Consider the below question OG quantitative review 2nd edition, Q 68, Page 70:
When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer K such that k +N is a multiple of 35?
The way I tried solving this question is by writing the formula dividend = divisor * quotient + remainder. However, 1.5 - 2 mins later I found myself going no where. So another idea popped up which is to test the numbers, 1, 6, 11, 16,... which leave a remainder of 1 when divided by 5. I was secretly confident that I could arrive at the answer soon and had I continued I would have arrived at the answer in 1.5 minutes, making the total time to answer the question 3.5 minutes.
Question: I am confused as to whether the approach I have taken above works on every question. After 2 minutes, should I have skipped the question and went to the next question? While 1.5 minutes for the second approach might seem a bit excessive, I spent most of the time hesitating whether to continue with the question or skip the question.
In summary, what is the best strategy you recommend in such scenarios wherein I find myself taking the wrong approach and 2 - 2.5 minutes later I realize the correct solution? Also assume that I have spent at least 20 seconds in the beginning trying to brainstorm different ideas and went with the first approach described above.