When a number n is divided by 8, the remainder is 5. Which of the following could be the value of 2n - 3?
Read the question carefully. Multiple numbers could be divided by 8 and produce a remainder of 5, but you are not asked to find every possible number. You are asked something entirely different.
Identify the bottom line. What is a possible value of 2n + 5?
Assess your options. You could work backwards from your answer choices, subtracting 5, dividing by 2, and then checking to see whether the resulting number produces a 5 when divided by 8, but that is a lot of steps. Instead of having to repeat these steps (possibly 5 times for each of your answer choices), work from the information that the problem gives you.
Attack the problem. Your Knowsys handbook has a specific method for finding a variable divided by a certain number and producing a certain remainder. First, write the problem out so that there is no confusion:
Next, add the divisor and the remainder to find one possible value of n:
n = 5 + 8 = 13
Your next step is to try out the number 13 by plugging it in the equation that you were given:
2(13) - 3 = 23
Does that match any of your answer choices? Yes!
Loop back. You just proved that this answer can work, so you are finished! Select your answer.
The correct answer is (D).
This is a medium level question.