33. 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?
b. 110
c. 111
d. 126
a. 119
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HEY DEAR.....!!
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.
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