# DATA SUFFICIENCY

## Quant Topic 1 - Data Sufficiency: Choose between the following:

- A. If Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- B. If Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- C. If BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- D. If EACH statement ALONE is sufficient.
- E. If Statements (1) and (2) TOGETHER are not sufficient.

**1. Is the area of a right angled triangle greater than 25 square feet?(1) One of the perpendicular sides is 6 feet. (2) The largest side is 10 feet.**

**2. Is z an even number?
(1) 5z is an even number. (2) 3z is an even number.**

**3. In a work force, the employees are either managers or directors. What is the percentage of directors?
(1) The average salary for manager is $5,000 less than the total average salary. (2) The average salary for directors is $15,000 more than the total average salary.**

**4. What is the sum of the digits of the positive integer n where n < 99?
(1) n is divisible by the square of y. (2) y^4 is a two-digit positive odd integer.**

**5. What is the value of x, given x is a positive number?
(1) x^3 is a 2-digit positive odd integer. (2) x^4 is a 2-digit odd integer.**

**6. Joanna bought only $0.15 stamps and $0.29 stamps. How many $0.15 stamps did she buy?
(1) She bought an equal number of $0.15 stamps and $0.29 stamps. (2) She bought $4.40 worth of stamps. **

**7. What is x?
(1) |x| < 2 (2) |x| = 3x – 2 **

**
8. A sequence has 15 terms a1 to a15 where an = an–1 + k, where k is a non-zero constant. How many terms in the sequence are greater than 10?
(1) a1 = 24 (2) a8 = 10
**

**9. If a and b are both positive integers, is ba+1 – bab odd?
(1) a is odd (2) b is even **

**10. If x is a positive integer, is x! + (x + 1) a prime number?
(1) x < 10 (2) x is even **

# PROBLEM SOLVING

## Quant Topic 2 - Problem Solving

**1. Last month 15 homes were sold in Town X. The average (arithmetic mean) sale price of the homes was $ 150,000 and the median sale price was $130,000. Which of the following statement must be true?
I. at least one of the homes was sold for more than $165,000 II. at least one of the homes was sold for more than $130,000 and less than $150,000 III. at least one of the homes was sold for less than $130,000 **

**2. If x is positive which of the following could be correct ordering of 1/x, 2x, x^2?
I. x^2< 2x < 1/x II. x^2< 1/x < 2x III. 2x < x^2< 1/x **

**3. In FIGURE 1, triangle PQR has a right angle at Q and a perimeter of 60. Line segment QS is perpendicular to PR and has a length of 12. PQ > QR. What is the ratio of the area of triangle PQS to the area of triangle RQS? **

** 4. The height of isosceles trapezoid ABDC is 12 units. The length of diagonal AD is 15 units. What is the area of trapezoid ABDC in FIGURE 2? **

# SENTENCE CORRECTION

## Verbal Topic 1 - Sentence Correction

** 1. Before learning how to make a synthetic growth hormone, scientists had to remove it painstakingly in small amounts from the pituitary glands of human cadavers. **

** 2. Many environmentalists, and some economists, say that free trade encourages industry to relocate to countries with ineffective or poorly enforced antipollution laws, mostly in the developing world, and that, in order to maintain competitiveness, rich nations have joined this downward slide toward more lax attitudes about pollution.**

**3. Industrialization and modern methods of insect control have improved the standard of living around the globe while at the same time they have introduced some 100,000 dangerous chemical pollutants that have gone virtually unregulated since they were developed more than 50 years ago. **

** 4. Greatly influenced by the Protestant missionary Samuel Kirkland, the Oneida was the only one of the five-nation Iroquois League that sided with the colonists during the American Revolution. **

** 5. Even though Clovis points, spear points with longitudinal grooves chipped onto their faces, have been found all over North America, they are named for the New Mexico site where they were first discovered in 1932. **

**6. The artist Renoir’s last word was “flowers,” spoken as they arranged a bouquet of roses just picked from his garden in a vase on his bedroom windowsill. **

** 7. Used by many natural history museum curators in the preparation of animal skeletons for display, dermestid beetles feed on the decaying flesh of animal carcasses, pulling with its mouthparts to strip the bone of any residual fat or muscle tissue. **

