Analyzing 2009 PSLE Killer Math Question 18

Yes, it is the time of the year where tears spill over tough / killer PSLE math questions again.



From anecdotal evidence and discussions with parents of my students, maybe it is safe to conclude that the wave of PSLE Math killer questions occur in alternate years. Such killer questions always manage to draw out some precious tears from our precocious students. It is the same teary situation on 8 Oct 2009. The main culprit was said to be Question 18.

Let's have a glimpse of what this monster question is all about:

Q18 PSLE 2009 (5 m)
Jim bought some chocolates and gave half to Ken. Ken bought some sweets and gave half to Jim. When Jim ate 12 sweets while Ken ate 18 chocolates, the ratio of Jim's number of sweet to number of chocolate is 1: 7 while the ratio of Ken's number of sweets to number of chocolate is 1: 4. How many sweets did Ken buy?

Let's try to understand what made this question a killer. Most students find this question challenging due to Three main reasons:

1) Most students have not been exposed to logical-connect technique to make sense of two separate sets of clues.

2) Most students will be caught off guard as there is a "twist" embedded in the question, which required higher order crititcal thinking from students.

3) Lack of mental toughness

We will discuss in details in future blog on how to develop the above skills that most students lack so that such killer questions can be slayed effectively.

Without further ado, Here it is. Hope you enjoy the solution and experience a relief that such Killer question can be slayed after all.

SOLUTION: uMOLOCO FRAMEWORK

Understand & model

Logical connect

Using ratio given, we work backward to get the original unit of sweets and chocolate:
At first, 1 s = 1u +12 (add back); 1 c = 7u

Using cross multiply on Ken's numbers:
(1u + 12) x 4 = (7u -18) x 1
4u + 48 = 7u - 18
66 = 3u
22 = 1u

Number of sweets Ken bought = 2 x (1u + 12)
= 2 x (22 + 12)
= 68

But how do we know if our answer is correct? In tackling a tough question, it can be unnerving to arrive at a solution but unsure if it is correct or if all hard work end up in vain. Fear not, in our next update we will show you an effective way to confirm if the answer is correct.

John Yong