**NTS Quantitative Reasoning Practice Test 1**

#### Once a month, a crop duster sprays a triangular area defined by three farm houses: A, B, and C, as indicated in the figure. Farmhouse C is located 7 kilometers due east of farmhouse B, as shown. If farmhouse A is located 10 kilometers further west than farmhouse C, what is the total area that the crop duster sprays?

Explanation: The area of any triangle = height. Using 7 kilometers as the base of the triangle in this 1/2 x base x, problem, the triangle's height is the north-south (vertical) distance from A to an imaginary line extending west from B. Given that farmhouse A is located a total of 10 kilometers farther west than farmhouse C, the extension is 3 kilometers long. The triangle's height is 4 kilometers ( by the Pythagorean theorem). Accordingly, the area of triangle 3^2 + 4^2 = 5^2. ABC = 1/2 x 7 x 4 = 14

#### The arithmetic mean (average) of two numbers is . If the first number is Q, which of the following Expressions represents the other number?

Explanation: Apply the formula for determining arithmetic mean (called AM below), or simple average. Letting x equal the other number, solve for x, AM = (Q+x)/2, PQ = (Q+x)/2, 2PQ=Q+x, 2PQ-Q=x

#### How many ounces of soy sauce must be added to an 18-ounce mixture of peanut sauce and soy sauce consisting of 32% peanut sauce in order to create a mixture that is 12% peanut sauce?

Explanation: Letting x equal the number of ounces of soy sauce added to the mixture, 18 +x equals the total mount of the mixture after the soy sauce is added. The amount of peanut sauce (5.76 ounces) must equal 12% of the new total amount of the mixture, which is 18 +x. You can express this as an algebraic equation and solve for x: 5.76=12(x+18) = 30=x

#### At a particular ice cream parlor, customers can choose among five different ice cream flavors and may choose either a sugar cone or a waffle cone. Considering ice cream flavor and cone type, but NOT the arrangement of ice cream scoops, how many distinct triple-scoop cones with three different ice cream flavors are available?

Explanation: Let {A, B, C, D, E} represent the set of ice cream flavors. 10 triple-scoop combinations are available: {ABC}{ABD}{ABE}{ACD}{ACE}{ADE} {BCD}{BCE}{BDE}{CDE} Each of these combinations is available on either of the two cone types. Thus, the total number of distinct triple-scoop cones having three different ice-ream flavors is 20.

#### The figure above shows a solid cube 3 inches on a side but with a 1-inch square hole cut through it. How many square inches is the total surface area of the resulting solid figure?

Explanation: Without the square hole, each of the cube's six outer surfaces contains 9 square inches, for a total of 54 square inches of outer surface area. The square hole reduces that total outer surface area by 2 square inches, to 52. Each of the four inner surfaces (inside the hole) accounts for an additional 3 square inches, for a total of 12 square inches of inner surface areas. The solid's total surface area is 52 + 12 = 64 square inches.

#### If x + y = a, and if x - y = b, then x =

Explanation: Add the two equations: x+y=a and x-y=b then x = 1/2 (a+b)

#### If one dollar can buy m pieces of paper, how many dollars are needed to buy p reams of paper? [1 ream = 500 pieces of paper.]

Explanation: The number of dollars increases proportionately with the number of pieces of paper. The question is essentially asking: "1 is to mas what is top?" First, set up a proportion (equate two ratios, or fractions). Then convert either pieces of paper to reams (divide m by 500) or reams to pieces (multiply p by 500). (The second conversion method is used below.) Cross-multiply to solve for x: 1/m=x/500p then x=500p/m

#### The table shows the distribution of daily low and daily high temperatures in a certain location during each of the 30 days in April. Recorded low and high temperatures were rounded to the nearest Fahrenheit degree (F°). What was the range of daily high temperatures during the month of April?

Explanation: The table does not indicate the highest temperature recorded during April, and so it is not possible to determine the range of temperatures for April.

#### Kirk sent $54 to the newspaper dealer for whom he delivers papers, after deducting a 10% commission for himself. If newspapers sell for 40 cents each, how many papers did Kirk deliver?

