Question 15 of 36intermediate🔧 ApplyShort Answer2 marks

The numbers 13 and 31 are prime numbers. Both these numbers have same digits 1 and 3. Find such pairs of prime numbers up to 100.

Correct Answer

Explanation: We need to find two-digit primes where reversing the digits gives another prime.

Step 1: List two-digit primes and check their reversals.

Step 2: 13 → 31 (both prime) ✓

Step 3: 17 → 71 (both prime) ✓

Step 4: 37 → 73 (both prime) ✓

Step 5: 79 → 97 (both prime) ✓

Note: Other pairs like 11 → 11 (same number), 23 → 32 (32 not prime), etc. don't work.

Answer: Pairs of prime numbers up to 100 with the same digits are (13, 31), (17, 71), (37, 73), (79, 97).

Exercise: Figure it Out (Section 3) | Q: 6 | (Page Page 8)
For More Understanding

Explanation

We need to find two-digit primes where reversing the digits gives another prime. Checking all two-digit primes: 13↔31 (both prime), 17↔71 (both prime), 37↔73 (both prime), 79↔97 (both prime). Other pairs like 11↔11 (same number), 23↔32 (32 not prime), etc. don't work.

Solution Steps

  1. Step 1: List two-digit primes and check their reversals.

  2. Step 2: 13 → 31 (both prime) ✓

  3. Step 3: 17 → 71 (both prime) ✓

  4. Step 4: 37 → 73 (both prime) ✓

  5. Step 5: 79 → 97 (both prime) ✓

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