Question

BRAIN-TEASERS
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?​

Answer 1

Explanation:

Sol: 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.

Answer 2

There are 119 mangoes in the basket