Explanation: $54 is 90% of what Kirk collected. Express this as an equation: 54 = .90 x

#### As shown in the figure, from runway 1 airplanes must turn 120° to the right onto runway 2 or 135° to the left onto runway 3. Which of the following indicate(s) a complete turn from one runway to another? I. 45° II. 85° III. 105°

Explanation: The key to this problem is in determining the interior angles of the various triangles formed by the runways. The interior angle formed by the 120°- turn from runway 1 to 2 is 60° (a 180°-turn would reverse the airplane's direction). Similarly, the interior angle formed by the 135°- turn from runway 1 to 3 is 45° (180° - 135°). Two right-triangle "angle triplets" emerge: a 45°-45°-90° triplet and a 30°- 60°-90° triplet, as shown in the figure below.

#### In a geometric sequence, each term is a constant multiple of the preceding one. If the first three terms in a geometric sequence are 22, x, and 28, which of the following could be the sixth term in the sequence?

#### M college students agree to rent an apartment for D dollars per month, sharing the rent equally. If the rent is increased by $100, what amount must each student contribute?

Explanation: The total rent is D + 100, which must be divided by the number of students (M).

#### In the figure above, the centers of all three circles lie on the same line. The radius of the middle-sized circle is twice that of the smallest circle. If the radius of the smallest circle is 1, what is the length of the boundary of the shaded region?

Explanation: Since the smallest circle has a radius of 1, the middle-sized circle has a radius of 2, and, therefore, the diameter of the large circle must be 6, whichmakes its radius 3. The arc of a semicircle is half the circle's circumference-- that is, r. So the length of the boundary of the shaded region is the sum of PI, the arcs of the three semicircles: PI + 2 PI + 3PI = 6PI

#### Among registered voters in a certain district, the ratio of male to female voters is 3:5. If the district currently includes 2,400 registered voters, how many additional males must register to make the ratio 4:5, assuming the number of female voters remains unchanged?

Explanation: Given a 3:5 male-female ratio and a total of 2,400 voters, the number of male voters must be of 3/8 2,400, or 900. Accordingly, female voters must account for the remaining 1,500. Determine the number of male voters needed altogether for a 4:5 male female ratio (assuming the number of female voters remains unchanged at 1,500) by setting up a proportion and solving for that number: 4/5 = x/1500

#### Two square rugs R and S, which have a combined area of 20 square feet, are placed on a rectangular floor whose area is 112 square feet, as shown above. Measured east to west, each rug is placed the same distance from the other rug as from the nearest east or west edge of the floor. If the area of rug R is four times the area of rug S, how far apart are the rugs?

#### The chart shows the portions of all four types of trees on Main Street. If there are 140 trees altogether on Main Street, how many of the trees are pine?

#### In the figure shown, if y = 130 and z = 100, then x =

#### In triangle ABC, side AB is congruent to side BC. If the degree measure of B is b, which of the following represents the degree measure of A?

#### At ABC Corporation, five executives earn $150,000 each per year, three executives earn $170,000 each per year, and one executive earns $180,000 per year. What is the average salary of these executives?

#### The table shows the average price of gasoline among 50 gasoline-service stations on three different days, along with the number of stations charging more and less than the average on each day. Based on the information in the table, which of the following statements about the price of gasoline among all 50 stations must be true? I. On February 1st, the median price was less than the average price II. On March 1st, the average price was equal to the median price. III. The median price on March 1st was less than the median price on January 1st.

Explanation: Statement I must be true. On February 1st, more stations charged less than the average price than greater than the average price; in other words, the median price was less than the average price. Statement II must be true. On March 1st, the number of stations charging more than the average price was the same as the number of stations charging less than the average price; in other words, the median price was the same as the average price. Statement III must be true. The median price on March 1st was the same as the average price: $2.40. The median price on January 1st was greater than the average price of $2.50.

#### During a 5-day festival, the number of visitors tripled each day. If the festival opened on a Thursday with 345 visitors, what was the attendance on that Sunday?

#### Round 907.457 to the nearest tens place.

#### At a certain high school, the respective weights for the following subjects are: Mathematics 3, English 3, History 2, Science 2 and Art 1. What is a student's average whose marks were the following: Geometry 89, American Literature 92, American History 94, Biology 81, and Sculpture 85?

#### Ginger over the course of an average work-week wanted to see how much she spent on lunch daily. On Monday and Thursday, she spent $5.43 total. On Tuesday and Wednesday, she spent $3.54 on each day. On Friday, she spent $7.89 on lunch. What was her average daily cost?

#### What is 1230.932567 rounded to the nearest hundredths place?

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