9 (Girls)
5 units – 3 units ----- 9 – 3
2 units ----- 6
1 unit ----- 3

Total number of students

Girls ---- 3 + 3 = 6
Boys ---- (5 x 3) + 3 = 18

6 + 18 = 24

Answer: 24 students

Rosyth Sch 2006 PSLE Math Prelim Q35 - alternative method

Daniel is thinking of three consecutive odd numbers. The average of the first and second number is 40, while the average of the second and third numbers is 42. List the three numbers.

Solution

Original post to this question can be found here.

Average of 1st and 2nd numbers ----- 40
Total of 1st and 2nd numbers ----- 40 x 2 = 80

1st ----1 unit
2nd ---- 1 unit + 2
Total of 1st and 2nd ---- 2 units + 2 ---- 80


2nd ---- 1 unit + 2
3rd ---- 1 unit + 2 + 2
Total of 2nd and 3rd ---- 2 units + 6

Total of 1st and 3rd is
(2 units + 2) + (2 units + 6)
= 4 units + 8

Average of 1st and 3rd is
(4 units + 8) divided by 2
= 2 units + 4

From Total of 1st and 2nd,
2 units + 2 ----- 80
2 units ----- 80 – 2 = 78
1 unit ----- 78 divided by 2 = 39

Answer:
1st number is 39
2nd is 41
3rd is 43

Mothers know best

Got this video clip from an ex-P6 student. She emailed it to us.

Mothers are designed all to be the same so that children will all grow up to be the same.

Rosyth Sch 2006 PSLE Math Prelim Q46

At a fun fair, there were 49 more children than women. There were 3/5 as many men as women. Given that the number of women was 25% of the total number of people at the fun fair, how many people were at the fun fair?

Solution

Men ----- 3 units
Women ----- 5 units
Children ----- 5 units + 49
Total ----- 13 units + 49

(Women) 5 units ----- 25%
1 unit ----- 25% divided by 5 = 5%
13 units ----- 13 x 5% = 65%

Remaining 49 people ----- 100% - 65% = 35%
35% ----- 49 people
(35% divided by 7)= 5% ----- (49 divided by 7) = 7
5% ----- 7
(5% x 20) = 100% ----- (7 x 20) = 140
100% ----- 7 x 20 = 140

Answer: There were 140 people at the fair.

Rosyth Sch 2006 PSLE Math Prelim Q45

Ali, Billy and Caven had some cards. Ali would have twice as many cards as Billy if Billy gave 28 cards to Ali. Both Billy and Caven would have the same number of cards if Caven gave 84 cards to Billy. Given that Caven had 112 more cards than Ali at the beginning, find the number of cards each of them had at the beginning.

Solution

Ali ----- 2 units – 28 (at first)
Billy ----- 1 unit + 28 (at first)
Caven ----- 1 unit + 28 + 84 + 84 (at first)

At first,
(Caven) – (Ali) ---- 112
(1 unit + 28 + 84 + 84) – (2 units – 28) ----- 112
(1 unit + 196) – (2 units – 28) ----- 112
224 – 1 unit ----- 112
224 – 112 ----- 1 unit
1 unit ---- 112

Ali at first
(2 x 112) – 28 = 196

Billy at first
(112) + 28 = 140

Caven at first
(112) + 28 + 84 + 84 = 308

Answer: Ali had 196, Billy had 140 and Caven had 308

Rosyth Sch 2006 PSLE Math Prelim Q44

A rectangular tank 2.5 m long and 1.2 m wide is filled with water from two taps. Tap A fills it with water at the rate of 12 litres per minute and Tap B fills it up with water at the rate of 15 litres per minute. Both taps are turned on at the same time. What is the height of the water in the tank after 8 minutes?

Solution

Tap A ----- 12 litres per min
Tap B ----- 15 litres per min
Total ----- 27 litres per min

1 min ----- 27 litres
8 min ----- 8 x 27 litres = 216 litres or 216 000 cubic cm

Volume = Length x breadth x height
216 000 cubic cm = 250 cm x 120 cm x height
height = 216 000 cubic cm divided by (250 x 120) square cm

height = 7.2 cm (Answer)

Rosyth Sch 2006 PSLE Math Prelim Q43

Mrs Yu paid $16.20 for some eraser and pencils. An eraser cost 15 cents and a pencil cost 45 cents. She bought 12 more pencils than erasers. How many erasers did she buy?

Solution

1 eraser ----- $0.15
1 pencil ----- $0.45
1 set (of 1 eraser, 1 pencil) ----- $0.60

She bought -----
Unknown number of sets + 12 pencils ----- $16.20
(? x $0.60) + (12 x $0.45) ----- $16.20
(? x $0.60) + $5.40 ----- $16.20
? x $0.60 ----- $16.20 - $5.40 = $10.80
? ----- $10.80 divided by $0.60 = 18 (sets)

18 sets ----- 18 erasers

Answer: She bought 18 erasers.

Rosyth Sch 2006 PSLE Math Prelim Q42

The average mass of Bob and his five friends is 43 kg. Bob is 3 kg heavier than the average mass of his five friends. Find the mass of Bob.

Solution

Total mass of Bob and 5 friends -----
43 kg x 6 = 258 kg

If Bob had been 3 kg less, the total mass would be -----
258 kg – 3 kg = 255 kg

Average ---- 255 kg divided by 6 = 42.5 kg

But since Bob is 3 kg heavier -----
42.5 kg + 3 kg = 45.5 kg

Answer: The mass of Bob is 45.5 kg.

Rosyth Sch 2006 PSLE Math Prelim Q41

In the figure below, AB is parallel to DE and ACDG is parallel to EF. ABC is an isosceles triangle with Angle ABC = 36 degrees. Find Angle DEF.



Solution

Angle BAC ---- (180 – 36) degrees divided 2 = 72 degrees
Angle EDG ----- 72 degrees
Angle DEF ----- (180 – 72) degrees = 108 degrees (Answer)