If x and y are integers, and = 1.64, which of the following CANNOT be a value of x?

At the end of August, a store discounts all swimsuits by 40 percent to 50 percent. At the beginning of October, all remaining swimsuits are discounted by an additional 10 percent. What is the lowest possible original price of a swimsuit that cost $27 in October?

What is the area of the region enclosed by the graph of the equation x²+y²=|x|+|y|?

What is the area of the region enclosed by the graph of the equation  x²+y²=|x|+|y| ?

The permutation function P is defined by the formula

P(n,r)=

where n and r are positive integers. What is the least value of r for which P(10, r) > 1,000 ?

If x=, which of the following must be true?

The table above gives sale information for the 20 bathroom cleaners in the United States in 2010. For each product, the table describes the brand of the product, the product type, fragrance, unit sales, percent change in unit sales since 2009, total dollar sales, percent change in dollar sales since 2009, average price of each unit sold, and the dollar change in price since 2009.

Consider each of the following statements about these sales figures. For each statement, indicated whether the statement is true or false, based on the information provided in the table.

In a study conducted in Pennsylvania, servers in various restaurants wrote ""Thank you"" on randomly selected bills before presenting the bills to their customers. Tips on these bills were an average of three percentage points higher than tips on bills without the message. Therefore, if servers in Pennsylvania regularly wrote ""Thank you"" on restaurant bills, their average income from tips would be significantly higher than it otherwise would have been.

Which of the following is an assumption on which the argument relies?

The Kalladian Labor Statistics Bureau keeps track of wage rates in 25 foreign countries. In one of these countries, Ellmark, hourly wages for manufacturing workers declined last year by 31 percent, calculated in Kalladian florins; no other country registered as large a decline. In Ellmark last year, however, hourly wages for manufacturing workers actually increased in terms of Ellmark’ national currency.

If the statements above are true, which of the following must also be true?

Scientists typically do their most creative work before the age of forty.  It is commonly thought that this happens because aging by itself brings about a loss of creative capacity. However, studies show that a disproportionately large number of the scientists who produce highly creative work beyond the age of forty entered their field at an older age than is usual.  Since by the age of forty the large majority of scientists have been working in their field for at least fifteen years, the studies’ finding strongly suggests that the real reason why scientists over forty rarely produce highly creative work is not that they have simply aged but rather that they generally have spent too long in a given field.  

In the argument given, the two portions in boldface play which of the following roles?