### Brain Teasers

# What is the Number?

There is a number.

1. If it is not a multiple of 4, then it is between 60 and 69.

2. If it is a multiple of 3 it is between 50 and 59.

3. If it is not a multiple of 6 it is between 70 and 79.

What is the number?

1. If it is not a multiple of 4, then it is between 60 and 69.

2. If it is a multiple of 3 it is between 50 and 59.

3. If it is not a multiple of 6 it is between 70 and 79.

What is the number?

### Answer

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## Comments

I'm sort of scratching my head over this one. Maybe I need another cup of joe.

I'm with you, scubee. This one made no sense to me at all. Can someone explain it?

It's more logic than math. Not all three statements can be true.

If it is a multiple of 3, it can only be 51, 54, or 57.

If it is not a multiple of 6, then it is 71, 73, 74, 75, 76, or 77.

If it is not a multiple of 4, then it is 61, 62, 63, 65, 66, or 67.

It can't be a multiple of 3, because none of those numbers are multiples of 4 or 6.

It can't be a number between 60 and 69, because if it is a multiple of 6, then it is a multiple of 3, too.

So, it has to be a number that is a multiple of 4, but not 3 or 6.

If it is a multiple of 3, it can only be 51, 54, or 57.

If it is not a multiple of 6, then it is 71, 73, 74, 75, 76, or 77.

If it is not a multiple of 4, then it is 61, 62, 63, 65, 66, or 67.

It can't be a multiple of 3, because none of those numbers are multiples of 4 or 6.

It can't be a number between 60 and 69, because if it is a multiple of 6, then it is a multiple of 3, too.

So, it has to be a number that is a multiple of 4, but not 3 or 6.

I get it now.

its nice but i cant understand

dswilborn, thanks for that! Not sure what about it had be so stumped.

it is great it's a challenge i love challenges

ts is fun

this is fun

i love this this is awesome

Did lab123 mean 'between'

to be inclusive or exclusive of the limits of the ranges?

to be inclusive or exclusive of the limits of the ranges?

Huh?

the answer is the same regardless if the ranges are inclusive or exclusive.

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