Mathematical Reasoning Mock Test 15: 2027 NSW Selective Format

Big idea: All probabilities for one pick must add up to 1 (100%).

Step 1 — Indigo from the "twice as many" rule

If there are twice as many indigo marbles as amber marbles, then:

P(indigo) = 2 × P(amber) = 2 × 0.2 = 0.4

Step 2 — Add the probabilities you know

Picture the four colours filling the whole probability bar from 0 to 1:

0         0.2      0.55       0.95 1.0
|──amber──|──coral──|──indigo──|lime|
   0.20      0.35      0.40    0.05

Step 3 — Lime is what is left

P(lime) = 1 − 0.95 = 0.05

Answer: 0.05

Repeatable checklist

1. Turn "twice as many" into double the probability (same bag, one pick).

2. Add every probability you know.

3. Subtract from 1 to find the last colour.

Common traps

• 0.1 — answer from the Janison question (different numbers).
• 0.95 — added the three known probabilities but forgot to subtract from 1.
• 0.3 — used coral's probability or mixed up colours.
• 0.5 — doubled the wrong probability.

Step 1 — How much did Fern eat?

The whole bar is 5/5.

Dana + Evan: 1/5 + 2/5 = 3/5

Fern (the rest): 5/5 − 3/5 = 2/5

Whole bar (5 equal pieces):
┌──────┬─────────────┬─────────────┐
│ Dana │    Evan     │    Fern     │
│  1/5 │     2/5     │     2/5     │
└──────┴─────────────┴─────────────┘

Benchmarks:
  Half (½)  = 2.5 pieces   →  Fern's 2 pieces < half     ✓
  Quarter(¼) = 1.25 pieces →  Dana's 1 piece  < quarter  ✗
  ¾ of bar  = 3.75 pieces  →  Dana+Evan = 3 pieces < ¾   ✓

Step 2 — Test each statement

Use the same denominator when comparing (often 10 or 20 works well).

Statement 1: "Fern ate less than half of the bar."

• Half = 1/2 = 5/10
• Fern = 4/10
• 4/10 < 5/10 → True ✓

Statement 2: "Dana ate more than one quarter of the bar."

• One quarter = 1/4 = 5/20
• Dana = 1/5 = 4/20
• 4/20 is not more than 5/20 → False ✗

Statement 3: "Dana and Evan ate less than three quarters of the bar altogether."

• Three quarters = 3/4 = 15/20
• Dana + Evan = 3/5 = 12/20
• 12/20 < 15/20 → True ✓

Answer: statements 1 and 3 only

Repeatable checklist

1. Add the given fractions; subtract from 1 (or from 5/5, 6/6, etc.) for "the rest".

2. Rewrite fractions with a common denominator before comparing.

3. Test each statement separately — do not assume two true statements must be "1 and 2".

Traps in the options

• Statement 2 only — 1/5 looks small but is less than 1/4.
• Statements 1 and 2 only — statement 2 is false.