Complex Problems

This lesson isn't about a new maths skill. It's about managing complexity - knowing when to invest time, when to bail out, how to break problems into sub-steps, and how to verify your answer without redoing the whole calculation. Roughly 30-40% of QR questions are multi-step. How you handle them determines your overall score.

Before starting any calculation, classify the question. This takes 3-5 seconds and prevents you from spending 60 seconds on a problem that should take 15.

If you classified a question as "simple" and find yourself on step 3 of a calculation, stop. Either you misidentified the complexity (re-read the question) or you're overcomplicating the approach.

Not every question is worth 43 seconds. Learn to spot the ones that'll eat time without giving you marks.

1. Can't identify the approach in 5 seconds. If you don't know the first step, you won't figure it out under time pressure. Flag it.
2. Data overload. The exhibit is a massive table with 8+ columns, or a diagram with many unlabelled parts.
3. Close answer choices. Options like 12.4 / 12.6 / 12.8 / 13.0 - high precision needed, one rounding error costs the mark.
4. 3+ calculation steps visible. "Find the percentage change in profit margin after accounting for the currency adjustment and tax…" - each step is a chance to make an error.
5. Negative / missing-group questions. "How many did NOT attend?" = total − attended. Not hard, but one extra step.

The Skip Process

1. Identify the skip signal (5 sec)
2. Eliminate any obviously wrong answers (5 sec) - too big, too small, wrong units, impossible
3. Pick from the remaining options (2 sec)
4. Flag the question (1 sec)
5. Move on

Total: ~13 seconds. You've preserved ~30 seconds for a question you can answer.

When you decide a complex question is worth attempting, break it into sub-calculations. Each sub-calculation should produce a single number you can use in the next step.

Write down intermediate results on your whiteboard. Memory errors cause more wrong answers than calculation errors. If you're juggling two numbers in your head while typing a third into the calculator, one of them will slip. The 2 seconds you spend writing saves the 15 seconds you'd spend recalculating after a memory slip.

The Chain Method

Problem: "Company A sold 1,200 units at £45 each. They offered a 15% discount on 300 units. What was the total revenue?"

Sub-calc A (full-price revenue): (1200 − 300) = 900 units × 45 = £40,500
Sub-calc B (discounted revenue): 45 × 0.85 = £38.25 discounted price → 300 × 38.25 = £11,475
Sub-calc C (total): 40,500 + 11,475 = £51,975

Three clean steps. Use memory (P) to store sub-calc A, then add sub-calc B.

Worked Example: Multi-Step with Table Data

Question: The table shows employee data. What percentage of total salary expenditure goes to the Marketing department?

Sub-calc A: Marketing total = 18 × 38,000 = £684,000
Sub-calc B: Company total = (25 × 34) + (18 × 38) + (32 × 42) + (15 × 29) = 850 + 684 + 1,344 + 435 = 3,313 (in thousands)
Sub-calc C: Percentage = 684 / 3313 × 100 = 20.6%

Calculator with memory + zero-stripping: 25 * 34 = 850 (P) → 18 * 38 = 684 (P, memory 1534) → 32 * 42 = 1344 (P, memory 2878) → 15 * 29 = 435 + C = 3313. Then 684 / 3313 * 100 = 20.6%. Time: ~35 sec.

Planning Your Sub-Steps

For problems with 3+ steps, mentally label each sub-result before you start calculating: "I need: (A) full-price revenue, (B) discounted revenue, then A + B." This prevents the common error of losing track of what you're calculating halfway through.

After calculating, spend 3 seconds on a sense check. Does the answer make sense?

Order-of-Magnitude Check

Your calculated answer: £347.50.

Quick check: 1,200 units at ~£45 each is ~£54,000 total. £347.50 is way too small for 1,200 units. Something went wrong.

This 5-second check catches errors that would otherwise cost marks.

Estimation Shortcuts

Round and bound: for 24.7 × 38.2, round down to 24 × 38 = 912 and round up to 25 × 39 = 975. Answer must be between 912 and 975. If only one answer choice falls in this range, you're done.

Factor of 10: is the answer in the hundreds, thousands, or millions? If three options are ~300 and one is ~3000, check magnitude first.

Parity check: odd × odd = odd. Even × anything = even. If your answer is 347 but should be even, something is wrong.

Formula: Missing = Total − Given.

"425 tickets were available. 287 were sold on Day 1 and 96 on Day 2. How many remain unsold?"

Total: 425. Sold: 287 + 96 = 383. Unsold: `425 − 383 = 42`.

Not hard, but it takes one extra step. Factor that into your time budget.

The Double-Negative Trap

"What percentage of customers did NOT choose options other than A?"

"NOT" + "other than" = double negative = "did choose A".

Read carefully. Rephrase in plain English before calculating.

1. Read the question.
2. Can I identify the approach in 5 seconds? No → skip (eliminate + guess + flag).
3. How many calculation steps?

After calculating: does the answer match one of the options?

• Yes → check magnitude (sense check) → submit.
• No → re-read the question. Did you answer what was asked? (Common: calculated revenue but asked for profit; calculated total but asked for per-unit.)

Don't attempt every question in order. Move through the set strategically:

First pass (aim to complete in ~2 min):

• Answer all "no calculation" and "simple calculation" questions
• Skip any question where you can't see the approach immediately

Second pass (remaining time in the set):

• Return to flagged complex questions
• You now know the exhibit well from the first pass
• Attempt if time allows, guess if it doesn't

The simple questions in a set force you to read and understand the exhibit. By the time you return to the hard question, you already know where the numbers are.

Trap 1: Answering the wrong question

You calculate total cost, but the question asks for cost per item. Re-read the question after calculating to make sure your answer matches what was asked.

Trap 2: Sunk cost fallacy

You've spent 30 seconds and are stuck. You think "I've already invested time, I should finish." No - cut your losses. Guess, flag, move on. 30 wasted seconds is better than 60.

Trap 3: Calculator chain errors

Long chains of operations accumulate rounding errors. For 3+ step problems, do each step separately and note intermediates on your whiteboard or in memory.

Trap 4: Misreading the exhibit under pressure

The most common QR error is pulling the wrong number from a table or chart - wrong row, wrong column, wrong axis. Slow down for 0.5 seconds when extracting data - it saves recalculating.

Next lesson: 3.8 Triage & Technique Map - the complete QR system pulling everything together, with triage classifications and time management.