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, March 25, 2009

### Tao Nan School P5 SA2 2006 Math Q48

At an exhibition, 30% of those present were boys. 5/14 of the remainder were girls and the rest were adults. There were 45 more adults than boys. How many more children than adults were there at the exhibition?

Solution

Boys ----- 30%
Girls ----- 5/14 x 70% = 25%
Adults ----- 100% - 30% - 25% = 45%

Adults more than boys ---- 45
45% - 30% ----- 45
15% ----- 45 (more adults than boys)
1% ----- 45 divided by 15 = 3

30% (boys) + 25% (girls) – 45% (adults) = 10%
10% ----- 10 x 3 = 30

Supertough said...

Hi Mr Song and all,

I have a few questions that require your assitance.

Q1.

Tom has 35 socks in the box which consisted of 3 different colours, blue, grey and black. There are 12 blue socks, 9 greys socks and 14 black socks.

How many socks should Tom take out in order to be absolutely certained that there is a pair of same socks of each kind? (Ans: 28)

For Q2 and Q3, can it be solve by model drawing. Most of my friends solve using algebra.
I sincerely hope that someone can solve these questions without the use of algebra.

Q2.

Steve is 4 times as old as my son. In 20 years from now, i will be twice as old as my son. How old are we now?

Ans : Steve - 40 , Son - 10

Q3.

Two years ago, James was 1 1/2 times as old as his son. Five years from now, James will be 1 1/3times as old as his son. In how many years time will James be 1 1/4times as old as his son.

Supertough said...

Apologies. Notice some error. Below is the amended one. Please kindly show working and model drawing so that all can benefit from it.

Q1.

Tom has 35 socks in the box which consisted of 3 different colours, blue, grey and black. There are 12 blue socks, 9 greys socks and 14 black socks.

How many socks should Tom take out in order to be absolutely certained that there is a pair of same socks of each kind? (Ans: 28)

For Q2 and Q3, can it be solve by model drawing? Most of my friends solve using algebra.
I sincerely hope that someone can solve these questions without the use of algebra.

Q2.

Steve is 4 times as old as my son. In 20 years from now, Steve will be twice as old as my son. How old are we now?

Ans : Steve - 40 , Son - 10

Q3.

Two years ago, James was 1 1/2 times as old as his son. Five years from now, James will be 1 1/3 times as old as his son. In how many years time will James be 1 1/4 times as old as his son.

Anonymous said...

Hi

Where did you get your Q3?
My answer is 12 years.But, I find it strange, the age gap between father and son is only 7.

Supertough said...

Hi Anonymous,

Many students will be grateful to you if you can provide your solution for these 3 questions...

My teacher once told us that you will only be given 1 mark for answer. The rest of the 4 marks come from working. In other words, you will lose 4 marks if the working is wrong despite that your answer is correct.

The answer is Q3 is correct, which is 12 years.

Supertough said...

The amended Q3...

Two years ago, James was 1 1/2 times as old as his brother. Five years from now, James will be 1 1/3 times as old as his brother. In how many years time will James be 1 1/4 times as old as his brother.

Ans: 12 years time

tianzhu said...

Hi
first 9 socks --- all blue
second batch of 9 socks --- all grey
third batch of 9 socks --- all black
Next sock --- whether blue,grey or black, he is certain of a pair of socks similar in colour.
Therefore the answer is (9*3)+1 = 28

tianzhu said...

Steve is 4 times as old as my son. In 20 years from now, Steve will be twice as old as my son. How old are we now?

The age gap is always constant.
Draw a model
2 units = 20
1 unit = 10
4 units = 40
Therefore Steve is 40 and his son is 10

tianzhu said...

Two years ago, James was 1 1/2 times as old as his brother. Five years from now, James will be 1 1/3 times as old as his brother. In how many years time will James be 1 1/4 times as old as his brother.

Draw a model.
1 unit = 7

James is now 23 yesrs old and his brother is 16 years.

In 12 years time james will be 5/4 times as old as his brother.
(35 and 28)

Supertough said...

Hi Thanks for the comprehensive explanation...

Q4.

Peter went to his friend house at 11 00 hrs which showed the correct time on his watch. It started to lose 14 minutes per hour until 3 hours ago it had completely stopped.

What is the correct time on his watch when it shows the incorrect time at 1450 hrs?

Simplicity said...

Hi, my waorking with concise explanation:

Tom has 35 socks in the box which consisted of 3 different colours, blue, grey and black. There are 12 blue socks, 9 greys socks and 14 black socks.

How many socks should Tom take out in order to be absolutely certained that there is a pair of same socks of each kind?

Solution

1st round:

9 blue = 4 pairs (8) + 1 (without pair)

2nd round:

9 grey = 4 pairs (8) + 1 (without pair)

3rd round:

9 black = 4 pairs (8) + 1(without pair)

Last round:

Notice that there is 1 sock which is left without a pair for the 3 rounds.

What colour you pick for the last round does not matter.

For instance,

If i pick blue, grey or black, either one of them will absolutely form a pair.

Anonymous said...

The questions is so simple. Don't know what is the fuss all about!