Graduate Management Admission Test (GMAT) Foundational Skills and Error Avoidance Syllabus

Foundational Skills and Error Avoidance syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Foundational Skills and Error Avoidance in Graduate Management Admission Test (GMAT), not a summary of it.

1. 1

   Mental Maths and Computation

   3 topics

   • Fast Calculation Techniques
     • Common fraction-percentage equivalents
     • Squares, cubes and useful number facts
   • Working Without a Calculator
     • Quant section calculator restriction
     • On-screen calculator in Data Insights
   • Avoiding Computational Errors
     • Sign and decimal-place mistakes
2. 2

   English Language Precision

   3 topics

   • Grammar for Verbal Accuracy
     • Subject-verb agreement
     • Pronoun reference and modifiers
   • Reading Dense Prose
     • Parsing long and complex sentences
   • Vocabulary in Context
3. 3

   Common Trap Recognition

   3 topics

   • Quant Answer Traps
     • Partial-answer and reversed-value traps
   • Verbal Answer Traps
     • Out-of-scope and extreme-language choices
   • Data Insights Traps
     • Misreading units, axes and scales

Foundational Skills and Error Avoidance flashcards for Graduate Management Admission Test (GMAT)

20 of 50 cards from the Foundational Skills and Error Avoidance deck — real questions with worked answers.

1. What is the fast technique for multiplying a number by 5 without a calculator?

   Multiply by 10 and then halve the result (since $5 = \frac{10}{2}$). For example, $48 \times 5 = \frac{480}{2} = 240$.

2. How can you quickly multiply a two-digit number by 11 (e.g. $11 \times 36$)?

   Split the digits, add them, and place the sum in the middle: $3\,(3+6)\,6 = 396$. If the inner sum exceeds 9, carry the tens digit to the left.

3. What fraction equivalents should be memorized for the percentages $12.5\%$, $16.\overline{6}\%$, $33.\overline{3}\%$, $37.5\%$ and $66.\overline{6}\%$?

   $12.5\% = \frac{1}{8}$, $16.\overline{6}\% = \frac{1}{6}$, $33.\overline{3}\% = \frac{1}{3}$, $37.5\% = \frac{3}{8}$, and $66.\overline{6}\% = \frac{2}{3}$.

4. What is the fast way to find a percentage such as $15\%$ of a number mentally?

   Break it into $10\% + 5\%$: find $10\%$ by moving the decimal one place left, then add half of that for the $5\%$. E.g. $15\%$ of $80 = 8 + 4 = 12$.

5. What is the difference-of-squares shortcut for products like $48 \times 52$?

   Use $(a-b)(a+b) = a^{2} - b^{2}$ around the midpoint: $48 \times 52 = 50^{2} - 2^{2} = 2500 - 4 = 2496$.

6. How do you quickly square a number ending in 5, such as $35^{2}$?

   Take the tens digit $n$, compute $n(n+1)$, and append $25$. For $35$: $3 \times 4 = 12$, so $35^{2} = 1225$.

7. What is a fast method to divide a number by 5?

   Multiply by 2 and divide by 10 (since $\div 5 = \times \frac{2}{10}$). E.g. $135 \div 5 = \frac{270}{10} = 27$.

8. In fast calculation, why is it usually better to simplify (cancel) before multiplying fractions?

   Cancelling common factors first keeps the numbers small and reduces arithmetic errors, e.g. $\frac{8}{15} \times \frac{5}{12} = \frac{8}{12} \times \frac{5}{15} = \frac{2}{3} \times \frac{1}{3} = \frac{2}{9}$.

9. What is the divisibility rule for 3 and for 9?

   A number is divisible by 3 if the sum of its digits is divisible by 3, and divisible by 9 if the digit sum is divisible by 9.

10. What are the divisibility rules for 4 and 8?

    A number is divisible by 4 if its last two digits form a number divisible by 4, and divisible by 8 if its last three digits form a number divisible by 8.

11. What is the divisibility rule for 11?

    Take the alternating sum of the digits; if the result (including 0) is divisible by 11, the number is divisible by 11. E.g. for $2728$: $2-7+2-8 = -11$, which is divisible by 11.

12. When working without a calculator, how should you estimate $\sqrt{50}$?

    Bracket it between perfect squares: $\sqrt{49}=7$ and $\sqrt{64}=8$, so $\sqrt{50} \approx 7.07$, just above 7.

13. What is the benchmark approximation for $\sqrt{2}$, $\sqrt{3}$, and $\sqrt{5}$?

    $\sqrt{2} \approx 1.41$, $\sqrt{3} \approx 1.73$, and $\sqrt{5} \approx 2.24$.

14. Without a calculator, how do you compare two fractions like $\frac{3}{7}$ and $\frac{5}{11}$?

    Cross-multiply: compare $3 \times 11 = 33$ with $5 \times 7 = 35$. Since $33 < 35$, $\frac{3}{7} < \frac{5}{11}$.

15. What estimation strategy reduces error when answer choices are spread far apart?

    Round each value to convenient benchmarks and approximate, since wide-spread choices mean precise computation is unnecessary; pick the closest answer to your estimate.

16. When dividing by a decimal without a calculator, what should you do first?

    Multiply both the dividend and divisor by the same power of 10 to make the divisor a whole number, e.g. $\frac{4.2}{0.07} = \frac{420}{7} = 60$.

17. What is a reliable process to catch a computational error after solving a problem?

    Estimate the expected magnitude before computing, then check that your exact answer is consistent with that estimate; a large mismatch signals an arithmetic slip.

18. What is the 'units digit check' for verifying a multiplication?

    The units digit of a product equals the units digit of the product of the operands' units digits. E.g. $123 \times 47$ must end in $1$, because $3 \times 7 = 21$.

19. Why is keeping track of signs a major source of avoidable error, and how do you guard against it?

    Sign mistakes flip results entirely; guard by writing each negative explicitly, using brackets when substituting (e.g. $(-3)^{2} = 9$, not $-9$), and re-checking the sign of the final answer.

20. What error commonly arises from misreading question units (e.g. minutes vs. hours), and how is it avoided?

    Answers come out off by a conversion factor; avoid it by underlining the units in the question and confirming your final answer is expressed in the units asked for.

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