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

Edit

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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