Question

Kayla is thinking of a 3-digit number. * It is divisible by 18. * It is a palindrome (It reads the same left-to-right as it does right-to-left, like 252 and 848). * It is one less than a multiple of 5. What is Kayla’s number?

Answer 1

414

Explanation:

EE

Answer 2

• 414

Explanation:

Let the number be aba as it is a palindrome

It divisible by 18, so it is an even number with sum of digits divisible to 9

• 2a + b = 9k

It is one less than a multiple of 5:

• aba = 100a + 10b + a = 101a + 10b

Multiple of 5 will end with 0 or 5, it has to be 5 as a is even, then:

• a = 5 - 1 = 4

The number 4b4 is divisible by 9 only if b = 1:

• 2*4 + b = 9k ⇒ b = 1

So the number is:

• 414

Lets verify:

• 414/18 = 23
• 414 + 1 = 415- divisible by 5
• 414 - is palindrome