Real Numbers — Questions & Answers

Sample questions from Real Numbers

1. Q1. The LCM of 10 and 15 is:

   • A.5
   • B.30✓
   • C.150
   • D.10
   Solution

   10=2×5, 15=3×5. LCM = 2×3×5 = 30.

2. Q2. Which of these has a non-terminating repeating decimal expansion?

   • A.91 divided by (2² × 5³ × 7)
   • B.13 divided by 625
   • C.7 divided by 80
   • D.23 divided by (2³ × 5² × 11)✓
   Solution

   D is correct. After cancelling, 23 and the denominator share no factor, and the 11 that remains is neither 2 nor 5, so the expansion repeats. A looks like it repeats because of the 7, but 91 = 7 × 13, so the 7 cancels and what is left is 13 divided by (2² × 5³), which terminates. B is 13 divided by 5⁴ and terminates. C is 7 divided by (2⁴ × 5) and terminates. The lesson is that the test applies only after the fraction is reduced.

3. Q3. How many prime numbers are between 1 and 20?

   • A.6
   • B.7
   • C.8✓
   • D.9
   Solution

   Primes between 1 and 20: 2,3,5,7,11,13,17,19 — total 8.

4. Q4. The HCF of 10 and 15 is:

   • A.2
   • B.5✓
   • C.10
   • D.15
   Solution

   10=2×5, 15=3×5. Common prime = 5. HCF = 5.

5. Q5. Which of the following is a factor of 36 but NOT of 24?

   • A.4
   • B.6
   • C.9✓
   • D.12
   Solution

   Factors of 36: 1,2,3,4,6,9,12,18,36. Factors of 24: 1,2,3,4,6,8,12,24. 9 is in 36 but not 24.

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