IMO Mathematics Olympiad (SOF) Class 10: Questions 1 of 958
MCQ▾
Question
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.  2,6 

c.  6,2 

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