Let a be a positive integer.Which of the following statements must be true? (Choose all that apply.)
Answer(s): C
a - 1 > 0 is not always true (e.g., a = 1 gives 0, not >0).(-1)a > 0 is only true when a is even, so it is not always true.(-1)2a > 0 is always true because 2a is even, and (-1)even = 1
When a certain stock exchange closed on Tuesday, of the stocks closed at the same price as on the previous day. Of the remaining stocks, 3 stocks closed at a higher price for every 4 stocks that closed at a lower price.What fraction of all the stocks on this exchange closed at a higher price than on the previous day?
Answer(s): A
× = of all stocks closed higher.
A sequence of numbers P1, P2, P3, ..., Pn, ... is defined by P1 = 1, P2 = 2, and for all integers n > 2.What is the value of P5?
P3 = (2/1)2 = 4, P4 = (4/2)2 = 4, P5 = (4/4)2 = 1
A report contains a list of the annual salaries of 100 professionals at a firm, including Raj. All of the salaries are different, and 52 percent of the salaries are less than or equal to Raj's salary.If the 15 lowest salaries and the 3 highest salaries were to be removed from the list, approximately what percent of the remaining salaries would be less than or equal to Raj's salary?
Answer(s): D
There are 100 distinct salaries, and 52% are Raj's, so Raj is 52nd when ordered from lowest to highest.Salaries below Raj: 51Remove the 15 lowest 15 of those 51 are removed, leaving 51 - 15 = 36 below Raj.Remove the 3 highest all above Raj, so Raj's position relative to lower salaries is unchanged.Remaining salaries: 100 - 18 = 82Number of remaining salaries Raj = 36 (below) + 1 (Raj) = 37 Proportion Raj = 37/82 45%The closest answer choice is 46%.
FILL BLANKThe ratio of the number of freshmen to the number of sophomores enrolled in a psychology course was 2 to 1. After 2 freshmen added the course and 1 sophomore dropped the course, the ratio of the number of freshmen to the number of sophomores changed to 9 to 4.How many sophomores were originally enrolled in the course?
Let the original numbers be:Freshmen: fSophomores: sAfter changes:2 freshmen added f + 21 sophomore dropped s - 1Substitute f = 2s:Cross-multiply:4 (2s + 2) = 9(s - 1)8s + 8 = 9s - 98 + 9 = 9s - 8s17 = s
Post your Comments and Discuss GRE GRE Test exam prep with other Community members:
Our website is free, but we have to fight against AI bots and content theft. We're sorry for the inconvenience caused by these security measures. You can access the rest of the GRE Test content, but please register or login to continue.