IMO Level 1- Mathematics Olympiad (SOF) Class 10: Questions 1 of 1025
Question MCQ▾
If a679b is a five digit number in base 10 and is divisible by 72, then the values of a and b are ________
Choices
Choice (4) | Response | |
---|---|---|
a. | 3,2 | |
b. | 6,2 | |
c. | 2,6 | |
d. | 2,3 |
Answer
a.
Explanation
- Number is a679b is divisible by 72
- So, that number is also divisible by 8 and 9, as
- And we know divisibility rule for 8, that if numbers last three digits divisible by 8
- So, whole number is also divisible by 8
- So, 79b is also divisible by 8
- So, only b = 2
- We get 792 that is divisible by 8 and rest of the value of b form numbers these numbers are not divisible by 8
- So, we get b = 2 and our number is becomes a6792
- Now we check divisible rule for 9 as our number is also divisible by 9
- Sum the digits. If the result is divisible by 9, then the original number is divisible by 9
- So,
- Now at a = 3, we get
- 9 that is divisible by 9, and rest of the numbers form by different value of a are not divisible by 9
- So, our number will be 36792
- So, and
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