IMO- Mathematics Olympiad Class 10: Questions 1 of 958

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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

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Ques. Time

Answer

a.

Explanation

  • Number is a679b is divisible by 72
  • So, that number is also divisible by 8 and 9, as Equation
  • 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 Equation 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, Equation

Equation

Equation

  • Now at a = 3, we get
  • 9 that is divisible by 9, and rest of the numbers form by different value of a Equation are not divisible by 9
  • So, our number will be 36792
  • So, Equation and Equation
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