Percentage evaulation Queestion from GRE?

Question

A question from GRE book says: A candidate who gets 30 percent marks in an examination fails by 30 marks,but another candidate who gets 42 percent marks get 42 more marks than necessary for passing.Find the maximum number of marks and total necessary for passing. I started with it by: Let passing marks =x Then for Student1; (x-30) Student 2;(x+42) But what should I equate it to get them compared and find 'x' and then total marks?

Answer 1

Its easier if you find the total marks. Supposing total marks as M, two equations that you should equate are:

30% of M + 30 = Pass

42% of M = Pass + 42 which equates to 42% of M -42 = Pass

Now equating two Pass equation you get, 30% of M + 30 = 42% of M - 42.

You can solve for M which gives you 600. So total marks was 600. Passing marks was 210.

Student 1 got 30% of 600, meaning 180 so failed by 30 marks.

Student 2 got 42% of 600, meaning 252 so got 42 points more than needed to pass.