This blog is managed by Song Hock Chye, author of Improve Your Thinking Skills in Maths (P1-P3 series), which is published and distributed by EPH.

## Wednesday, April 14, 2010

### CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q18

Sparkles Jewellery Shop sold diamonds, rubies and emeralds. 3/5 of the gemstones were diamonds. There were 168 fewer rubies than diamonds. The ratio of the number of rubies to the number of emeralds was 7:3. After some rubies were sold, 30% of the remaining gemstones in the shop were rubies and emeralds.
a) How many rubies were sold?
b) Find the percentage decrease in the number of gemstones. Leave your answer as a fraction.

Solution Rubies --> 7/10 of 2/5 = 14/50
Diamonds - Rubies --> 168 (more diamonds than rubies)
3/5 - 14/50 = 168
16/50 --> 168
1/50 --> 168 divided by 16 = 10.5

Rubies + Emeralds (2/5 of whole)
20/50 --> 20 x 10.5 = 210
2/5 of whole --> 210
1/5 of whole --> 210 divided by 2 = 105
(Diamonds) 3/5 of whole --> 3 x 105 = 315

After selling, Rubies and Emeralds make up 30%, while Diamonds make up 70%.
Diamonds 70% --> 315
10% --> 315 divided by 7 = 45
Rubies and Emeralds 30% --> 3 x 45 = 135

(a)
(Rubies and Emeralds before selling) - (Rubies and Emeralds after selling)
--> 210 - 135 = 75

(b)

Percentage decrease in number of gemstones

1/50 of gemstones --> 10.5
50/50 of gemstones -> 50 x 10.5 = 525

75 rubies sold
--> (75/525) x 100% = 14 and 2/7 %

### CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q17

The number of boys to the number of girls in Happy Kindergarten was 3:5. The number of boys to the number of girls in Merry Kindergarten was 4:5. Both kindergartens had the same number of boys. When 10 girls from Happy Kindergarten joined Merry Kinderten, the ratio of the number of boys to the number of girls in Happy Kindergarten became 2:3. Find the total enrolment of the 2 kindergartens.

Solution

Happy
B : G
3 : 5
(multiply both by 4)*
12 : 20
(Total units --> 12 + 20 = 32)

Merry
B : G
4 : 5
(multiply both by 3)*
12 : 15
(Total units --> 12 + 15 = 27)

* Happy (x4) and Merry (x3) to make the number of units for boys in both kindergartens the same, because the number of boys are the same for both kindergartens.

After 10 girls left Happy to join Merry,
Ratio in Happy
B : G
2 : 3
(multiply by 6)**
12 : 18

** (x6) to make units for boys 12 again.

Number of units for girls in Happy before transfer --> 20 units
Number of units for girls in Happy after transfer --> 18

20 units - 18 units --> 10
2 units --> 10
1 unit --> 10 divided by 2 = 5

Total for enrolment for both kindergartens
Happy --> 32 units
Merry --> 27 units
32 units + 27 units --> 59 units
59 units --> 59 x 5 = 295

### CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q16

Ali and Minhua were playing a card game using 96 cards. In the first game, Minghua lost 1/5 of his cards to Ali. In the second game, Ali lost 1/3 of his cards to Minghua. After the second game, both boys had the same number of cards. How many cards did Ali have at first?

Solution Before 1st game
Minghua --> 5 units
Ali --> 11 units
Total 16 units --> 96
1 unit --> 96 divided by 16 = 6
11 units --> 66

### CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q15

There were some prizes ot be won at a Shop and Win Contest. 35% were cash prizes and there rest were household items. Some cash prizes were given out and the percentage of cash prizes decreased to 22%. If there were 54 more household items than cash prizes at first, find the number of cash prizes being removed.

