# 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

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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