TEAS Study Guide: Math
A public health lecture was 1 hour 25 min long. The program started at 0940. At what time did it finish? 815 1105 1055 1140
1105
Sam, Paul, and Dean share a sum of money in the ratio 14:16:18 respectively. Given that Sam receives $2100, how much does Dean receive? $2000 $2700 $2400 $5100
$2700 Explanation: $2100/14 = 150 150(18) = $2700
In a sale, all prices are reduced by 40%. Calculate the original price of an article whose sale price is $42. $105 $58.80 $72 $70
$70 Explanation: Think: If prices are reduced by 40%, then the customer is paying 60% of the original cost. This 60% is $42 and we need to find the original price. Let x be the original price of the article. To develop a proportion for solving, say "60% is to 100% as $42 is to x" and write that in proportion form: 60/100=42/x 60x = 4200 x = 4200/60 x=70
Sebastian purchased a brand new car three years ago for $35,000. The following year its value was estimated at $23,850, and the year after that the price dropped to $20,400. Approximately what was the percentage change in the value of Sebastian's vehicle between one year and two years after its purchase? -14% -42% 86% 14%
-14% Explanation: Given that the price of the car is going down, the percent change will be negative. Dividing the price of the car two years after purchase ($20,400) by the price of the car one year after purchase ($23,850) represents how much of the one-year value remained after two years: 20,400÷23,850 ≈ 0.86 This is equivalent to 86% of the value one year after purchase. Since the one-year value is represented by 100%, subtracting 86% - 100% reveals that there was a -14% change in the value of Sebastian's car between its prices one year and two years after purchase.
What is the value of this expression? 2×(5-8×10)+5 -55 -145 -50 -15
-145 Explanation: Remember, PEMDAS is the order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. Remember it by learning "Please Excuse My Dear Aunt Sally." 2×(5-8×10)+5 Using PEMDAS, start inside the parentheses, beginning with multiplication: 2×(5-80)+5 following with subtraction, still within the parentheses: 2×(-75)+5 Continue with multiplication: (-150)+5 and finish with addition: -145
Find the value of 9+(-41)-(-3)+11 -24 -18 24 64
-18
Find the value of (3)(-4)(-3)(5)(-2) 17 -1 -360 360
-360
Which of these expresses 33/80 as a decimal? 4.125 0.0412 0.4125 0.345
.04125 Divide the numerator by the denominator: 33÷80=0.4125
What is the decimal equivalent of 0.33% 0.33 0.033 33.0 0.0033
0.0033 Explanation: .33÷100 = 0.0033
Express 48 square centimeters in square meters. 4800 square meters 0.048 square meters 0.48 square meters 0.0048 square meters
0.0048 square meters Explanation: (100cm)2=(1m)2 10,000cm2=1m2 48÷10,000 = 0.0048
Arrange the numbers 0.09, 0.099, 0.9, 0.009, and 0.091 in order, from least to greatest. 0.09, 0.9, 0.091, 0.099, 0.009 0.009, 0.09, 0.9, 0.091, 0.099 0.009, 0.09, 0.091, 0.099, 0.9 0.09, 0.099, 0.009, 0.9, 0.091
0.009, 0.09, 0.091, 0.099, 0.9
Evaluate: 0.07 x 0.4 2.8 0.28 28 0.028
0.028
Evaluate 0.30 - 0.03 2.7 0.27 0.027 0.3
0.27
Express 2/7 as a decimal, with the answer correct to 2 decimal places. 0.3 0.285 0.29 3.5
0.29 Explanation: 27 = 0.2857 = 0.29
What is the percent equivalent of 0.0067? 67% 0.67% 6.7% 0.067%
0.67% Explanation: 0.0067⋅100=0.67 %
What is the value of b in the equation: 12/(4b−10)−8/(2b−6)=0 -1 4 1 8
1 Explanation: 12/(4b−10)−8/(2b−6)=0 12/(4b−10)=8/(2b−6) Cross multiply 12(2b-6) = 8(4b-10) 24b-72 = 32b-80 Solve for b -72+80 = 32b-24b 8 = 8b 8/8 = b 1 = b
