After stealing the gold, seven thieves hid in a cave and started dividing their

Question

After stealing the gold, seven thieves hid in a cave and started dividing their loot. When divided evenly, there were six gold pieces left over. After fighting for the remainder, one thief was killed. When the six thieves tried to distribute the gold evenly this time, they found two left over pieces. Again, they fought and another thief died. This time, the five thieves were able to evenly divide the gold. Given that they had more than 1,000 pieces and less than 1, 200, how many pieces did they have?

Explanation / Answer

According to given data we can say that gold pieces are between 1000 and 1200.

From given data:-

1. Seven thieves divided gold evenly but they left over with 6 remainder ,

that means ,the number of gold pieces are divided by 7 and we should get remainder as 6

2 .From 7 thieves one was killed ,remaining 6 thieves divided the gold evenly but they left over with 2

that means ,the number of gold pieces are divided by 6 and we should get remainder as 2.

3. Then after another thief killed, remaining 5 thieves divided the gold equally with no remainder

that means ,the number of gold pieces are divided by 5 and we should get remainder as 0

FROM POINT (1)

we can say ,a number is divided by 7 and remainder should be 6

Take a number which is divided by 7 and gets 6 as remainder from 1000 to 1200

Below following are the numbers which are divided by 7 and get remainder as 6

1007 1014 1021 1028 1035

1049 1056 1063 1070 1077

1084 1091 1098 1105 1112

1119 1126 1133 1140 1147

1154 1161 1167 1174 1181

1189 1196

FROM POINT (3)

take a number which is divisibile by 5 from above follwing numbers , the numbers are

1035 1070 1105 1140

From Point (2)

check above numbers when we divided with 6 ,we should get remainder as 2

so , 1070 is the number when it divided by 6 it gets remainder as 2

check 1070 with all conditions,

when we divided 1070 with 7, we get remainder as 6

when we divided 1070 with 6 , we get remainder as 2

and also we divided 1070 with 5 ,we get reaminder as 0

all conditions are satisified

hence 1070 is the number of gold pieces stole by thieves

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