ICAP QAT common mistakes
ICAP QAT · Understand the traps and how to avoid them.
Reading a percentage-change question and computing the new value as original × (1 + r) when the question asks for the percentage change relative to the new base (or vice versa), for example reporting a rise from 80 to 100 as 20% instead of 25%.
The candidate pattern-matches the word 'increase' to the first formula that comes to mind and never writes down which quantity is the base. Percentage problems are the highest-volume topic in quantitative aptitude papers, so this habit is rehearsed thousands of times without a base check.
What to do instead
Before any arithmetic, write the sentence 'change ÷ original base = x' with the base named explicitly (old value, new value, or a stated reference). For successive changes, chain multipliers (1.2 × 0.9) rather than adding percentages, and sanity-check direction: a 20% rise followed by a 20% fall must land below the start.
Solving ratio and proportion questions by setting up cross-multiplication on the wrong pairing, e.g. treating 'A:B = 3:4 and B:C = 6:5' as A:B:C = 3:4:5 instead of equalising the shared term to get 9:12:10.
Ratios are taught as fraction pairs, and candidates mechanically copy the numbers into a three-part ratio without noticing that B has two different values in the two statements. Under time pressure the shared-term step feels like extra work and is skipped.
What to do instead
Always rewrite every ratio so the repeated term matches: multiply the first ratio by 6 and the second by 4 to make B = 24, then read off A:B:C. Practise a fixed three-line template (list ratios, equalise the common term, scale) and apply it to every ratio question, including mixture and partnership problems.
Applying the simple-interest formula to compound-interest questions, or compounding annually when the question specifies half-yearly or quarterly compounding, producing an answer that is close but wrong among the options.
Simple interest is learned first and is arithmetically lighter, so under exam pressure the candidate defaults to P×R×T/100 and ignores the word 'compounded'. Distractor options are deliberately built from the simple-interest result, which reinforces the error.
What to do instead
Circle the compounding frequency in the question stem before computing. Use A = P(1 + r/n)^(nt) with n = 1, 2, or 4 as stated, and for two-year problems verify with the shortcut P(r/100)² for the interest on interest. If two options differ only slightly, that is a signal the question is testing compounding, not simple interest.
Mixing up the work-rate formula when one worker leaves or joins mid-project: adding the individual times (A takes 10 days, B takes 15, so together 25 days) instead of adding rates (1/10 + 1/15 = 1/6, so 6 days).
Time feels additive in everyday experience, and the reciprocal relationship between time and rate is counter-intuitive. Candidates also forget to convert a combined rate back into days at the end, leaving an answer in units of 'work per day'.
What to do instead
Convert every worker to a rate in work-units per day before combining, sum the rates, then invert for time. Use the LCM method (assume 30 units of work; A does 3/day, B does 2/day, together 5/day → 6 days) because it keeps everything in integers and makes mid-project changes easy to model.
Solving relative-speed problems without fixing a frame of reference, for example adding the speeds of two trains moving in the same direction, or forgetting to add train length to platform length when computing crossing time.
The candidate visualises the motion loosely rather than writing the relative velocity. Train problems also hide two distances (train length and platform length), and only one is usually stated prominently, so the second is dropped.
What to do instead
State the frame explicitly: same direction → subtract speeds; opposite direction → add. Write 'total distance = length of train + length of platform (or second train)' before dividing by relative speed. Convert km/h to m/s by multiplying by 5/18 at the start, never mid-calculation.
Treating every average as an arithmetic mean, including cases where the question gives speeds over equal distances or weighted group averages, and averaging the averages (e.g. averaging 40 km/h and 60 km/h to get 50 km/h for a round trip whose true average is 48 km/h).
The arithmetic mean is the only average most candidates use daily, and the harmonic-mean case is easy to miss because the numbers look symmetric. Similarly, group averages tempt a simple mean of the two group means, ignoring group sizes.
What to do instead
Ask what the denominator is: for equal distances use the harmonic mean 2xy/(x+y); for group averages weight by the number of items in each group. A quick check: the true average of two speeds over equal distance is always below the arithmetic mean, so an answer of exactly 50 should be treated as suspect.
Mis-solving mixtures and alligation by assuming volumes are additive after replacement, e.g. removing 10 litres from a 100-litre milk-water mixture and topping up with water, then computing the new concentration as a simple subtraction rather than multiplying by the remaining fraction.
The candidate models the operation as removing pure milk rather than removing the mixture at its current concentration. Repeated replacement compounds the error, and the arithmetic looks plausible enough that no check is performed.
What to do instead
Use the replacement formula: final amount of original component = initial amount × (1 − replaced/total)^n. Alternatively track the fraction remaining after each step multiplicatively. Verify with a two-step manual trace for small n before trusting the formula.
Answering permutation questions with combinations (or the reverse) because the candidate never checks whether order matters, e.g. counting the number of ways to choose a committee of 3 from 10 as 10×9×8 instead of 120.
The words 'select' and 'arrange' are used loosely in question stems, and the formulas nPr and nCr look similar. Candidates who memorise formulas without the order test cannot distinguish them under time pressure.
What to do instead
Apply an explicit test: swap two chosen items and ask whether the outcome is a different result. If yes, it is a permutation. Write nCr = nPr / r! next to every problem and, for mixed cases (choose then arrange), multiply the combination by the factorial of arrangements.
Computing probability of 'at least one' by adding individual probabilities instead of using the complement, and failing to adjust the denominator when sampling without replacement (e.g. two aces from a deck computed as (4/52)² instead of (4/52)×(3/51)).
The complement rule requires a mental inversion that is not intuitive, and the 'with replacement' assumption is the default in everyday reasoning. Double-counting in the addition also goes unnoticed because the result is under 1.
What to do instead
For any 'at least one' phrasing, immediately write P(at least one) = 1 − P(none). For draws without replacement, decrement both numerator and denominator at each step. Check that no computed probability exceeds 1 and that mutually exclusive events were not added when they overlap.
Losing marks on data-interpretation sets by reading the wrong column or axis, ignoring the units in the legend (thousands vs millions, percentage vs absolute), or answering a 'percentage of total' question with the raw figure.
Data-interpretation sets are dense and time-limited, so candidates skim the chart title and legend and jump to the first number that matches an option. Unit labels are small and easy to overlook, and the arithmetic is often correct but applied to the wrong quantity.
What to do instead
Spend the first ten seconds writing down the axis labels, units, and total base for each chart before touching the questions. Restate each question in symbols (e.g. 'A as % of total = A / Σ × 100') and only then substitute numbers. Cross-check any answer against the visual magnitude of the bar or slice.