Multiple choice

When 3738, 5659, and 9501 are divided by the greatest possible number (x), the remainder in each case is (y). What is the sum of (x) and (y)?

  1. $783$
  2. $3637$
  3. $3673$
  4. $3738$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Find HCF of differences: 5659 - 3738 = 1921, 9501 - 5659 = 3842. HCF(1921, 3842) = 1921 (since 3842 = 2 × 1921). Check if 1921 divides all: 3738 ÷ 1921 = 1 remainder 1817, 5659 ÷ 1921 = 2 remainder 1817, 9501 ÷ 1921 = 4 remainder 1817. So x = 1921, y = 1817. Sum = 1921 + 1817 = 3738. Option D is correct.