Chat with tutor

Ask Questions, Get Answers

Questions  >>  Olympiad-Math  >>  Class 5  >>  Number Sense

Find the 3 digit number. Its one's digit and hundred's digit are both divisible by 2. The one's digit and ten's digit are both divisible by 3. It's ten's digit is an odd multiple of 3, and its hundred's digit is 2 less than the one's digit.

(A) 596 (B) 949 (C) 496 (D) 896

1 Answer

Let the three digits be X (hundreds), Y (tens) and Z (units).
It's tens digit is an odd multiple of 3. The multiples of 3 are 3, 9, 12 etc., so Y (tens) has to be either 3 or 9 since it is a single digit.
The ones digit and tens digit are both divisible by 3 and the ones and hundreds by 2. So, the ones digit is divisible by both 2 and 3.
The only single digit number divisible by both 2 and 3 is 6. Therefore, Z = 6 (units).
It is also given that the hundred's digit is 2 less than the one's digit, i.e, it is 2 less than 6 = 4. Therefore, X = 4 (hundreds).
The two possibilities are are 436 and 496. Since 436 is not one of the 4 options, 496 is the answer.
Help Clay6 to be free
Clay6 needs your help to survive. We have roughly 7 lakh students visiting us monthly. We want to keep our services free and improve with prompt help and advanced solutions by adding more teachers and infrastructure.

A small donation from you will help us reach that goal faster. Talk to your parents, teachers and school and spread the word about clay6. You can pay online or send a cheque.

Thanks for your support.
Please choose your payment mode to continue
Home Ask Homework Questions
Your payment for is successful.
Clay6 tutors use Telegram* chat app to help students with their questions and doubts.
Do you have the Telegram chat app installed?
Already installed Install now
*Telegram is a chat app like WhatsApp / Facebook Messenger / Skype.