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.

Thursday, July 23, 2009

Rosyth Sch 2006 PSLE Math Prelim Q35 - alternative method

Daniel is thinking of three consecutive odd numbers. The average of the first and second number is 40, while the average of the second and third numbers is 42. List the three numbers.


Original post to this question can be found here.

Average of 1st and 2nd numbers ----- 40
Total of 1st and 2nd numbers ----- 40 x 2 = 80

1st ----1 unit
2nd ---- 1 unit + 2
Total of 1st and 2nd ---- 2 units + 2 ---- 80

2nd ---- 1 unit + 2
3rd ---- 1 unit + 2 + 2
Total of 2nd and 3rd ---- 2 units + 6

Total of 1st and 3rd is
(2 units + 2) + (2 units + 6)
= 4 units + 8

Average of 1st and 3rd is
(4 units + 8) divided by 2
= 2 units + 4

From Total of 1st and 2nd,
2 units + 2 ----- 80
2 units ----- 80 – 2 = 78
1 unit ----- 78 divided by 2 = 39

1st number is 39
2nd is 41
3rd is 43


Anonymous said...

Dear Mr Song

From your first step, you can already get the answer

Total of 1st and 2nd ---- 2 units + 2 ---- 80

1 unit --- 39 , which is the first number.

Why do you need to go further?

Anonymous said...

Hi Mr Song

Is Coco's approach acceptable in PSLE?

Average of 1st No. and 2nd No. = 40 ==> 1st No. = 40 - 1 = 39. 2nd No. = 40 + 1 = 41. Average of 2nd No. and 3rd No. = 42 ==> 2nd No. = 42 -1 = 41. 3rd No. = 42 + 1 = 43. Hence the 3 numbers are 39, 41 and 43.

So in Exam, all you need to write down will be 40 - 1 = 39. 40 + 1 = 41. 42 + 1 = 43. The 3 numbers are 39, 41 and 43.

To convince you that I live up to my nick "Maths Professor", you can draw a model - a big unit and a small unit. In between the 2 units mark out the average. Mark out the difference of 2. So small unit is Average - 1 and Big unit is Average + 1. Convinced?

Consecutive No. 1, 3, 5, etc. So there is a difference of 2 between consecutive no. Hence just minus 1 from ave gives the smaller no. and add 1 to ave gives the larger no.

Anonymous said...

Hi Mr Song

Is solar eclipse covered in PSLE Science syllabus?

Excel Eduservice said...

Yes, first step can get answer.

I was explaining in detail, using the average method, as requested in the original post under the comments section.

Did not think that of unit method when I posted then.

Solar eclipse is not in many science textbooks but I have seen some schools put it in their assessment papers. Cannot remember the school and year.

Anonymous said...

Hi Mr Song

Thank you.
Questions on averages usually look easy and at first glance.But they can be difficult to grasp and tricky.

Anonymous said...

Help !: 5 trained workers take 20 days to paint a room. 8 untrained workers can do the same task in 20 days.How long would a team of 4 trained and 4 untrained workers take to finish the same task?

Help !: 10 workers can complete a painting job. If there are 2 more workers, the painting job will be completed 6 days sooner. If the same painting job were to be done 21 days earlier, how many additional workers are needed ?

Help !: Mr Tan drives from Town A to Town B, a distance of 720 km,at a constant speed. When he returns from Town B to Town A, he saves an hour of travel time by increasing his average speed by 10 km/h. Find the total time taken for the whole journey (to and fro).

Anonymous said...

Help !: In a racing competition, two cars A and B are moving at the same constant speed of 80 km/h for 2 hours. Then Car B has an engine problem causing a stoppage of 2 hours. If Car A continues at the original speed, find the speed at which Car B should travel to catch up with Car A in another 4 hours.

Help !: Two trains start from Station A to Station B at a difference of 2 hours. They travel at the same speed of 60 km/h. The travel from Station A to B and back is on a continuing basis with a stop pf 1 hour on reaching the stations. If the distance between the two stations is 180 km, find the number and time of crossings in a day (24 hours) for the two trains.

Anonymous said...

LCM of 25 and 40 is 200 seconds. They will meet at the starting point every 200 seconds. Since Ruby completed each round in 25 seconds, thus, Ruby will have completed 200/25 = 8 rounds....Is the answer correct?

Multiple of 25 : 25, 50, 75, 100, 125, 150, 175, 200, 225 and Multiple of 40 : 40, 80, 120, 160, 200, 240....

Anonymous said...

If N is a 6-digits number, A7938B , such that it is divisible by 88. A and B are different digits. A is twice of B. Find A

Anonymous said...

Confused =X: can anyone help me with this?Car A left Town X for Town Y while Car B left Town Y for Town X and both cars left at the same time. The ratio of their respective speed is 5 : 4 initially. After they passed each other, Car A reduced its speed by 1/5 while Car B increased its speed by 20 %. When Car A reach Town Y, Car B was still 25 km away from Town X. What is the distance between Town X and Town Y?

A van left Metropolis Town and travelled towards Gotham Town at an average speed of 80km/h. An hour later, a car left Metropolis Town and travelled towards Gotham Town at an average speed of 100km/h. The car passed Keystone Town, which was halfway between Metropolis Town and Gotham Town, 30 minutes earlier than the van. The car reached Gotham Town at 10pm. At what time did the van leave Metropolis Town for Gotham Town?

Anonymous said...

i think this method would make y'all understand better it's algebra

let x be the smallest number.
40x2=80(total of 1st and 2nd)
42x2=84(total of 2nd and 3rd)
80+84=164(sum of 1st, 3rd and 2 of the second number)
x+x+2+x+2+x+4= 164
So, 4x+8=164
156/4=39(1st number)
39+2=41(2nd number)
39+4=43(3rd number)
hope y'all get it :D