# CRITICAL REASONING

## Verbal Topic 2 - Critical Reasoning

**1. Everyone who has graduated from Topnotch High School has an intelligence quotient (IQ) of over 120. Most students with an IQ of over 120 and all students with an IQ of over 150 who apply to one or more Ivy League universities are accepted to at least one of them.
The statements above, if true, best support which of the following conclusions? **

**2. In response to the increasing cost of producing energy through traditional means, such as combustion, many utility companies have begun investing in renewable energy sources, chiefly wind and solar power, hoping someday to rely on them completely and thus lower energy costs. These sources require significant initial capital investment, but the operating costs are not so high; so the utility companies claim that they will provide stable energy supplies at low costs. As one can easily see, these sources will be less risky for the utilities than non-renewable sources, such as gas, oil, and coal, whose prices can fluctuate dramatically according to availability.
The claim of the utility companies assumes which of the following? **

**
3. Doctor: Research shows that adolescents who play video games on a regular basis are three times as likely to develop carpal tunnel syndrome as are adolescents who do not play video games. Federal legislation that prohibits the sale of video games to minors would help curb this painful wrist condition among adolescents.
The doctor’s conclusion depends on which of the following assumptions?
**

# READING COMPREHENSION

## Verbal Topic 3 - Reading Comprehension

##### In the past decade, rapid technological progress and a greater demand for high-quality digital imaging have led to dramatic advances in video display technology. The dominant technology currently used in most consumer product displays is the active matrix liquid crystal diode display (LCD). LCDs apply thin-film transistors (TFTs) of amorphous or polycrystalline silicon sandwiched between two glass plates. The TFTs supply voltage to liquid-crystal-filled cells, or pixels, between the sheets of glass. When hit with an electric charge, the liquid crystals untwist to an exact degree to filter white light generated by a lamp. This filtered light shines directly on the viewing screen or, in the case of projection televisions, is projected through a small chip that acts as a lens. LCDs that are capable of producing color images, such as in televisions and computers, reproduce colors through a process of subtraction, blocking out particular color wavelengths from the spectrum of white light until only the desired color remains. It is the variation of the intensity of light permitted to pass through the matrix of liquid crystals that enables LCD displays to present images full of gradations of different colors. The nature and functioning of LCD displays present many advantages relative to other display technologies. The amount of power required to untwist the crystals to display images, even dark ones, is much lower than that required for analogous processes using other technologies, such as plasma. The dense array of crystals displays images from computer or other video graphics sources extremely well, with full color detail, no flicker, and no screen burn-in. Moreover, the number of pixels per square inch on an LCD display is typically higher than that for other display technologies, so LCD monitors are particularly good at displaying large amounts of data with exceptional clarity and precision. As a result, LCD TVs are considered the best display platform for video games, high definition television, movie special effects, and other graphics-intensive uses.

**
1. The tone of the passage could best be described as
**

**
2. The passage indicates that each of the following may be considered an advantage of LCD displays relative to other display technologies EXCEPT
**

**
3. The process through which an LCD monitor displays different colors is most closely analogous to
**

# INTEGRATED REASONING

## Integrated Reasoning

**Drop down 1 **

**
Drop down 2
**

# ANALYTICAL WRITING

## Analytical Writing

The Directions (always fixed): Discuss how well reasoned you find this argument. In your discussion be sure to analyze the line of reasoning and the use of evidence in the argument. For example, you may need to consider what questionable assumptions underlie the thinking and what alternative explanations or counterexamples might weaken the conclusion. You can also discuss what sort of evidence would strengthen or refute the argument, what changes in the argument would make it more logically sound, and what, if anything, would help you better evaluate its conclusion.

** Sample Argument Task # 1 The following appeared in a memorandum from the business department of the Apogee Company. “When the Apogee Company had all its operations in one location, it was more profitable than it is today. Therefore, the Apogee Company should close down its field offices and conduct all its operations from a single location. Such centralization would improve profitability by cutting costs and helping the company maintain better supervision of all employees.” Discuss how well reasoned...etc. **

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