Ruiya Math Blog · No. 4 · One Thinking Move
One difference can point left or right.
Most questions have one answer. But when a number is described only by its difference from another number, it may sit on either side. The second answer is not a mistake—it is a possibility you must test.
A Ruiya-original PSLE-style practice guide for Primary 5, Primary 6 and PSLE
The first useful observation
‘Differs by’ does not say cheaper or more expensive. Draw both directions before you calculate any percentage.
A difference of $7.20 means one price can be $7.20 below or $7.20 above the known price.
The challenge
The jacket-price challenge
- • A jacket originally costs $72.
- • One buyer pays $57.60 after a 20% discount.
- • Another buyer pays a price that differs by $7.20 from $57.60.
- • What are the two possible discount percentages for the second buyer?
This is a Ruiya-original analogue, not a past-paper question.
Why this strategy fits
Use a picture your brain already understands.
Stand on the middle stair of a staircase. A step 2 stairs away can be 2 stairs higher or 2 stairs lower. Distance alone does not choose a direction.
Place the known price in the middle. Start at $57.60. The second price is $7.20 away, so it can be $57.60 − $7.20 = $50.40 or $57.60 + $7.20 = $64.80.
Find each discount amount. From $72 to $50.40 is a reduction of $21.60. From $72 to $64.80 is a reduction of $7.20.
Turn each reduction into a percentage. $21.60 ÷ $72 = 30% and $7.20 ÷ $72 = 10%. Keep both because both prices fit the words.
Check your answer
10% off $72 is $64.80; 30% off $72 is $50.40. Both are exactly $7.20 from $57.60.
Answer: The second buyer could receive a 10% discount or a 30% discount.
Traps to watch for
The usual wrong turn is often a very reasonable first thought.
Assuming ‘difference’ means lower
That throws away the $64.80 possibility without a reason.
Finding a percentage of the sale price
A discount percentage is compared with the original $72, not with $57.60.
Stopping after the first answer
When a direction is not stated, always ask: what happens on the other side?
How an examiner can change it
Keep the thinking move, not the story.
A question may say ‘the age differs’, ‘the length is different by’, ‘the temperature changes by’ or ‘the total is x more or less’. Make a two-branch mini-table before choosing one path.
Try a fresh variation
A bag costs $90. One shopper pays $72. Another pays an amount that differs by $9 from $72. What are the two possible discount percentages?
Do not look for the same numbers. Ask which relationship is still doing the work.
Outside the exam
A useful model helps you make a fair decision.
When comparing a budget with an actual bill, a difference tells you the size of the gap—not whether you overspent or underspent. You need both directions until the context chooses one.
Try it with Ruiya
Want help choosing the first step?
Send Ruiya a hard question and ask: “What is the relationship I should notice before I calculate?”
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