SIFT Math Practice Questions

whole = part/percent = 17/(4/10) = 17 x (10/4) = 170/4 = 42.5

40% of what number is equal to 17?

D. - 36 tons x 3 man hours = 108 man-hours to stack 36 tons. 108/6 = 18 people needed to complete stacking in 6 hours

Assume that it takes an average of 3 man-hours to stack 1 ton of a particular item. In order to stack 36 tons in 6 hours, the number of people required is a. 9 b. 12 c. 15 d. 18 e. 21

1,000 = 1.05 (1,300x) 1,000 = 1365x x = 1000/1365 x = 0.73, or 73%

Dave wants to purchase a new telescope, but he can afford to spend $1,000 total. If the current price of the telescope he wants is $1,300 and sales tax is 5%, how much will the telescope have to be discounted for him not to exceed his budget?

Triangle Inequality Theorem c-b < a < a + b 13 - 5 < a < 13 + 5 8 < a < 18 13 + 5 + 8 < a < 13 + 5 + 18 26 < a < 36

Which of the following could be the perimeter of a triangle with two sides that measure 13 and 5? A. 24.5 B. 26.5 C. 36 D. 37 E. 37.5

The measures of the angles of any triangle have to add up to 180 degrees, or it's not a triangle. Further, a right triangle, by definition, has one angle that is 90 degrees. Only choice C. fits these criteria

Which of these angle measure sets would fit a right triangle? A. 40, 40, 100 B. 60, 60, 60 C. 40, 50, 90 D. 40, 40, 90 E. 30, 45, 90

The probability of picking 5 from set n and 18 from set P is = 1/4 * 1/5. The probability of picking 9 from set n and 14 from set P is = 1/4 * 1/5. Hence Solution is : 2*(1/20) = 0.1

n is an integer chosen at random from the set {5, 7, 9, 11 } p is chosen at random from the set {2, 6, 10, 14, 18} What is the probability that n + p = 23 ? A. 0.1 B. 0.25 C. 0.2 D. 0.3

775t + 625t = 3,500 1400t = 3,500 t = 2.5

A Navy and Marine F/A-18E Super Hornet each leave Miramar Air Station at the same time. The Marine Super Hornet is flying due east at 775 mph and the Navy Super Hornet is flying due west at 625 mph. How long will it take for the two aircraft to be separated by 3,500 miles?

C. 58% - First, find the total number of students in the classroom: 13 + 18 = 31 There is an 18 in 31 chance that a name chosen randomly will be a girl's name. To express this as a percentage, divide 18 by 31, then multiply by 100: 18/31 * 100% = 58%

A classroom contains 13 boys and 18 girls. If a student's name is chosen randomly, what is the probability it will be a girl's name? a. 36% b. 42% c. 58% d. 72%

Set up an equation to find the number of people wearing neither white nor blue. Subtract the number of people wearing both colors so they are not counted twice. 21 = 7 + 6 + neither - 5 neither = 13

A company interviewed 21 applicants for a recent opening. Of these applicants, 7 wore blue and 6 wore white, while 5 applicants wore blue and white. What is the number of applicants who wore neither blue nor white?

C. - Since the problem does not give us specific length of the sides of the cube, we have to think of ratios - how the size of the first cube relates to the second cube. The good part about this is that we can pick a size, work things out, and in doing so come to understand the principles involved. So, if the sides of our first cube are 2 units long, the length of our second cube's sides will be 4 units. Since the formula for the volume of a cube is simply the cube (x^3) of the length of the sides, the volume of the first cube will be (2x2x2) cubic units, and the volume of the second cube will be 64 (4x4x4) cubic units -a ratio of 8:64, or 1:8 (if you want to have even more confidence that you are on the right track, pick another value for this length of the sides of the original cube and work things through again to confirm). This means that, since the weight is proportional to volume, the weight of the second cube will be 5x8 = 40 lbs.

A metal cube weighs 5 lbs. How many pounds will another cube made of the same metal weigh it its sides are twice as long? A. 10 B. 25 C. 40 D. 50 E. 60

Circumference = 2πr, or πd 600 = 2r + 2πr 600 = 2r + 6.28r 600 = 8.28r 72 = r

A patrol aircraft has a maximum range of 600 miles without refueling. If the aircraft departs the airfield and is tasked to make a maximum range circular orbit around the field and return, what is the maximum radius of that orbit? (Use 3.14 for pi)

area of circle = (pi)(r)^2 40-degree segment = 40/360 = 1/9 = pi (15)^2 =225(pi) = 706.5 (1/9) = 78.5

A surveillance radar can detect moving objects up to 15 km away. If radar is able to cover a 40-degree segment of a circle around the radar, how many square miles is the detection field? (Use 3.14 for pi)

Surface area of walls = 2 (12x9) + 2 (10x9) = 2(108) + 2 (90) 216 + 180 396 - surface area of two doors and window surface area of two doors and wind = 2 (8x3) + (3x4) = 2(24) + 12 =48 + 12 =60 396 - 60 = 336 ft^2

Allison wants to paint her new room. The room measures 12 feet (length) by 10 feet (width) by 9 feet (height) and has two 8 foot by 3 foot doors that will not be painted and a 3 foot by 4 foot window. If she is not painting the ceiling, how much area will she need paint to cover?

