Q&A - PSLE Math

[charsen]

Michaelia0816:

Tianzhu,

Pls help,

1)Each of the three cards shown below is printed with a different whole number.
The biggest number is 42. When these number are added two at a time, the sums are 57,64 and 77. What are the other 2 numbers?

2) A forty- page newspaper, which consists of only one section, has a sheet with page 9 and page 10 missing. What other pages are missing?

Pls done it by today as I am going to have math prelim the next day~.~

For Q2 , my solution may not be the best. But this is what I was able to arrive at.
Every Sheet of page has 4 pages. Num 1 appears in Pg1, Num 2 appears in Pg2, Num 38 in Pg3, Num 40 in Pg4 of the first sheet of paper. Continuing this way we'll get something like this where Odd pages will appear in Pg1 and Pg3. Even pages will hence be in Pg2, Pg4 of every sheet. Also, Pg1,2 will be consecutive numbers and Pg3,4 will be consecutive numbers.

Sheet# Pg1 Pg2 Pg3 Pg4
1 1 2 39 40
2 3 4 37 38
3 5 5 35 36

Let F be the number in first page and L be the number in the Pg4 and N be the sheet number.
If we look at the pattern above, we can see for a given N, F = (N-1)x2 +1.
Also, the sum of numbers in Pg1 + Pg4 is constant and is equal to 41
We can find number 9 appears in Pg1 of Sheet 5.
Remaining pages of Sheet 5 (missing sheet)
Pg2 --> number 10
Pg4 --> 41 -9 = 32
Pg3 --> 32-1 = 31

Missing pages beside 9, 10 are 31 and 32

[superksmum]

charsen:

superksmum:

Hi please help on this question (Henry Park Prelim 2011, question 16).


Mr Lee took 7 hours to travel from Town A to Town B while Mr Wong took 8 hours to travel from Town B to Town A. Both of them did not change their spped throughout the journey. Both of them started off at the same time and moved towards each other. 3 hours later, they were 110km apart. What was the speed Mr Lee was driving?

Thank you.

Hi
In 3 hours, lee drove 3/8 of the journey.At the same time,wong took 3/7 of the journey.So,we should make the denominators 8 and 7 to be 56 since the distance in both is common.

Lee travelled 24U and wong travelled 21U.
56u-24U-21U=11U
11U-110km
1U-110/11=10km
Distance lee travelled--->10x24=240km
Lee's speed------>240/3=80km/h(ANS)

:thankyou: charsen

[charsen]

catddy2002:

Hi,


Pls help to solve these 2 questions:

1) At a party, there were some balloons, 40 balloons burst and 25% of the remaining ballons flew away. If only 2/3 of the balloons were left, how many balloons were there at first?

2) Jarmanye planned to cycle from Town A to Town B. If she cycled at 20km/h, she would reach Town B at 2 pm. If she cycled at 12 km/h, she would reached Town b at 3.30 pm. What was the distance between Town A and Town B?

Thanks

Hi
Q1.Equating 75% of remainder and 2/3 of total.Equalizing numerators,
3/4 of remainder=2/3 of total
6/8 of remainder = 6/9 of total
Total no. of balloons---->9U
9U-8U=1U
1u=40
9u=40x9=360 balloons(ANS)

Q2.Imagine there are 2 persons,A and B.A is cycling at 20km/h and B is travelling at 12km/h.The difference in speed is 8km/h.When A reached Town B at 2.00p.m,the difference in distance is 12x1 1/2=18km.

18/8=2 1/4h
Distance between town a and b------>20x2 1/4=45km(ANS)

[tianzhu]

2DMommy:

Please help me with these :


Find the sum of 35 + 37 + 39 + 41 + 43 ........ + 231 + 233.

What is the short cut to this question ?

Thank you.

Hi

It may not be the shortest way, but this is my preferred way as students would be using the very familiar way of find the sum of odd numbers starting from 1.

