# Math Puzzle 38

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**1.**From a basket of mangoes when counted in twos there was one extra, counted in threes there were two extra, counted in fours there were three extra, counted in fives there were four extra, counted in sixes there were five extra. But counted in sevens there were no extra. At least how many mangoes were there in the basket?

**2.**A boy was asked to find the LCM of 3, 5, 12 and another number. But while calculating, he wrote 21 instead of 12 and yet came with the correct answer. What could be the fourth number?

**3.**There were five pieces of cloth of lengths 15 m, 21 m, 36 m, 42 m, 48 m. But all of them could be measured in whole units of a measuring rod.What could be the largest length of the rod?

**4.**There are three cans. One of them holds exactly 10 liters of milk and is full. The other two cans can hold 7 liters and 3 liters respectively. There is no graduation mark on the cans. A customer asks for 5 liters of milk. How would you give him the amount he ask? He would not be satisfied by eye estimates.

**5.**Which two digit numbers when added to 27 get reversed?

**6.**Cement mortar was being prepared by mixing cement to sand in the ratio of 1:6 by volume. In a cement mortar of 42 units of volume, how much more cement needs to be added to enrich the mortar to the ratio 2:9?

**7.**In a solution of common salt in water, the ratio of salt to water was 30:70 as per weight. If we evaporate 100 grams of water from one kilogram of this solution, what will be the ratio of the salt to water by weight?

**8.**Half a swarm of bees went to collect honey from a mustard field. Three fourth of the rest went to a rose garden. The rest ten were still undecided. How many bees were there in all?

**9.**Fifteen children are sitting in a circle. They are asked to pass a handkerchief to the child next to the child immediately after them. The game stops once the handkerchief returns to the child it started from. This can be written as follows : 1→3→5→7→9→11→13→15→2→4→6→8 →10→12 →14→1. Here, we see that every child gets the handkerchief.(math puzzle 38)

(i) What would happen if the handkerchief were passed to the left leaving two children in between? Would every child get the handkerchief?

(ii) What if we leave three children in between? What do you see? In which cases every child gets the handkerchief and in which cases not? Try the same game with 16, 17, 18, 19, 20 children. What do you see?

**10.**Take two numbers 9 and 16. Divide 9 by 16 to get the remainder. What is the remainder when 2 × 9 is divided by 16, 3 × 9 divided by 16, 4 × 9 divided by 16, 5 × 9 divided by 16... 15 × 9 divided by 16. List the remainders. Take the numbers 12 and 14. List the remainders of 12,

12 × 2, 12 × 3, 12 × 4, 12 × 5, 12 × 6, 12 × 7, 12 × 8, 12 × 9, 12 × 10,12 × 11, 12 × 12, 12 × 13 when divided by 14. Do you see any difference between above two cases?

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