OAT Quantitative Reasoning common mistakes
OAT Quantitative Reasoning · Understand the traps and how to avoid them.
When a problem gives a rate in one unit (e.g., miles per hour) and asks for an answer in another (feet per second), the candidate multiplies or divides by a single conversion factor and stops, producing an answer that is off by a factor of 60 or 3600.
Multi-step unit conversions are treated as one-step operations because the candidate converts only the unit that is visibly different and forgets that both the numerator and denominator units must be converted. Under time pressure, the first plausible number is accepted without checking dimensional consistency.
What to do instead
Before computing, write the target unit as a fraction (e.g., ft/s) and set up a chain of fractions with units that cancel diagonally until only the target units remain. Cancel units on paper as if they were algebraic symbols; if anything other than ft/s survives, the setup is wrong. Practice three-factor chains (miles→feet and hours→minutes→seconds) until the cancellation is automatic.
The candidate computes a percent change using the new value as the denominator (or subtracts percentages of different bases), giving a wrong percent increase or decrease, especially in successive-percent problems like 'price rises 20% then falls 20%'.
The formula (new − old)/old is recalled imprecisely, and successive percent changes are incorrectly added or subtracted (20% − 20% = 0) rather than applied sequentially to a changing base. The candidate does not register that the second percent acts on a different base amount.
What to do instead
Anchor every percent-change problem with the template: change ÷ original × 100. For successive changes, use multipliers: a 20% increase is ×1.20, a 20% decrease is ×0.80, and the combined effect is 1.20 × 0.80 = 0.96, a 4% net decrease. Do five multiplier drills mixing increases and decreases before the exam so the base-shift is recognized instantly.
When solving an inequality, the candidate divides or multiplies both sides by a negative number and keeps the inequality sign pointing the same way, then selects an answer choice with the reversed interval.
The rule that the inequality flips is memorized as a footnote but not linked to the operation being performed; the candidate is focused on isolating the variable and treats the sign as decoration. It is also easy to miss when the negative coefficient appears after several simplification steps.
What to do instead
Adopt a habit: circle every negative multiplier or divisor the moment it appears. After isolating the variable, test one value from the proposed solution set in the original inequality; if it fails, the sign is wrong. Do a set of ten inequalities deliberately containing negative coefficients and verify each answer by substitution.
On work-rate and combined-rate word problems, the candidate adds the times (e.g., 4 hours + 6 hours = 10 hours) instead of adding the rates, or averages the two times to get the combined time.
The numbers in the problem are times, and the candidate operates on the visible numbers rather than the underlying quantity (work per hour). The reciprocal relationship between rate and time is not internalized, so the arithmetic feels natural even though it is wrong.
What to do instead
Convert every rate to 'fraction of job per hour' before touching the calculator: 1/4 + 1/6 = 5/12 job per hour, so the job takes 12/5 hours. Sanity-check the result: the combined time must be less than either individual time. Drill five two-worker and two three-worker problems using the fraction-of-job method.
The candidate computes the area of a composite figure by adding all the labeled side lengths and treating the sum as area, or applies the perimeter formula when area is requested (and vice versa).
The formula sheet is skimmed and the words 'area' and 'perimeter' are not distinguished at the moment of computation; composite figures also invite adding every number on the diagram. The candidate does not pause to identify what quantity the question asks for.
What to do instead
Before computing, write the requested quantity and its unit (square units for area, linear units for perimeter) at the top of the scratch work. For composite figures, decompose into rectangles and triangles, compute each area separately, and sum only areas. Check that the answer's unit matches the question's unit.
On data-interpretation questions with a table or described chart, the candidate reads the row or column totals as if they were the category values, or compares two categories using totals instead of per-capita/percentage figures.
Tables present totals prominently and the candidate grabs the largest number near the category label. The distinction between absolute counts and rates is blurred when both appear in the same table.
What to do instead
Restate the question in your own words before reading the table ('which group has the highest rate per person, not the highest count'). Circle the exact cells needed and write the ratio explicitly before dividing. If a total is used, verify it is the denominator, not the numerator.
The candidate treats 'AND' and 'OR' probability questions identically, adding probabilities when events are independent and should be multiplied, or multiplying when events are mutually exclusive and should be added.
The words are read as ordinary English connectives, and the candidate does not check whether the events can co-occur. Without drawing a sample space or writing the rule, the operation choice defaults to whichever was used most recently in practice.
What to do instead
For every probability question, first classify the events: mutually exclusive (cannot both happen → add) or independent (one does not affect the other → multiply). Write the rule beside the computation. When events are neither, use P(A or B) = P(A) + P(B) − P(A and B) and confirm with a quick sample-space sketch for small cases.
When asked for the median or mode of a data set, the candidate reports the mean, or computes the median without first ordering the values, producing the middle of the unsorted list.
The mean is the most practiced measure, so it is computed by default. For the median, the candidate finds the middle position in the given order, which is only correct if the data happen to be sorted.
What to do instead
Sort the data explicitly before finding the median, and for an even count average the two middle values. Write the definition of the requested statistic next to the work (median = middle of ordered list; mode = most frequent). Practice with unsorted sets containing an even number of values and with sets having no mode or two modes.
The candidate sets up a ratio or proportion with the terms in mismatched order (e.g., apples:oranges on one side and oranges:apples on the other), then cross-multiplies and gets a plausible but incorrect value.
The setup is done quickly without labeling the units of each term, so the correspondence between the two ratios is assumed rather than verified. Cross-multiplication then produces a clean number that looks trustworthy.
What to do instead
Write each ratio with its units attached (apples/oranges = apples/oranges) and confirm the units match on both sides before cross-multiplying. Alternatively, solve by finding the unit rate first (cost per item, items per dollar) and scaling. Check the answer against the direction of the question: more items should cost more, not less.
On algebraic word problems, the candidate assigns a variable to the wrong quantity or fails to translate a phrase like 'five less than three times a number' into the correct expression, then solves a correct equation for the wrong setup.
Translation from English to algebra is done phrase-by-phrase left to right, so 'five less than' is written as 5 − 3x instead of 3x − 5. The candidate also skips defining the variable explicitly, losing track of what x represents.
What to do instead
Begin every word problem with 'Let x = ___' in full words. Translate comparison phrases by their structure: 'less than' reverses order, 'of' means multiply, 'is' means equals. After building the equation, plug the answer back into the original English sentence to confirm it satisfies the stated relationship, not just the equation.