# Question

I am a 2 digit even number.The digit in the ones place is a factor of 6. The digit in the hundreds place is a multiple of 4. The sum of all the digits is 14. What number am I?

Firstly, I think the number has 3 digits.

The first step to such questions is to look for obvious clues.

The digit in the hundreds place is a multiple of 4.”

The digit is 4 or 8.

4 _ _ or 8 _ _

The next step is to look at related sentences.

Look at these 2 sentences:

The digit in the ones place is a factor of 6.

The digit in the ones place is 1, 2, 3, or 6.

I am a 3 digit even number.

The digit in the ones place is 2, 4, 6, 8 or 0.

Comparing the sentences, the digit in the ones place is either 2 or 6.

_ _ 2 or _ _ 6

Let’s look at the possible combinations which add up to 14:

482

426

842

806

The only way to find out the number is to look at the question’s source to see if there are other clues which are not shown here.

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*I assume there was a typo, it is a 3 digit number, otherwise there will not be a number in the hundreds place.

Factors of 6: 1,2 and 3

Since it is an even number, the digit at the ones place must be 2, as 1 and 3 are not even.

Multiples of 4 (that are below 10): 8

14-8-2= 4

The number is thus:

842

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