A train traveled at a constant speed for 180 miles

While one can create equations to solve this question, you can use your numerical skills to solve this and come out equally satisfied at the end.

For starters, we can safely ignore numbers like 25 since 25 is not a factor of 180. Of all the other answer options, the one that most of us would instinctively pick up would be 30, i.e. answer option C.

If the train was going at 30 miles per hour, it would take 6 hours to travel 180 miles.

When the train started travelling 6 miles per hour FASTER, it covered distance at the rate of 36 miles per hour.
Note, that 36 is a factor of 180 as well. Also note that adding 6 to the numbers in the other answer options will render them practically useless since they will cease to be factors of 180. This is enough evidence that we are headed in the right direction.

The train would take 5 hours to cover 180 miles at 36 miles per hour. The train ride is definitely one hour shorter in this case.

By taking 30, all the constraints mentioned in the question were satisfied. 30 has to be the answer that we are looking for.
The correct answer option is C.

Nope, we're looking for a speed in miles per hour! Careful: 180 is a distance (in miles).

I will approach this question backwards, that is from the options onwards. Distance = 180 miles,
looking at the options I will first go to C that is 30, so I will get the time = 180/30, which is 6 hrs

Now coming to the If situation here, which would make our speed to 36miles/hr , which would make our time as 180/36 which is 5 hours. Hence we have proved what the question wanted us to do.

(Hint: while selecting the option see if you add 6 to them will they be easy for you to divide. You will see in most cases it would be no. Hence we are going with the option c at first itself )

What is the faster way to solve this Quadratic equation, I was at this point [x^2+6x-1080=0] but took me forever to solve for the answer as it is a large number. Can you refer to any Youtube etc. I know it's very basic but when the number becomes 1080, it's hard for me to find a pair of 30 and 36, which will give me the 6x, maybe my methods are not efficient. This question seems like a time burner ..... GMATNinja Bunuel?