First find the sum of 1 + 3 ………… 233

Number of odd numbers ------- (233+1)/2 ------ 117

Sum of odd numbers ------- 117*117 ------- 13689

Then find the sum of odd numbers from 1 + 3 ……… 33

Number of odd numbers ------- (33+1)/2 ------ 17

Sum of odd numbers ------- 17*17 ------ 289

Sum of 35 + 37 + 39 + 41 + 43 ........ + 231 + 233 ------- 13689 – 289 ------- 13400

Another possible way, almost similar to find the sum of even numbers from 1 to 100.

Number of odd numbers ------- (233+1)/2 ------ 117

Number of odd numbers ------- (35+1)/2 ------ 18

117 - 18 ------ 99

99 + 1 ------ 100

100/2 ------ 50

Pair up the numbers.

233 + 35 ------ 268

231 + 37 ------- 268

268*50 ------- 13400

Best wishes

[catddy2002]

charsen:

catddy2002:

Hi,


Pls help to solve these 2 questions:

1) At a party, there were some balloons, 40 balloons burst and 25% of the remaining ballons flew away. If only 2/3 of the balloons were left, how many balloons were there at first?

2) Jarmanye planned to cycle from Town A to Town B. If she cycled at 20km/h, she would reach Town B at 2 pm. If she cycled at 12 km/h, she would reached Town b at 3.30 pm. What was the distance between Town A and Town B?

Thanks

Hi
Q1.Equating 75% of remainder and 2/3 of total.Equalizing numerators,
3/4 of remainder=2/3 of total
6/8 of remainder = 6/9 of total
Total no. of balloons---->9U
9U-8U=1U
1u=40
9u=40x9=360 balloons(ANS)

Q2.Imagine there are 2 persons,A and B.A is cycling at 20km/h and B is travelling at 12km/h.The difference in speed is 8km/h.When A reached Town B at 2.00p.m,the difference in distance is 12x1 1/2=18km.

18/8=2 1/4h
Distance between town a and b------>20x2 1/4=45km(ANS)

Thanks Carsen! :thankyou:

[Tiramisu Coco]

Hi, pls help with this qtn. Thks!


http://m.flickr.com/photos/82618212@N07/7837766706/lightbox/

[Chan09]

Any takers on this whether there is an easier way to solve than trial and error? Tks


Is there a faster method to solve this?
Eveyday A gets 10 additional new cards. On every third day he gives 3 cards away. If A starts with 8 cards on the first day, on which day will he have exactly 180 cards?

Thank you.

[superhappy]

Chan09:

Any takers on this whether there is an easier way to solve than trial and error? Tks


Is there a faster method to solve this?
Eveyday A gets 10 additional new cards. On every third day he gives 3 cards away. If A starts with 8 cards on the first day, on which day will he have exactly 180 cards?

Thank you.

Hi, pls help on this question:

1. The ratio of Jim's savings to Ken's savings is 1:2.
Jim received some money and his savings increased by 60%.
What percentage of Ken's money must be decreased so that their savings are equal?

Thanks !

[tianzhu]

Chan09:

Any takers on this whether there is an easier way to solve than trial and error? Tks


Is there a faster method to solve this?
Eveyday A gets 10 additional new cards. On every third day he gives 3 cards away. If A starts with 8 cards on the first day, on which day will he have exactly 180 cards?

Thank you.

Hi

Yes, you may use TR.

Alternatively try to establish a pattern.

Consider the first 3 days.

A started with 8 cards. On the 3rd day, A will get (8+10+10 – 3) -------25

Subsequently for the next three days, A will get (30-3) which is 27.

180 – 25 ------- 155

155/27 -------- 5.74

So, you’ll get 5 groups of 27 which is 135

135+25 ------ 160

On the 18th day, he’ll have 160 cards.(5*3 + 3 ----- 18)

180 – 160 ------- 20

20/10 -------- 2

Hence, A will get exactly 180 cards on the 20th day.

Best wishes

[tianzhu]

Michaelia0816:

2) A forty- page newspaper, which consists of only one section, has a sheet with page 9 and page 10 missing. What other pages are missing?

Pls done it by today as I am going to have math prelim the next day~.~

Hi

Try to see a pattern.This will help you in solving this question.

If you need the solution, please let me know.I'll try to do the slide tomorrow.

Best wishes