Hi, this is actually my first post here but I have been checking out gmat club for awhile. I was hoping somebody could help explain the approach and answers to the following three problems. Your help would be greatly appreciated! These are taken from the new PP second test. Unfortunately they don't have explanations on the new software
1) What is the greatest prime factor of 4*(17th power) - 2*(28th power)
I have no idea how to approach this. Should you factor? Im sure there is some kind of trick. Of course I understand you can covert the first term to become a base of 2.
2) If ax+b=0, is x>0?
I understand how you can set ax=-b here but am not sure where to go from there after you determine that a>-b. Of course you now know that a>ax but x could still be negative or a fraction. I am not sure where to go after this. Help...
3) A certain car averages 25 miles per gallon of gasoline when driven in the city and 40 miles per gallon when driven on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and 50 miles on the highway?
This question I got right with a guess as I was running out of time. I feel like I understand how to do it but can't get the answer to correspond to the work that I do. The answer is 36. How do you get that number. I assumed here you multiply 25 by 10 and 50 by 40, add them, and divide by 60. However this comes out to 37.5. Any ideas?
Thank you for answering my questions. I am sure they are quite easy, I just am having a little trouble with methodology.