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.

## Tuesday, September 20, 2011

### Catholic High School 2010 PSLE Math Prelim Paper 2 Q17

Daniel had 40% more stickers than Brandon. Daniel and Brandon each gave 20% of their stickers to Calvin. As a result, Calvin's stickers increased by 80%. If Daniel has 20 more stickers than Calvin in the end, how many stickers did Brandon have at first?

Solution

At first

Daniel ---- 100% + 40%
Brandon ---- 100%
Calvin ---- 1 unit

After Daniel and Brandon each gave 20% of their stickers to Calvin…
Daniel ---- 100% + 40% - (28%)*
Brandon ---- 100% - (20%)**
Calvin ---- 1 unit + (28% + 20% of Dan and Bran --> 80% of 1 unit)#
Hence Calvin --- 1 unit + (48% of Dan and Bran --> 80% of 1 unit)

* 20% of 140% = 28%
** 20% of 100% = 20%
# Cal received 28% + 20% = 48% of (Dan + Bran), which is equal to 80% of Cal's original amount of 1 unit.

80% of 1 unit ---- 48% of total of Dan and Bran
0.8 unit ---- 48%
1 unit ---- 48% divided by 0.8 = 60%

In the end Calvin
1 unit + (48% from Dan and Bran)
= 60% + 48%
= 108%

(Daniel) more than (Calvin) in the end
(140% - 28%)## - (108%)
= 112% - 108%
= 4%
## Danile had 140% at first but gave 28% to Calvin

Daniel had 20 more stickers than Calvin in the end
4% ---- 20
1% ---- 20 divided by 4 = 5

Brandon at first
100% ---- 100 x 5 = 500

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## Wednesday, September 14, 2011

### Catholic High School 2010 PSLE Math Prelim Paper 2 Q18

At a conference made up of speakers and participants, there were 20% more men than women. The ratio of male speakers to female speakers was 8:5. There was an equal number of male and female participants.
a) Find the ratio of male speakers to male participants at the conference.
b) Halfway, 40 male participants left the conference and another 60 female participants joined the conference. In the end, there were 3/4 as many male participants as female participants remaining behind. How many speakers were there at the conference?

Solution

Male ----- 120%
Female ----- 100%

Speakers
Male : Female
8 (parts) : 5 (parts)

Participants
Male : Female
1 (unit) : 1 (unit)

Men ----- 8 parts + 1 unit
Women ----- 5 parts + 1 unit

But since there are 20% more women than men,
Women ----- 5 parts x 120% + 1 unit x 120%
= 6 parts + 1.2 units

Men ----- Women
8 parts + 1 unit ----- 6 parts + 1.2 units
8 parts - 6 parts ----- 1.2 units - 1 unit
2 parts ----- 0.2 unit
1 part ----- 0.1 unit
10 parts ----- 1 unit
or
1 unit ----- 10 parts

(a)
Male Speakers ----- 8 parts
Male Participants ----- 1 unit or 10 parts

Male Speakers : Male Participants
8 : 10
4 : 5

(b)
Speakers
Male : Female
8 (parts) : 5 (parts) -- (altogether 13 parts)

Participants
Male : Female
1 (unit) : 1 (unit)
10 (parts) : 10 (parts) -- (before)
- 40 : + 60 -- (40 males left; 60 females joined)
3 (units) : 4 (units) -- (3/4 as many male as females in the end)

(Male) 3 units ----- 10 parts - 40
(Female) 4 units ----- 10 parts + 60

(Female) - (Male)
4 units - 3 units ----- 10 parts + 60 - 10 parts - (-40)
1 unit ----- 60 + 40
1 unit ----- 100

(Male after)
3 units ---- 3 x 100 = 300

(Male before)
10 parts ---- 300 + 40 (need to add the 40 who left)
10 parts ----- 340
1 part ---- 34

All speakers
13 parts ---- 13 x 34 = 442

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## Wednesday, September 07, 2011

### Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q18

The figure below shows 2 completely-filled tanks being emptied of the water from 2 different taps. The taps at Tank A and Tank B were turned on at 7 am and 8.30 am respectively, until both tanks were completely empty. At 11 am, the water level in both the tanks was the same. At 12.30 pm, Tank B was completely empty and Tank A was only completely empty at 1 pm. If the rate of the flow of water from each tap was constant throughout, what was the height of Tank A?

Solution ** At 11 am, water level in both Tanks were the same.

Note that 3/8 of B's height is the same as 2/6 or 1/3 of A's height.

(3/8) of B ----- (2/6) or (1/3) of A

(1/8) of B ----- (1/3) of A divided 3 = (1/9) of A

(8/8) of B (B's height) ----- 8 x (1/9) = (8/9) of A

* Remaining (1/9) of A ----- 5 cm
(This is the difference in height between Tank A and B)

(9/9) of A (A's height) ----- 9 x 5cm = 45 cm

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### Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q17

The average length of 6 ropes was 80 cm. The average length of 4 ropes of the ropes A, B, C and D was 15 cm more than the average length of the remaining 2 ropes E and F.
a) Find the average length of ropes E and F. Give your answer in metres.
b) If Rope E had been 18 cm shorter and Rope F had been 12 cm longer, they would have been of the same length. Find the actual length of Rope E.

