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.