E. - for helicopter X, the problem specifies that increases and decreases in hovering ceiling due to temperature are evenly graduated. Therefore, since 40 degree increase in temperature decreases the hovering ceiling by 2600 ft, it's reasonable for this problem to expect that a 40 degree decrease would result in a 2600 ft increase in hovering ceiling.

An increase in temperature decreases hovering ceiling for all helicopters, and the decreases in temperature have the opposite effect; this occurs in an evenly graduated manner for helicopter X. The hovering ceiling (in ground effect) chart for helicopter X in humid air at 60 degrees Fahrenheit shows 3,900 ft. and 1300 ft at 100 degrees Fahrenheit. Based on the data above, what hovering ceiling would you expect when similarly loaded in humid air at 20 degrees Fahrenheit? A. 2600 ft B. 3200 ft C. 3900 ft D. 5200 ft E. 6500 ft

E. - One million x 12 = 12 million = 12,000,000 (nickels per year); 12,000,000 x .05 = $600,000

Assume that the U.S. Mint produces one million nickels a month. The total value of the nickels produced during a year is: a. $50,000 b. $60,000 c. $250,000 d. $500,000 e. $600,000

D. - If the radius of the wheel is 1 meter, its diameter is 2 meters. The circumference is pi x diameter = 2 x 22/7. The distance traveled is 35 x 2 x 22/7 = 70 x 22/7 = 220

How many meters will a point on the rim of a wheel travel if the wheel makes 35 rotations and its radius is one meter? a. 110 b. 120 c. 210 d. 220 e. 240

B. 113 - The formula for the area of cirlc is pi*r^2. The diameter of a circle is equal to twice its radius. Therefore, to find the radius of this circle, it is necessary to divide the diameter by 2: 12 / 2 = 6 cm Then, use the formula to find the area of this circle: pi * 6^2

If a circle has a diameter of 12 cm, what is its area? a. 38 cm^2 b. 113 cm^2 c. 276 cm^2 d. 452 cm^2

D. 5

If the product of 6 integers is negative, at most, how many of the integers can be negative? A. 2 B. 3 C. 4 D. 5

C. - 1/2 * 1/2 * 1 = 1/4 cu. ft. ; 1/4 of 62.4 = 15.6 pounds

If the weight of water is 62.4 pounds per cubic foot, the weight of the water that fills a rectangular container 6 inches by 6 inches by 1 foot is a. 3.9 pounds b. 7.8 pounds c. 15.6 pounds d. 31.2 pounds e. 62.4 pounds

Let x = 1/4; y = 1/8 --> x/y = 2 A. both x and y are integers --> Incorrect B. x = ny where n is an integer --> 1/4 = 2*(1/8) --> Correct C. either x or y is negative --> incorrect D. y / x is an integer --> Incorrect Answer: B

If x / y is an integer, which of the following statements must be true? A. both x and y are integers B. x = ny where n is an integer C. either x or y is negative D. y / x is an integer

B. - First determine the aviator-to-aircraft ratio (i.e., how many aircraft per pilot) for both years. The 1950 ratio was 715:1242 or 1:1.737 (divide the second number of aircraft by the number of aviators for a 1:x ratio). For 1970, the ratio was 22,250:11,446 or 1:0.514. Next, determine the amount of change in the aircraft part of the ratio: 1.737 - 0.514 = 1.223 Next, compare the difference to the 1950 number of aircraft and calculate it as a percentage; do this by using a proportion and cross-multiplying: 1.223 / 1.737 = x / 100 1.737x = 122.3 x = 122.3 / 1.737 x = 70.409% = 70.4%

In 1950, the U.S. Army had 715 pilots and 1,241 aircraft; in 1970, the Army had 22,250 pilots and 11,446 aircraft. What is the difference, expressed as a percentage, in the ratio of aviators to aircraft between the two years? In other words, how many aircraft were there in each of the two specified years? Round your final answer to the nearest tenth of a percentage point. A. Increase of 70.4% B. decrease of 70.4% C. decrease of 70.6% D. decrease of 31.1% E. increase of 82.2%