Solution

Before
Cash --> 35%
Household Items consists of
--> 35% + 30%(54 items) = 65%

30% --> 54
1% --> 54 divided by 30 = 1.8
(Cash before) 35% --> 35 x 1.8 = 63
(Household Items) 65% --> 65 x 1.8 = 117

After
Cash became --> 22%
Household Items --> (remaining) 78%

78% --> 117
1% --> 117 divided by 78 = 1.5
(Cash after) 22% --> 22 x 1.5 = 33

Cash before - Cash after --> Cash prizes removed
63 - 33 = 30

### CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q14

There were ducks, goats and hens at a farm. 15% of the animals were ducks. There were 180 fewer ducks than hens. The remaining 121 animals were goats. What percentage of the animals at the farm were goats? Levae your answer correct to 2 decimal places.

Solution * 180 more hens than ducks, therefore hens --> 15% + 180.
** Ducks (15%) and hens (15% + 180), therefore goats give the remaining 70% less 180.

70% - 180 --> 121
70% --> 121 + 180 = 301
10% --> 301 divided by 7 = 43
100% 10 x 43 = 430

Percentage of animals were goats
--> (121/430) x 100% = 28.139% ~ 28.14%

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### CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q13

Abbie, Ellen and Faheem sold umbrellas to raise funds for charity. Each umberlla was priced at \$22.50. Abbie sold 1/6 of the umbrellas while Ellen and Faheem sold the remaining umbrellas in the ratio of 2:7 respectively. If Faheem sold 364 umbrellas more than Abbie, what was the total amount of money collected by them?

Solution

Abbie --> 1/6
Remaining --> 5/6

Since ratio for Ellen : Faheem is 2 : 7,
Faheem sold 7/9 of remainder

Faheem (7/9 of the remaning 5/6)
--> 7/9 x 5/6 = 35/54

(Faheem - Abbie) --> 35/54 - 1/6 = 13/27
13/27 --> 364 (Faheem sold 364 more than Abbie)
1/27 --> 364 divided by 13 = 28
27/27 --> 27 x 28 = 756

756 x \$22.50 = \$17 010

### CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q12

The figure below is made up of 2 squares and a rectangle. The ratio of the area of A to the area of B to the area of C is 9:4:3. The ratio of the unshaded part of B to the unshaded part of C is 4:1. If the shaded part is 56 square cm, find the area of A that is not covered by B. Solution (C) 3 parts --> 56 sq cm + 1 unit
(multiply by 4)
(C) 12 parts --> 224 sq cm + 4 units
(B) 4 parts --> 56 sq cm + 4 units

12 parts - 4 parts --> 224 sq cm - 56 sq cm
8 parts --> 168 sq cm
1 part --> 168 sq cm divided by 8 = 21 sq cm

(A - B) 5 parts --> 5 x 21 sq cm = 105 sq cm

### CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q11

Jai, Maira and Lynn have 760 stickers altogether. Jai has 8/9 as many stickers as Maira and 6/11 as many stickers as Lynn. If Jai and Lynn want to have an equal number of stickers, how many stickers must Lynn give to Jai?

Solution (48 + 54 + 88) units --> 760 stickers
190 units --> 760
1 unit --> 760 divided by 190 = 4

Lynn must give Jai 20 units for Lynn and Jai to have equal number of stickers.
20 units --> 20 x 4 = 80

### CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q10

In September, Rafael received a monthly salary of \$2698 and she saved 20% of it. In December, her salary was reduced by 5% and she continued to save 20% of her salary. How much less was her savings in December compared to that in September? Leave your answer correct to the nearest dollar.

Solution

Sep --> 20% x \$2698 = \$539.60

5% x 539.6% = \$26.98 ~ \$27

### CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q9

At a shop, the ratio of the number of stalks of roses to the number of stalks of carnation was 4:5. Mrs Tan sold 176 stalks of carnations and was left with thrice as many stalks of roses as carnations. How many stalks of carnations did she have at first?

Solution * 'Before' x3 and 'After' x4 to make the Roses have an equal number of units of 12 each because no roses were sold.

