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GMAT Number System — practice questions

Explore 14 free Number System questions in GMAT Quantitative Reasoning. Open each question or exercise to read its content, reference answers and available explanation.

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Number System questions and exercises with answers

Showing questions 1–14 of 14.

What is the prime factorisation of 360?Read the answer and worked solution →For which value of n does $6^n$ end with the digit zero?Read the answer and worked solution →How many divisors does the number $N = 2^3 \times 3^2 \times 5$ have?Read the answer and worked solution →What is the HCF of 18 and 24?Read the answer and worked solution →What is the LCM of 12 and 18?Read the answer and worked solution →HCF of two positive integers a and b is 5. Their LCM is 200. If a = 25, what is b?Read the answer and worked solution →Which of the following is a rational number?Read the answer and worked solution →Which fraction has a TERMINATING decimal expansion?Read the answer and worked solution →The product of a non-zero rational number and an irrational number is always:Read the answer and worked solution →Every composite number can be expressed as:Read the answer and worked solution →The prime factorisation of 253 is:Read the answer and worked solution →The product 2 x 3 x 7 x 11 x 23 equals:Read the answer and worked solution →A number leaves remainder 3 when divided by 7 and remainder 3 when divided by 5. The smallest such number above 3 is:Read the answer and worked solution →How many prime factors, counted with repetition, does 21252 = 2^2 x 3 x 7 x 11 x 23 have?Read the answer and worked solution →

Worked practice questions

What is the prime factorisation of 360?

  1. $2^3 \times 3 \times 5^2$
  2. $2^3 \times 3^2 \times 5$
  3. $2^2 \times 3^3 \times 5$
  4. $2 \times 3^2 \times 5^2$
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Correct answer: B. $2^3 \times 3^2 \times 5$

360 = 8 × 45 = 2³ × 9 × 5 = 2³ × 3² × 5. Verify: 8 × 9 = 72, 72 × 5 = 360.

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For which value of n does $6^n$ end with the digit zero?

  1. For n = 1 only
  2. For n = 2 and higher
  3. Only for n = 5
  4. No natural number n works
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Correct answer: D. No natural number n works

A number ends with 0 only if its prime factorisation contains both 2 AND 5. 6^n = (2 × 3)^n = 2^n × 3^n. The prime 5 never appears, so 6^n never ends in zero, no matter how large n is.

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How many divisors does the number $N = 2^3 \times 3^2 \times 5$ have?

  1. $6$
  2. $12$
  3. $24$
  4. $30$
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Correct answer: C. $24$

Number of divisors = product of (exponent + 1) for each prime. (3+1) × (2+1) × (1+1) = 4 × 3 × 2 = 24.

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More Quantitative Reasoning topics

Modern MathematicsQuantitative ReasoningAlgebraPermutations and CombinationsLogical ReasoningQuantitative AptitudeAverages and MixturesSimple and Compound Interest