BRAIN-TEASERS
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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. Atleast
how many mangoes were there in the basket?
Answers
n is a multiple of 7, and 1 short of a multiple of 3 or 4 or 5 or 6
Division by 6 takes care of division by 3, so n+1 = 4 x 5 x 6 x K
(where K will ensure it’s a multiple of 7)
So n = 119*K, and 119 is divisible by 7, so K = 1 and n = 119
HOPE THIS HELPS U
PLZZ MARK ME BRAINLIEST
Answer:
Solution :
Let the number of mangoes be n.
When n is divided by 2, it leaves remainder 1.
When n is divided by 3, it leaves remainder 2.
When n is divided by 4, it leaves remainder 3.
When n is divided by 5, it leaves remainder 4.
When n is divided by 6, it leaves remainder 5.
The remainder in each case is 1 less than the divisor.
∴(n+1) is the LCM of 2,3,4,5and6.
LCM of 2,3,4,5and6=60
If n+1=60, then n=59
But 59 is not divisible by 7.
If n+1=60∗2 , then n=119.
119 is divisible by 7 and satisfies all the given conditions.
Hence the number of mangoes in the basket =119
Step-by-step explanation:
hope it helps you