GRE Quantitative common mistakes
GRE Quantitative · Understand the traps and how to avoid them.
Computes a percent increase followed by the same percent decrease as a net change of zero (e.g., 20% up then 20% down treated as 'back to the start'), or adds/subtracts percentage points when successive percent changes should compound.
Percentages are intuitively treated as additive quantities added to a starting amount, because everyday language ('up 20, down 20') invites that reading; the multiplicative structure only shows up when the factors are written out.
What to do instead
Convert every percent change to a multiplier before doing anything else: +20% -> x1.2, -20% -> x0.8. Multiply the multipliers (1.2 x 0.8 = 0.96) and only then translate back to a percent. Never add or subtract percents that are applied in sequence.
Uses the wrong quantity as the base of a percent comparison, e.g., answering 'A is what percent greater than B' by computing (A-B)/A instead of (A-B)/B, or computing percent change against the new value rather than the original.
The word order in the sentence is processed loosely and the formula (difference)/(something) is applied with whichever number is salient, and the number that appears last in the sentence or the larger number feels like the natural denominator.
What to do instead
Locate the word 'than' (or 'of') and treat the quantity immediately following it as the denominator. Write the fraction as a labeled sentence before computing: (A - B) / B, where B is whatever follows 'than'.
Divides both sides of an equation by a variable expression, silently discarding a solution (e.g., x^2 = 5x solved as x = 5, losing x = 0; or x^2 - x = 0 solved as x = 1).
Dividing to simplify is heavily over-practiced in routine algebra, and the implicit assumption that the divisor is nonzero is invisible when the divisor is a letter rather than a number.
What to do instead
Never divide by a variable. Move everything to one side, factor, and set each factor to zero. If division is truly needed, split into two cases first: divisor = 0 and divisor != 0, and check whether the discarded case yields valid solutions.
Solves the given equation for x, then stops and selects that value, when the question actually asks for 2x + 3, x^2, x + y, or 'the value of the expression'.
Procedural momentum: the equation is the most prominent object on the screen, so finding x feels like the goal and the last line of the question is skimmed rather than parsed.
What to do instead
Before writing any algebra, copy the target expression onto scratch paper under the heading 'FIND'. After solving, substitute into that exact expression and only then look at the answer choices. If the target is x + y, resist solving for each variable separately and manipulate the given equations as a system.
In Quantitative Comparison, tests one or two convenient values (usually positive integers greater than 1), gets a consistent result, and commits to A or B without probing cases that break the relationship.
A single confirming example produces strong subjective confidence, and the special values that flip comparisons (0, 1, negatives, fractions between 0 and 1) are exactly the ones that do not come to mind as 'typical' numbers.
What to do instead
Build a fixed test set and run every applicable value through it before choosing: -2, -1, -1/2, 0, 1/2, 1, 2, and one large number. Stop the moment two values give different orderings and choose D. If the quantities involve a variable raised to an even power or multiplied by an unknown-sign expression, treat the sign split as mandatory.
Treats a geometry figure as evidence: assumes an angle is 90 degrees because it looks square, assumes two segments are equal because they look equal, assumes lines are parallel or that a point is a midpoint, or measures a length by eye.
Visual processing delivers these judgments automatically and pre-consciously; the figure is processed as a diagram of the situation rather than as a deliberately unreliable sketch, and the test instructions about scale are read once and forgotten under time pressure.
What to do instead
Apply a rule at the start of every geometry question: only marked information (tick marks, right-angle squares, given values, stated parallel conditions) may enter the solution. Anything assumed must be tested by redrawing the figure in a distorted but condition-satisfying way; if the answer changes under the distortion, the assumption was invalid.
Substitutes the diameter where the radius belongs, or applies the area formula when the circumference is required (or vice versa), especially when a problem supplies the diameter, the area, or the circumference and asks for a different circle quantity.
The formulas 2(pi)r and (pi)r^2 are stored as a visual pair and retrieved by familiarity rather than by matching the formula to the named quantity; the diameter-to-radius conversion is a one-step transformation that is easy to skip when the given number is already 'a radius-shaped number'.
What to do instead
Write the quantity names and formulas down before substituting: r = d/2, C = 2(pi)r, A = (pi)r^2. Immediately convert any given diameter to a radius and box it. For reverse problems (given A, find C), go through r explicitly rather than combining formulas from memory.
Compares raw counts across groups with different totals, e.g., concluding that group A has a higher rate of X because A has more X's, when A is simply larger, or picking the tallest bar on a chart whose bars represent different-sized populations.
The counts are the numbers actually printed on the chart or in the table, and the eye is drawn to the largest absolute value; the denominators are in a legend or heading and are not attached to the numbers being compared.
What to do instead
Before comparing any two rows, columns, or bars, check whether the totals differ. If they do, convert every value to a rate (value / total, as a percent or per-capita figure) and compare the converted numbers. Write the conversion for each group rather than estimating from bar heights.
Combines subgroup averages by averaging the averages, e.g., reporting the overall mean of two groups as (mean1 + mean2)/2 when the groups have different sizes, or computing an overall median the same way.
The averages are the given numbers, and averaging them feels like the symmetric, neutral operation; the group sizes appear as separate context that seems irrelevant once an average is already known.
What to do instead
Convert every group mean back into a total: total = mean x n. Sum the totals, sum the sizes, and divide. Sanity-check by asking whether the overall mean must lie closer to the mean of the larger group; if your answer sits exactly at the midpoint, the sizes were probably equal or you averaged the averages.
Takes the median of a list with an even number of values by pointing at one of the two middle entries instead of averaging them, or re-sorts inconsistently and picks the middle of the original order.
The 'middle value' definition learned from odd-length examples is carried over unchanged, and the even case is a small extra step that is easy to omit once the two central entries have been located.
What to do instead
Rewrite the list in ascending order as a separate step, number the entries 1 through n, then apply the rule explicitly: odd n -> entry (n+1)/2; even n -> average of entries n/2 and n/2 + 1. Compute the average of the two middle values on paper even when it looks trivial.