Marvin bought a box of fruits. 30% of the fruits are apples and the rest are oranges. He realized that half of the apples were rotten and threw them away. He then bought some oranges and the number of oranges increased by 40%. After that, he found that there were 52 more fruits in the box. How many fruits were there in the box at first?

Solution

At first

Apples ----- 30%

Oranges ----- 70%

Threw half apples away, bought 40% more oranges,

Apples ----- 1/2 x 30% = 15%

Oranges ----- 70% + (40/100 x 70%) = 98%

Total ----- 15% + 98% = 113%

113% - 100% = 13% (increase in number of fruits)

13% ----- 52 fruits

1 % ----- 52% divided by 13 = 4

Number of fruits at first,

100% ----- 4 x 100 = 400

Answer: 400 fruits

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.

## Sunday, September 06, 2009

### Anglo Chinese School 2007 PSLE Math Prelim Q44

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Mathematics,
Percentage

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## 13 comments:

A shop sells two kinds of stools: stools with three legs and stools with four legs. There is a total of 31 stools in the shop and together they have a total of 110 legs. How many stools with three legs are in the shop?

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Two boats were following each other 330 metres apart along a straight canal. Both boats were travelling at a speed of 5 km per hour. At one point the canal widens. As each boat reached that point, it speeded up to 8 km per hour. One hour after reaching the wide section the first boat stopped. How far apart, in metres, were the two boats when the first boat stopped?

A space station has three robots that make repairs. They are Marp, Orti and Eddi. The Marp robot can make 12 repairs in 10 minutes. The Orti robot can make 10 repairs in 8 minutes. The Eddi robot can make 8 repairs in 6 minutes. The space station needs 100 repairs. Approximately how long will it take the three robots working together to complete 100 repairs?

On her birthday in the year 2013, Eve's age will be 1/60 of the year she was born. How old was Eve on her birthday in the year 2000?

Todd's bike has a combination lock. To unlock his bike Todd has a secret number that is greater than 100 but less than 1000. Todd's secret number is a square number and the cube root of his secret number is also a square number. What is Todd's secret number?

Aldo was clearing bushes from a 15 m2 area on a block of land. He took a total of 16 hours to clear 8 m2. Aldo's younger sisters, Gina and Marie, helped him clear the remaining land. Gina works at half Aldo's rate, and Marie works at one quarter Aldo's rate. How many hours did Aldo and his sisters take, working together at this rate, to clear the remaining land?

A restaurant dining room has two kinds of table, large and small. Each large table seats 18 people and each small table seats 9 people. There are exactly enough seats for 270 people. The ratio of the number of large tables to the number of small tables in the dining room is 3 : 4. How many large tables are there?

Jane, Ivan and Maria are playing a counting game. They each count from one to nine, then start counting from one again. Each person counts at a different pace. Jane says her numbers at one-second intervals. Ivan says his numbers at two-second intervals and Maria says her numbers at three-second intervals. They all start together by saying the number one. After how many seconds will they again all say the number one together?

A car follows another car along a straight stretch of an open highway at 100 km/h. The cars are 150 m apart. The cars approach a town. When each car reaches the town, it slows down at the same rate at 30 km/h. Both cars travel through the town at 30 km/h. How far apart (in metres) will the cars be when they are both travelling at 30 km/h?

Evan's computer has a computer virus. His computer infects two more computers with the virus every second. The infected computers each then infect two more computers every second. Two seconds after Evan's computer becomes infected nine computers in total are infected. How many computers are infected after six seconds?

Jane : 1, 2, 3, 4, 5, 6, .... Ivan: 2, 4, 6, 8, .... Maria : 3, 6, 9, 12, .... Since, they said the number one together after 6 second. 6 x 10 (10 numbers, including number 1) = 60 seconds...

Allie and Dave took part in a race.Allie's speed was 72m/min faster than Dave.When Allie completed the race in 1/3h,Dave had only completed 4/7 of the race. a)What is Dave's average speed? b)What is the time taken by Dave to complete the race?

Tina saves 80% as much as Mary and Randall saves 30% as much as Tina.Mary uses 16% of her savings to buy 8 similar pens.Each pen costs $4.How much did Randall save? is the answer $48?

Anyone did the solution for this Question? A car follows another car along a straight stretch of an open highway at 100 km/h. The cars are 150 m apart. The cars approach a town. When each car reaches the town, it slows down at the same rate at 30 km/h. Both cars travel through the town at 30 km/h. How far apart (in metres) will the cars be when they are both travelling at 30 km/h?

