1
Every wrong choice has a job.
n + (n+1) + (n+2) = 48
set up
3n + 3 = 48, n = 15
solve
largest = n + 2 = 17
the question's actual demand
| Choice | Who picks it |
|---|
| A. 17 | read the question |
|---|
| B. 48 | copied a number from the problem |
|---|
| C. 15 | stopped at n — the smallest |
|---|
| D. 16 | gave the middle one |
|---|
Three of the four are reachable by doing correct algebra and then answering the
wrong question.
Consecutive odd or even integers step by 2: n, n + 2, n + 4. For any three equally
spaced numbers the middle one is the sum ÷ 3 — three consecutive odd integers that add
to 57 have middle 19, so they are 17, 19 and 21.
2
The one-step-early trap.
By far the most common. You solve for x when x is not what was asked.
| Topic | You find | They want |
|---|
| consecutive integers | the first | the largest |
|---|
| the vertex | the time, t | the height, h |
|---|
| angles as expressions | x | the angles |
|---|
| systems | x only | x and y, or x + y |
|---|
| age problems | the age now | the age in 5 years |
|---|
| a rectangle from its perimeter | the width, from 2(l + w) = P | the length, or the area l × w |
|---|
The vertex trap, worked: a ball's height is h = −4t² + 24t metres after t seconds.
peak at t = −b2a = −24−8 = 3 s
this is a time, not the answer
h = −4(9) + 24(3) = −36 + 72 = 36 m
the maximum height
lands when h = 0: −4t(t − 6) = 0, so t = 6 s
t = 0 is the throw; a negative t is never a time
The habit that fixes it: underline the last few words of the question before you
start, and check your answer against them before you shade anything.
3
Sign, reciprocal and form traps.
sign flip
−4 offered beside 4
from one dropped minus
reciprocal
⅔ offered beside 32
from an inverted fraction
unsimplified
√8 offered beside 2√2
both are right; only one is listed
When two choices are a sign or a flip apart, that pair is the trap. Slow down and
decide which one your working actually gives.
If your answer is not listed
Try simplifying it, or rearranging into another form, before assuming you are
wrong. 2√2 and √8 are the same number.
4
The inequality flip.
Solve −2x + 5 ≥ −1.
−2x ≥ −6
subtract 5 from both sides
x ≤ 3
divide by −2 — the sign turns round
test x = 0: −2(0) + 5 = 5 ≥ −1 ✓
a value from the answer set works
test x = 4: −8 + 5 = −3, not ≥ −1
a value outside fails, as it should
Forgetting the flip gives x ≥ 3
That answer is always offered. It keeps the boundary 3 but points the wrong way, so
test one easy value such as 0 before you shade. Multiplying or dividing both sides by
a negative number is the only step that turns the sign round.
5
When they ask for a combination, get it directly.
“Find x + y” or “find a² + b²” is a hint: there is a route that never finds x, y, a or b.
If 3x + y = 14 and x + 3y = 10, find x + y.
add: 4x + 4y = 24
the coefficients match after adding
If a − b = 3 and ab = 10, find a² + b².
(a − b)² = a² − 2ab + b²
the square holds a² + b²
a² + b² = (a − b)² + 2ab
rearrange
= 9 + 20 = 29
check: a = 5, b = 2 gives 25 + 4
The planted choices
For x + y, expect the single values x = 4 and y = 2 among the choices. For a² + b², expect
(a − b)² = 9 and (a + b)² = 49. Each is a correct number that answers a different question.
6
Units and wording.
| Watch for | What it does |
|---|
| “not” or “except” | reverses the whole question |
|---|
| minutes vs hours | an answer 60 times out |
|---|
| cm vs m | 100 out, or 10,000 for areas |
|---|
| “percent” vs “decimal” | 0.35 against 35% |
|---|
| “how many more” | a difference, not a total |
|---|
| percent increase or decrease | divide the change by the OLD value: ₱80 → ₱100 is a 2080 = 25% rise, not 20100 = 20% |
|---|
A “not” question rewards the three choices you would normally eliminate. Circle the
word the moment you see it.
7
Variations: the off-by-one, the squared unit, and the lost root.
Counting both ends: how many integers from 15 to 42 inclusive? How many posts hold 60 m of straight fence, one every 5 m?
42 − 15 = 27 gaps, so 27 + 1 = 28 integers
a subtraction counts the gaps
60 ÷ 5 = 12 gaps, so 13 posts
a post at each end
What is different: the trap choice is exactly one less. Test it on a tiny case — 1 to 3 has 3 numbers, not 3 − 1 = 2.
A squared unit: the area of a 3 m by 2 m wall, in cm².
3 m = 300 cm, 2 m = 200 cm
convert each length first
300 × 200 = 60,000 cm²
6 m² × 10,000
What is different: 1 m² is 100 × 100 cm², not 100 cm². The trap choice, 600 cm², converts the area as if it were a length.
A root lost by dividing: solve x² = 2x.
x² − 2x = 0
bring everything to one side
x(x − 2) = 0
factor out x
x = 0 or 2
both check: 0 = 0 and 4 = 4
What is different: dividing both sides by x gives only x = 2, and “2 only” will be a choice. We never divide by something that could be zero.
8
Turning the traps into a tool.
The choices leak information about the intended method.
choices 15, 16, 17, 48
three are clustered
the outlier 48 is padding
rarely the answer
the cluster hides the real one
so read the question again
Three habits
Underline what is asked. Write the answer down before looking at the choices.
Then, if your answer sits next to a near-twin, re-read the last line once more.
On the exam
Nearly every UPCAT-type item carries at least one trap choice: the x instead of the
quantity asked, the unflipped inequality, the number copied from the stem. Before you
shade, spend ten seconds reading the last line again and asking which slip each
neighbouring choice came from.
✓
Check: does it satisfy the question?
the three integers
15, 16, 17
consecutive ✓
their sum
15 + 16 + 17 = 48
matches ✓
the question asked
the largest
17, not 15 ✓
Remember the flow
Underline what is asked · Solve · Check against it
Near-twin choices mark the trap.
