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