This question is asking you to apply your knowledge of right triangles to determine the length of the side and then calculate the shaded area of the lean-to (see figures below for a visualization of the problem). First, use the pythagorean theorem (x^2 + y^2 = z^2) to solve for the length of the missing side of the triangle, x: x^2 + (12)^2 = (20)^2 x^2 + 144 = 400 x^2 = 400 - 144 x^2 = 256 x = v256 x = 16 Use the formula for the area of a rectangle (xy = area) to determine the shaded area: 16 x 20 = 320 ft^2

Jonah and Sabrina have an outdoor swing set and a 20-foot square tarp. They want to build a "lean-to" using the swing set as one side and the tarp along the top provide them a shaded play area when it is hot. If they attach the tarp to the top of the swing set and secure the other side directly to the ground, how much shaded area will they have underneath the tarp?

E. - Lietenant Highspeed deposits 90% of $1047 = .9 x $1047 = $942.30 (remember to move the decimal two places to the left to convert a percentage to a decimal); this is his principal. We know the rate of %3.2 converts to a decimal of .032, and 32 months is 2 2/3, or 2.67 years. I = p*r*t I = $942.30 x .032 x 2.67 = $80.51 Adding back in the original principal ($80.51 + $942.30) gives us a total of $1022.81

Lieutenant Highspeed saved $1,047 while he was in his Basic Officer Course. If he deposits 90% of this amount in the local credit union at his first duty station, in an account with 3.2% simple annual interest, how much will he have in the credit union at the end of 32 months, presuming he can leave the account alone? The formula to calculate interest is interest = principal x rate x time. A. $1035.68 B. $1136.46 C. $1003.57 D. $1024.98 E. $1022.81

use this formula: l − f + 1 l is the number of the last problem f is the number of the first problem 125 − 74 + 1= 52 => the answer is B (52)

Ryan solves problems 74 to 125 inclusive in a logic exercise. How many problems does he solve? A. 53 B. 52 C. 51 D. 20

184 ft^2 - (x)(y) = area 42x = 2,100 x = 50 perimeter = 2x + 2y 2x42 + 2x50 =p 84 + 100 = p 184 ft^2

The Halls are moving to a new home and want to fence in a space for their dog, Molly. Previously, Molly had a fenced-in area of 2,100 square feet to play. One side of the new lawn is 42 feet long. If the Halls want the same space for Molly and use the 42 feet for one side of a rectangular space, how much fencing will they need to purchase?

E. - The square root of 36 = 6. Each side of the square = 6" x 6" x 2 = 12" . 12" x 12" = 144 square inches.

The area of a square is 36 inches. If the side of this square is doubled, the area of the new square will be a. 72 square inches b. 108 square inches c. 216 square inches d. 244 square inches e. none of the above

E. - Don't assume that points A, B, and C are on a straight line. Draw a diagram with 5 km between A and B; then draw a circle around point B with a radius of 2 km. Point C is somewhere on the perimeter of that circle, with a minimum distance of 3 km from point A and a maximum distance of 7 km. Any distance between those two can be correct.

The distance from point A to point B is 5 km; the distance from point B to point C is 2 km. Which of the following is the best choice for the distance from point A to point C? A. 3 km B. 7 km C. 5 km D. choice A or B E. Choice A, B or C

1st Term= 1 2nd term= 5 3rd term= 6/2=3 4th term=1+5+3/3= 3 '3' is a repeating number after 3rd term

The first term in a sequence is 1 and the second term is 5. From the third term on, each term is the average (arithmetic mean of all preceding terms. What is the 25th term in the sequence? A. 2.5 B. 3 C. 5 D. 25

E. - 200 feet x 200 feet = 40,000 square feet of floor area; 4,000 tons x 2,000 = 8,000,000 pounds; 8,000,000/40,000 = 200 pounds

The floor area in an Air Force warehouse measures 200 feet by 200 feet. What is the maximum safe floor load if the maximum weight the floor can hold is 4,000 tons? a. 100 pounds per square foot b. 120 pounds per square foot c. 140 pounds per square foot d. 160 pounds per square foot e. 200 pounds per square foot

40 degrees complementary angles = 90 degrees

The measure of one of the angles of a complementary angle is 50 degrees. What is the measure of the other complementary angle?

E. - in an isosceles triangle, two of the sides are equal. This means that the angles opposite them are equal, too; if one is 50 degrees, so is the other. To find the measure of the angle opposite the unequal side, start by adding the measure of the two equal angles: 50 + 50 = 100 degrees

The measure of one of the equal angles of an isosceles triangle is 50 degrees. What is the measure of the angle opposite the unequal side? A. 120 B. 180 C. 100 D. 130 E. 80