I make similar mistakes to raghavsp

I miss things in the first part of the question (I think it is officially called the stem) after I get to working at the problem. Recently I have started rewriting the sentences in inequalities.

So we take a look at the first part of the question.

bmwhype2 wrote:

If \(m\) is a positive integer, is \(\sqrt{m} \gt 25\) ?

Because it is written "....m is a positive integer..."

I write out "\(m>0\)" on my whiteboard

Then we continue on.

bmwhype2 wrote:

1. \(m\) is divisible by 50

Based on (1) m is the set

M {0,50,100,150.....n50}

It is key to remember that divisible means when \(m\) is divided by 50 there is no remainder. So M could equal 0. Except in this situation the stem tells us M>0.bmwhype2 wrote:

2. \(m\) is divisible by 52

As others have said (2) alone is not enough.

I took some time to calculate the smallest common denominator of \(\frac{m}{50}\) and \(\frac{m}{52}\). I came up with 1300.

Does anyone know a quick way to do this? I had to do trial and error until I found 1300 (25x52)

since k1 and k2 are both positive integers, min value the can take are 26a nd 25 respectively

so M can be expressed as 25*26n, where ncan be any natural number.