Carnations before --> 15 units
Carnations after --> 4 units
15 units - 4 units --> 176 (carnations sold)
11 units --> 176
1 unit --> 176 divided by 11 = 16
15 units --> 15 x 16 = 240

### CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q8

Kumar spent \$1729 on a set of encyclopedia. H spent 1/4 of the remainder on a camera and still had 2/5 of his money left. Find the total amount of money he had at first.

Solution 3/5 of money --> \$1729 + 1 unit
(multiply above by 3)
9/5 of money --> \$5187 + 3 units
2/5 of money --> 3 units

9/5 - 2/5 --> \$5187 + 3 units - 3 units
7/5 --> \$5187
1/5 --> \$5187 divided by 7 = \$741
5/5 --> 5 x \$751 = \$3705

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### CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q7

The figure below is made up of a square and a rectangle. The perimeter of the figure is 178 cm and the area of the square, PQRS, is 784 square cm. What is the length of ST? Solution

Square root of 784 square cm = 28 cm (length of 1 side of square)
2 lengths of rectangle --> (178 - 28 - 28 - 28 - 28) cm = 66 cm
1 length --> 66 cm divided by 2 = 33 cm
ST --> 33 cm + 28 cm = 61 cm

### CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q6

ABE is an isosceles triangle and BCDE is a rhombus. AED is a straight linie. Given that Angle ECG = 16 degrees, find Angle GCD. Solution

Ange BEA --> (180 - 33) divided by 2 = 73.5
Angle BED --> 180 - 73.5 = 106.5
Angle CED --> 106.5 divided by 2 = 53.25
Angle ECD = Angle CED = 53.5
Angle GCD = 53.25 - 16 = 37.25

### CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q5

The number of visitors to the zoo has been increasing by 8% each year since the year 2003. If the number of visitors in 2003 was 12 500, how many visitors went to the zoo in 2005?

Solution

Yr 2003 --> 12 500
Yr 2004 --> 108% x 12 500 = 13 500
Yr 2005 --> 108% x 13 500 = 14 580

### CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q4

A department store was offering a promotion for customers who bought T-shirts. Any customer who bought 3-T shirts would get a 50% discount on the 3rd T-shirt. Pamela bought 3 T-shirts and paid an average cost of \$11.90 for each T-shirt. Find the orginal price of one T-shirt.

Solution

Original Price of 1 T-shirt --> 2 units
Price of 3rd T-shirt --> 1 unit

2 T-shirts at original price + 1 discounted price T-shirt --> \$11.90 (avg)
(2 x 2 units) + 1 unit --> \$11.90 x 3 = \$37.50 (total)
4 units + 1 unit --> \$37.50
5 units --> \$37.50
1 unit --> \$37.50 divided by 5 = \$7.14
2 units --> 2 x \$7.14 = \$14.28

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### CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q3

Mr Ong had 5 kg or rice. After he sold 5/12 of it, he repacked the remaining rice into smaller packets of 2/3 kg each. How much rice had he left?

Solution

7/12 left --> 7/12 x 5 kg = 35/12 kg (35 twelfths kg)

Repacked this 35 twelfths kg into packets of 8 twelfths kg (2/3 kg --> 8/12 kg)
35 twelfths divided by 8 packets --> 4 wholes and 3 twelfths
3 twelfths (left unpacked) --> 3/12 --> 1/4 or 0.25

Answer: 1/4 kg or 0.25 kg left

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### CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q2

CHIJ St Nicholas Girls' Sch 2009 SA1 Paper 2 Q2

Evelyn left her house for a concert at 17 55. She took 1 h 5 min to reach the theatre but was 10 minutes late. What time did the concert begin?

Solution

1 h 5 min after 1755 h --> 1900h
10 min before 1900h --> 1850 h
1850h --> 6.50 pm

### CHIJ St Nicholas Girls' Sch 2009 P6 SA1 Paper 2 Q1

The table below shows the difference between the digits in some 2-digit numbers. List all the 2-digit numbers, from 40 to 100, in which the digits have a difference of 3. Arrange them in ascending order.

Answer: 41, 47, 52, 58, 63, 69, 74, 86, 96

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