If <i>ai> + 3|<i>bi>| = 50, what are a and b?

(1) 3|<i>bi>| = <i>ai> - 20

(2) |<i>bi>| $+\frac{a}{3}=\frac{50}{3}$

Last year the average health care cost per employee in Group G increased by <i>ni> percent and the average compensation per employee in group G increased by <i>mi> percent, where <i>ni> is greater than <i>mi>. By what percent did the ratio of health care cost per employee to compensation per employee increase, in terms of <i>ni> and <i>mi>?

In 1021, Murasaki Shikibu completed <i>The Tale of Genji, i>a work that, spanning over 50 chapters and 400 characters, and which many scholars, judging its psychological complexity, consider the first novel.

If and , which of the following must be equal to ?

  I.

 II.

III.

A set of numbers has the property that for any number t in the set, t + 2 is in the set. If -1 is in the set, which of the following must also be in the set?

I. -3

II. 1

III. 5

A square table has a square glass inlay in the center, and a wooden strip of uniform width surrounding the glass. If the ratio of the glass inlay to the wooden strip is 4 to 5, which of the following could be the width, in feet, of the wooden strip?

I.

II.

III. 1

Is <i>xi> even?

(1) <i>xi>² = <i>xi>

(2) <i>xi>³ = <i>x i>

If <i>pi> and <i>qi> are positive integers, can the fraction $\frac{p}{q}$ be expressed as a decimal with only a finite number of nonzero digits?

1. <i> q i>is a factor of 12.
2. <i>pi> is a factor of 12.

If , which must be greater than 1?

I.

II.

III.

If , which must be less than 1?

I.

II.

III.

Which of the following most logically completes the argument?

<i zoompage-fontsize="16">Aarnei> is an old Finnish artwork whose painter and exact date of composition are unknown. However, the painting portrays a riot thought to have taken place sometime between 1563 and 1567, and in the background of the scene stands a public building known to have been destroyed in 1565. Thus the riot depicted in the painting must have actually taken place between 1563 and 1565, assuming that _______.

When positive integer <i>mi> is divided by positive integer <i>ni>, the remainder is 27. If $\frac{m}{n}=75.018$, what is the value of <i>ni>?

Is the distance traveled in <i>ti> seconds at <i>ai> feet per second greater than the distance traveled in <i>si> seconds at <i>b i>feet per second?

1. <i>ti> is 30 greater than <i>si>.
2. <i>ai> is 30 greater than <i>bi>.

If x is a positive integer, does <i>zi> = 0?

(1) <i>zxi> = <i>xi>

(2) <i>z/xi> = <i>xi>

If <i>xi>, <i>yi> and p are positive integers, is p even?

(1) <i>pi> = <i>xyi> and <i>yi> is odd

(2) <i>pi> = $\frac{x}{y}$ and <i>xi> is odd