Multiple choice

Let x be the least number which on being divided by 8, 12, 15, 24, 25 and 40 leaves a remainder of 7 in each case. What will be the remainder when x is divided by 29?

  1. 18

  2. 27

  3. 19

  4. 20
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The number x that leaves remainder 7 when divided by 8, 12, 15, 24, 25, and 40 is LCM(8, 12, 15, 24, 25, 40) + 7. LCM = 600 (prime factors: 8 = 2³, 12 = 2²×3, 15 = 3×5, 24 = 2³×3, 25 = 5², 40 = 2³×5, so LCM = 2³×3×5² = 600). Therefore x = 600 + 7 = 607. Now find 607 ÷ 29: 29 × 20 = 580, remainder 27. So x mod 29 = 27. Option B is correct. Options A (18), C (19), and D (20) don't match the actual remainder.

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