Six-Digit Number Lock Riddle
XAT 2021 · Quantitative Ability & Data Interpretation · Medium · Number Systems
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
E
Explanation
Primes less than 15: 2, 3, 5, 7, 11, 13. Divisible by 2 and 5 last digit is 0. So the 6-digit number is . Divisible by . Multiples of 1001 are of the form . Therefore, . The first digit is 4.
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