I85PREP
⌘ K
CFAT study materials
CFAT study resources

CFAT: CFAT Problem Solving: Translate, Estimate, and Verify

CFAT · Work through your exam, one topic at a time.

All guide sections

CFAT Problem Solving: Translate, Estimate, and Verify

What Problem Solving measures

The CFAT's Problem Solving domain tests arithmetic, algebra, ratios and proportions, percentages, averages, geometry, logic, and data interpretation. Items are multiple-choice and are designed to be answered without a calculator. The score depends on setting up the correct relationship and avoiding answer choices that match a common wrong operation.

Core rules

  • Translate the words into an equation before calculating. Define the variable explicitly, such as 'let x be the original price'.
  • Keep units attached to every number. A rate in hours must be converted before it is combined with minutes.
  • For successive percent changes, multiply decimal factors. A 20% decrease followed by a 10% decrease is 0.80 times 0.90, not 0.70.
  • When algebra is messy, back-solve from the answer choices by substituting them into the condition.
  • Estimate first to eliminate impossible magnitudes, then calculate exactly only for the remaining choices.
  • Answer the quantity asked for, not an intermediate value.

Worked example

A jacket's price is reduced by 20%, and then the sale price is reduced by another 10%. What single discount is equivalent to the two reductions? Let the original price be P. After the first reduction the price is 0.80P. After the second reduction it is 0.90 times 0.80P, which equals 0.72P. The customer pays 72% of the original price, so the equivalent single discount is 28%. The trap answer is 30%, which comes from adding 20% and 10%. The second discount applies to the already reduced price, so the reductions compound.

Traps that cost marks

  • Adding successive percentages instead of multiplying their factors.
  • Taking a percentage of the wrong base, such as the sale price instead of the original price.
  • Mixing units, especially minutes and hours or centimetres and metres.
  • Solving for x when the question asks for 2x or for a total.
  • Using every number in the stem even when one is irrelevant.
  • Rounding too early and losing an exact answer choice.