What is the exact value of 0.4⋅3.5 ? 14 1.4 13.5 0.14
1.4 Explanation: Multiply: 3.5⋅0.4=1.40=1.4
A tank is 12 cm high with a square base. Its sides are 10 centimeters wide. What is the volume of the tank in cubic centimeters? 120 1200 600 4800
1200 Explanation: The formula for the volume of a rectangular solid is: Volume = length ⋅ width ⋅ height V=10⋅10⋅12=1200
Divide: 7/8÷1/16 7128 3 13 14
14 Explanation: 7/8÷1/16 7÷8 - 0.875 1÷16 = 0.0625 0.875÷0.0625 = 14
Given that 6x = 7y, find the ratio x : y. 42:6 7:42 7:6 6:7
7:6 Explanation: If 6x = 7y, then x=7 and y=6
Express 85% as a fraction in its simplest form. 5/8 17/20 17/200 8/5
17/20
Yesterday, Fatima trained for 6.25 hours, riding her bicycle under various conditions. During her workout, she managed to ride 114.75 miles total. What was her average speed during this training session? 18.22 miles per hour 21.00 miles per hour 19.61 miles per hour 18.36 miles per hour
18.36 miles per hour Explanation: 114.75÷6.25 - 18.36
Pete, Dan, and Carlyle had to dig a 2-foot deep trench to run conduit to their garage so they could wire it for electricity. To share the work, each agreed to dig 1/3 of the way from the house to the garage. Dan went first and dug 1/9 of the total distance early the next morning. What fraction of the total amount of work did Dan still need to complete? 2/3 8/9 3/9 2/9
2/9
John, Lucy and Emma share 60 pencils in the ratio 4:5:6. How many pencils does Lucy receive? 20 16 24 3
20 Explanation: 4:5:6 → 4+5+6 = 15 (60/15)5= 20
The town of Greenbody received 10.8 inches of rain in March, 5 inches in April, 3.47 inches in May, and 0.9 inches in June. What was the town's total rainfall over this four-month period? 40.17 4.69 20.17 14.92
20.17
Given that a = 4, b = - 6 and c = 8, what is the value of (a+2c)(b+2c)? 200 -104 20 -200
200 Explanation: (a + 2c)(b + 2c) Substitute given values for a, band c: [4 + 2(8)] [-6 + 2(8)] (4 + 16) (-6 + 16) (20)(10) = 200
Express this number as a percentage: 9/40 0.0225% 2.25% 22.5% 0.225%
22.5% Divide 9 by 40: 9÷40=0.225 Multiply 0.225 by 100% to express as percentage 0.225⋅100% = 22.5%
Given that a:12 = 4:10, find the value of a. 5/24 5/12 24/5 12/5
24/5 Explanation: a/12=4/10 Cross-multiply to solve: 10a=48 a = 48/10 Simplify: (48/10)/ 2 = 24/5=a
The cost of 1 pound of fruit is $3.40. How many pounds of food can be bought for $12.00? 0.35 pounds 35 pounds 3.53 pounds 6.3 pounds
3.53 pounds Explanation: Let x represent the number of pounds that can be bought for $12.00. 1/3.40=x/12 State equation as ratio of 1 pound is to $3.40, as x pounds is to $12.00 1(12)/3.40=x x=3.53
A map has the scale of 4 cm to 1 km. What is the actual area of a lake on ground which is represented as an area of 60 cm2 on the map? 3.75 km^2 0.26 km^2 15 km^2 3.75 cm^2
3.75 km^2 Explanation: 42cmsquare:12kmsquare , which gives 16 cm^2: 1 km^2 60cm^2/16 cm^2 = 3.75 km^2
What is the fraction equivalent of 0.032? 4/250 8/125 4/125 32/100
4/125
What percent of 15 is 6? 32% 20% 90% 40%
40% Explanation: 6 ÷ 15 = 0.4 .04⋅100 = 40%
When a number is subtracted from 125 and the result is divided by 12, the answer obtained is twice the original number. What is the number? 5 4 10 25
5 Explanation: Let a be the number: (125−a)÷12=2a 125−a=12(2a) 125−a=24a 125=24a+a 125=25a a=125÷25 a=5
In a library, 30% of the books are fiction and the rest are non-fiction. Given that there are 2,000 more non-fiction books than fiction books, what is the total number of books in the library? 4,000 5,000 6,000 3,000
