41. Find the remainder when 65203 is divided by 7.
42. Find the remainder when 67107 is divided by 7.
43. Find the remainder when 54124 is divided by 17.
44. Find unit digit of product (173)45 × (152)77 × (777)999.
45. The square of a number greater than 1000 that is not divisible by three, when divided by three, leaves a remainder of
46. If 146 Is divisible by 5n, and then find the maximum value of n.
47. Three friends, returning from a movie, stopped to eat at a restaurant. After dinner, they paid their bill and noticed a bowl of mints at the front counter. Sita took $$\frac{1}{3}$$ of the mints, but returned four because she had a monetary pang of guilt. Fatima then took $$\frac{1}{4}$$ of what was left but returned three for similar reasons. Eswari then took half of the remainder but threw two back into the bowl. The bowl had only 17 mints left when the raid was over. How many mints were originally in the bowl?
48. Some birds settled on the branches of a tree. First, they sat one to a branch and there was one bird too many. Next they sat two to a branch and there was one branch too many. How many branches were there?
49. If we divide the unknown two-digit number by the number consisting of the same digits written in the reverse order, we get 4 as quotient and 3 as remainder. If we divide the required number by sum of its digits, we get 8 as a quotient and 7 as a remainder. Find the number?
50. The last three-digits of the multiplication 12345 × 54321 will be
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