Question

Zahir and Raman are at the entrance of a dark cave. To enter this cave, they need to open a number lock. Raman sees a note on a rock: " ... chest of pure diamonds kept for the smart one ... number has six digits ... second last digit is 2, third last is 4 ... divisible by all prime numbers less than 15 ...". Excited, Zahir and Raman seek your help: which of these can be the first digit of the six-digit number that will help them open the lock?

A.
5
B.
3
C.
9
D.
1
E.
4

Accepted Answer

E. Primes less than 15: 2, 3, 5, 7, 11, 13. Divisible by 2 and 5 $\implies$ last digit is 0. So the 6-digit number is $abc420$. Divisible by $7 	imes 11 	imes 13 = 1001$. Multiples of 1001 are of the form $abcabc$. Therefore, $abc420 = 420420$. The first digit is 4.

Six-Digit Number Lock Riddle

Explanation

Practise this under exam conditions