# The driver of the taxicab was wanting in civility, so Mr. Sharma asked him for his number.......was the fellow's number?

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The driver of the taxicab was wanting in civility, so Mr. Sharma asked him for his number.
"You want my number, do you?" said the driver. "Well, work it out for yourself. If you divide my number by 2,3,4,5 or 6 you will find there is always 1 over; but if you divide it by 11 there ain't no remainder. What's more, there is no other driver with a lower number who can say the same."
What was the fellow's number?

posted Aug 18, 2017

LCM of 2,3,4,5,6 is 60
So, the reqd number = 60a +1, and is divisible by 11
60a+1 = 11b
b=(60a+1)÷11
= 5a +(5a+1)÷11
5a+1 should be divisible by 11
assigning the smallest value as a=2,
b= 5*2+(5*2 +1)÷11
b=11

+1 vote

Ans. 121
LCF of 2,3,4,5,6 is 60. Now in two steps you reach to 121.

+1 vote

121/2=1 is remainder
121/3=1 is remainder
121/4=1 is remainder
121/5=1 is remainder
but
121/11=no remainder
and it is the least number

1000000441 {10 digit phone number} works (leaves remainder 1 with 2,3,4,5,6 and is divisible by 11).

His (cab) number is 121.

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