Solution

Total of 6 ropes ----- 6 x 80cm = 480 cm

Average of A, B, C, D (4 ropes) is more than Average of E and F (2 ropes) by 15 cm.
This means each of the 4 ropes (A, B, C, D) has an average length that is 15 cm longer than the average of E and F.

Therefore, total length of A, B, C, D is longer than total length of E and F by
----- 4 x 15cm = 60 cm a)
3 units ----- 480cm - 60cm = 420 cm
1 unit (E + F) ----- 420cm divided by 3 = 140 cm

Average ----- 140cm divided by 2 = 70 cm or 0.7 m

b) 2 parts ----- 140 - 12 - 28 = 110
1 part ----- 110 divided by 2 = 55

E ----- 55 + 12 + 18 = 85

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### Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q16

Yanling had 60% more stamps than Lena. Tricia had 75% fewer stamps than Yanling. Yanling and Lena gave Tricia some stamps in the ratio 4:1. As a result, Tricia had 2 and 1/2 times as many stamps as before and Yanling had 300 stamps more than Lena in the end. How many sttamps did Lena give to Tricia?

Solution *** Tricia had 75% fewer stamps than Yanling
----- 25% of 160% is 40%.

# Tricia finally had 2 and half times as many stamps as before
----- 40% x 2.5 = 100%

Tricia's number of stamps increased by
---- 100% - 40% = 60%

Ratio given by Yanling and Lena was 4:1 -----
Y : L
4 : 1
(Total 5 units) ----- 60%

**(Lena gave) 1 unit ----- 60% divided by 5 = 12%
*(Yanling gave) 4 units ---- 4 x 12% = 48%

In the end, Yanling had more than Lena ----- 300
112% - 88% ----- 300
24% ---- 300
1% ---- 300 divided by 24 = 12.5

Lena gave Tricia 12% -----
12 x 12.5 = 150

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### Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q15

A car and a van started travelling from Town X to Town Y at the same time. The distance between the two towns was 225 km. Both vehicles did not change their speed. The car arrived at Town Y 3/4 h earlier than the van. When the car reached Town Y, the van was still 45 km away from Town Y. What was the speed which the car was travelling?

Solution * When the car reached Town Y, the van was still 45 km away. The car arrived at Town Y 3/4 h earlier than the van.

(Van) speed -----
45 km divided by (3/4) h
= 60 km/h

(Van) time for the whole journey -----
225 km divided by 60 km/h = 3 and 3/4 hours

Therefore, the car travelled in 3 h.

Speed of car -----
225 km divided by 3 h = 75 km/h

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### Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q13

The figure below shows 2 quarter circles and a rectangle. The radius of the big quarter circle is 8 cm. The radius of the small quarter circle is 4 cm. Find the difference in area between the two shaded parts of X and Y. Use the calculator value of pi and give your answer correct to 1 decimal place. Solution

Area of rectangle ----- 8 cm x 4 cm = 32 square cm

(1/4) x pi x 8cm x 8 cm
= 16(pi) square cm

(1/4) x (pi) x 4cm x 4cm
= 4(pi) square cm

16(pi) square cm - 4(pi) square cm
= 12(pi) square cm

Difference between the two shaded parts X and Y -----
(12 x pi) square cm - 32 square cm
approximately ----- 5.7 square cm

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### Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q9

The number of pens in Box X and Box Y are in the ration of 3:2. All the pens in Box Y are green. The ratio of green pens to blue pens in Box X is 4:5. There are 12 more green pens in Box Y than in Box X. How many blue pens are there?

Solution Green in Box X
(4/9) x (3/5) = 4/15

There are 12 more blue pens in Box X than in Box Y
(2/5) - (4/15) ----- 12
(6/15) - (4/15) ----- 12
2/15 ----- 12
1/15 ----- 12 divided by 2 = 6

Blue Pens
(5/9) x (3/5)
= 1/3
= 5/15

5/15 ----- 5 x 6 = 30

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### Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q6

Randy brought along a certain amount of money to buy files. If he bought the files at \$1.50 each, he would have \$17.50 left. If he bought the same number of files at \$2.70 each, he would have \$9.10 left. How much money did he bring along?

Solution 1 unit x \$1.50 + \$17.50 ----- 1 unit x \$2.70 + \$9.10
(\$2.70 x 1 unit) - (\$1.50 x 1 unit) ----- \$17.50 - \$9.10
(\$1.20 x 1 unit) ----- \$8.40
1 unit ----- \$8.40 divided by \$1.20 = 7

He brought along -----
(7 x \$2.70) + \$9.10
= \$18.90 + \$9.10
= \$28

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### Hokkien Huay Kuan Combined Primary 2010 PSLE Math Prelim Paper 2 Q5

At a bakery, muffins are sold at \$1 each. When a customer buys 5 muffins, she can buy one more at half the price. What is the greatest number of muffins that a customer can buy with \$20?

Solution

6 muffins ----- \$5.50 (Five at \$1; One at \$0.50)

3 groups of \$5.50 ----- 6 muffins x 3 = 18 muffins

(3 x \$5.50 = \$16.50) ----- 18 muffins

\$20 - \$16.50 = \$3.50 (remaining)

With the remaining \$3.50, the customer can buy another three muffins at \$1 each.

Total muffins ----- 18 + 3 = 21