Nan Yang Maths 2008 Q41: There was a total of 200 blue, red and green balls. There were twice as many red balls as blue balls. There were fewer green balls than red balls. The number of blue balls and red balls in each group was less than 100 and divisible by 3 and 4. How many green balls are there?

One of the functions of a heart is to pump blood that is rich in oxygen to all parts of the body. What is the another function of the heart in relation to the lungs of the body?

One way of controlling the population of mosquitoes was to spread a layer of oil on the surface of the water. Explain why this method can be used to control the populatioon of mosquitoes?

Another way of preventing the mosquitoes from breeding is to remove the stagnant water. Give a reason why the stagnant water should be removed.

State the conversion of energy that takes place when a solar powered calculator is used

Question 45 : James is thinking of the smallest six - digits number. The first four digits are different. The first digit of this number starts with 6 and this number can also be divisible by 3, 4 and 5. Find this number. [5 marks]

Question 12 : James is thinking of the smallest six - digits number. The first four digits are different. The first digit of this number starts with 6 and this number can also be divisible by 3, 4 and 5. Find this number. [5 marks]

Solution:

List out the possible digits:

0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

The number : 6 _ _ _ _ _

This number is divisble by 3, 4 and 5.

Start with 5 first.

To be divisible by 5, we can derive the last digit to be "0"

Thus, the number is 6 _ _ _ _ 0

Next we can pick 0, 1 and 2 as they are the smallest.

6 0 1 2 _ 0

To be divisble by 4,

the digits in the tens place can be:

0, 2, 4, 6 and 8

To be divisble by 3, sum of digits must be multiple of 3.

6 + 0 + 1 + 2 + A + 0 = A + 9

Posibble values of A are:

0 and 6. 2, 4 and 8 are not possible as they are not divisible by 3.

Thus, these are the possible numbers:

601200, 601260

But, the question stated that the number have to be small.

Thus, the smallest number

is 601200.

Check back:

LCM = 3 x 4 x 5 = 60.

601200/60 = 10020 (correct)

A number has 6 digits. This number is divisible by 9 and the number starts with 8. The digits are all different. Find the smallest of this number.

Number: 8 _ _ _ _ _ _. Pick 0, 1, 2, 3. Then the number will become 8 0 1 2 3 _. To find the last digit, sum of digits must be multiple of 9. 8 + 0 + 1 + 2 + 3 + A = 14 + A. 14 + A = 18. Thus, A = 4. So, the smallest number will be 801234.

[b]Notes on Simple Divisibility - Part 1:[/b]

1)To be divisible by 2, the number must ends in 0, 2, 4, 6 or 8.

2)To be divisible by 5, the number must ends in 0 or 5.

3)To be divisible by 25, the number must ends in 25, 50 or 75.

4)To be divisible by 4 and by 25 (5 x 5) or (2 fives), the number must ends in 00.

5)To be divisible by 8 and by 125 (5 x 5 x 5) or (3 fives), the number must ends in 000.

6)To be divisible by 16 and by 625(5 x 5 x 5 x 5) or (4 fives), the number must end in 0000.

A number has 6 digits. This number is divisible by 9 and the number starts with 8. The digits are all different. Find the [b]largest[/b] of this number.

Solution:

List down all the digits:

0, 1, 2, 3, 4, 5, 6, 7, 8 and 9

The number: 8 _ _ _ _ _

since all digits are different and the number has to be large,

we will pick 9 for the second digit and 7 for the third digit, 6 and 5 for the fourth and fifth digits respectively.

Thus, we will have,

8 9 7 6 5 _.

To be divisible by 9, sum of the digits of the number is multiple of 9.

8 + 9 + 7 + 6 + 5 + A = 35 + A

Multiple of 9 which is higher than 35 is 36 (9 x 4).

35 + A = 36

A = 1

Thus, the number is 897651.

Note: We cannot choose 45 (9 x 5) is because the value of A will have 2 digits. Value of A can only be in 1 digit.

Additional notes with reference to Muffins' statement that angles in a 4-sided figure ALWAYS add up to 360 degree. A 4-sided figure is called a quadrilateral aka 4-sided polygon. A triangle is also known as a 3-sided polygon. As in P5/P6, you will learn that all sum of its angles of a triangle added up to 180 degree. For a quadrilateral, all sum of its angles is 360 degree. The rule is that all the sum of angles in a polygon with n sides, where n is 3 or more, is 180 degree x (n-2). Applying this rule to the other polygons, you will have a 5-sided polygon aka pentagon with its sum of angles equal to 540 degree. For hexagon(6 sides), sum = 720 degree. Trying working out for the rest like Heptagon (7-side), Octagon (8-side), Nonagon (9-side) and Decagon (10-side). BTW, a polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others.

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