BRAIN TEASER
From a basket of mangoes when counted in three extra , counted in fives there were four extra , counted in sixes there were five extra. But counted in sevens there were no extra. Atleast how many mangoes were there in the basket ????
Answers
Answer:
Let the number of mangoes be x.
when x ÷ 2 leaves remainder as 1.
when x ÷ 3 leaves remainder as 2.
when x ÷ 4 leaves remainder as 3.
when x ÷ 5 leaves remainder as 4.
when x ÷ 6 leaves remainder as 5.
when x ÷ 7 leaves remainder as 0.
⇒ x is divisible by 7.
The remainder in each case is 1 less than the divisor.
⇒ (x + 1) is the LCM of 2, 3, 4, 5 and 6.
LCM of 2, 3, 4, 5 and 6 = 60.
If x + 1 = 60, then x = 59.
But 59 is not divisible by 7.
If x + 1 = 120, then x = 119.
119 is divisible by 7 also it satisfies all the conditions.
Hence the number of mangoes = 119.
Hope it helps :)
Answer:
119. The number has to be evenly divisible by seven for there to be no extras when counting in sevens, and it has to be odd in order for there to be one extra when counting by twos. It also can’t be evenly divisible by three through six. 119 is the first odd multiple of 7 that satisfies the requirements.
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