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AFCAT Number System — practice questions

Explore 5 free Number System questions in AFCAT 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 1–5 of 5.

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

Every composite number can be expressed as:

  1. A product of its prime factors
  2. A sum of two prime numbers
  3. A difference of two squares
  4. A multiple of every smaller number
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Correct answer: A. A product of its prime factors

1. Any natural number can be written as a product of its prime factors. 2. For instance 4 = 2 x 2 and 253 = 11 x 23. 3. The Fundamental Theorem of Arithmetic states this holds for every composite number, and the factorisation is unique apart from the order. 4. A sum of two primes is a different idea altogether, so option B is a trap. _Source: syllabus Maths, Ch 1 'Real Numbers', S1.2 The Fundamental Theorem of Arithmetic_

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The prime factorisation of 253 is:

  1. 11 x 23
  2. 7 x 36
  3. 13 x 19
  4. 3 x 84
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Correct answer: A. 11 x 23

1. Test the small primes in turn: 253 is odd, so 2 does not divide it. 2. Its digits sum to 10, so 3 does not divide it either, and it does not end in 0 or 5. 3. Dividing by 11 gives 253 / 11 = 23, and 23 is prime. 4. So 253 = 11 x 23. 5. The other options are not even products of two primes: 36, 84 and 19 x 13 = 247 all fail. _Source: syllabus Maths, Ch 1 'Real Numbers', S1.2 The Fundamental Theorem of Arithmetic_

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The product 2 x 3 x 7 x 11 x 23 equals:

  1. 10626
  2. 5313
  3. 1771
  4. 21252
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Correct answer: A. 10626

1. Multiply in stages to keep the arithmetic clean. 2. 7 x 11 = 77, and 77 x 23 = 1771. 3. Now bring in the remaining factors: 2 x 3 = 6. 4. So the product is 6 x 1771 = 10626. 5. 1771 is only the last three factors, and 5313 is 3 x 1771, so both are partial products. _Source: syllabus Maths, Ch 1 'Real Numbers', S1.2 The Fundamental Theorem of Arithmetic_

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