# I am a a four dight number I am less than 4900 but more than 3600 I am a square number I am a multiple of 15 and 5 what is my number

Firstly, you are between 3600 & 4900 and a square - this means you are between 60 and 70 as these are the square roots of 3600 & 4900 respectively. Since 5 is a prime number, only multiples of 5 have squares which are also multiples of 5. Therefore your square root must also be a multiple of 5. As the only number between 60 and 70 which is a multiple of 5 is 65, your square root is 65; thus you are 65x65 which is 4225. You also state that you are a multiple of 15, but 4225 is not a multiple of 15. By stating that you are a square number, you have implied that you are the square of an integer. I have just proved that this is not possible. Unfortunately, I must therefore inform you that you do not exist.Source(s):Pure mathematics and an expertise in mental calculations which has brought me the Grandmaster title and three world championships.

I feel like this is a trick question, because to be a square number, the square root of the value would have to be a positive integers, and there isn't a single positive integer in that range that would work. (see below) Lower bound: [latex] \sqrt{3600} [/latex] = 60 Upper bound: [latex] \sqrt{4900} [/latex] = 70 Evaluating all possible integers: 61^2 = 3721 62^2 = 3844 63^2 = 3969 64^2 = 4096 65^2 = 4225 66^2 = 4356 67^2 = 4489 68^2 = 4624 69^2 = 4761 To be divisible by 5 & 15, the number in the ones place has to be either a 5 or a 0, and there is only one value: 65^2 = 4225, but 4225/15 = 281.67 which is not a whole number. Thus, I reason not divisible by 15. My answer is 4125 because its the only number within the given range that happens to be square on a qwerty keyboard (see below) - don't know if that is correct 7 8 9 4 5 6 1 2 3