5,000 Explanation: Let: x be the number of fiction books in the library x + 2,000 = the number of nonfiction books Total number of books = x + (x + 2,000) The problem says that 30% of the total number of books are fiction 30/100[x+(x+2,000)]=x 30/100(2x+2,000)=x (60x+60,000)/100=x 60x+60,000=100x 100x-60x=60,000 40x=60,000 x = 1,500, the number of fiction books x + 2,000 = 1,500 + 2,000 = 3,500, the number of nonfiction books 1,500 + 3,500 = 5,000, the total number of books in the library
Evaluate this expression. Which of these answers is correct? 2/3⋅5/8 10/12 12/8 5/12 5/24
5/12 Explanation: Multiply the numerators: 2⋅5=10 Then multiply denominators: 3⋅8=24 The answer is 10/24. Reduce to its lowest terms by dividing: 10/24÷2/2=5/12
Simplify to a fraction in lowest terms: (6+9)/(6⋅9) 0.277 15/54 5/18 1/9
5/18
Solve the equation and choose the best answer: 9/b=b/4 6 36 6.2 7
6 Explanation: 9/b=b/4 Cross-multiply: 9⋅4=b⋅b 36=b^2 b^2=36 Then, find the square root of both sides: The actual square root of b^2 is ±b and the actual square root of 36 is ±6, so: b=±6 Of the answer choices for this question, 6 is the best choice since it is the only one that is true about the equation.
Ali is x years old and her sister Sara is (10x - 24) years old. Given that Sara is twice as old as Ali, what is Sara's age? 10 8 24 6
6 Explanation: State the problem in a mathematical equation: 2x=10x−24 2x−10x=−24 −8x=−24 x=−24−8 Ali's age: x=3 Sarah's age: 10x-24=10(3)−24=6
The price of a pencil box increased from $25 to $26.50. What is the percentage increase in the price? 35% 0.6% 6% 60%
6% Explanation: Subtract to find the difference or increase in price $26.50−$25.00=$1.50 Divide the increase with the previous price to compute for the rate of increase $1.50÷$25.00=0.06 Convert decimal to percentage form 0.06⋅100%=6%
A side of a square is 2.5 cm long. What is the area of square? 10 5 39 6.25
6.25 Explanation: The formula for solving the area of a square is: A = s x s (where s is the length of one side) A = 2.5 x 2.5 = 6.25 square centimeters
Given that 5 cm on a map represents 4 km on the ground, calculate the distance in km between two points, which are 8 cm apart on the map. 64 km 6.4 km 2.5 km 10 km
6.4 km Explanation: 4/5 = 0.8 0.8⋅8 = 6.4
What is the number a, if the result of adding a to 80 is the same as subtracting 2a from 272. -64 64 62 192
64 Explanation: State the problem in a mathematical sentence: a+80=272−2a a+2a=272−80 3a=192 a=1923 a=64
Brad plans to leave instructions with his broker to sell all of his shares in a particular company if the value of its stock rises more than 10% above the current price, but to purchase additional shares if the stock's value falls more than 10% below its present value. The stock is currently selling for $73.50 a share. Which expression represents the interval, n, between which the broker should neither buy nor sell any shares of the company's stock for Brad? 66.15<n<80.85 69.83<n<77.18 73.60<n<73.60 63.50<n<83.50
66.15<n<80.85 Explanation: If the value of the stock goes up by 10%, it will be at 110% of its present value, or 1.1 × 73.5 = 80.85. If it drops by 10%, it will be at 90% of it current value, or 0.9 × 73.5 = 66.15. Hence, n is greater than $66.15, but less than $80.85.
A teacher has a rectangular piece of paper which is 52 cm long and 38 cm wide. She cuts the paper into squares, each measuring 5 cm by 5 cm. What is the largest number of whole squares she cuts? 79.04 25 79 70
70 Explanation: The key to solving this problem is realizing that you are looking for the number of whole, 5 x 5 cm squares that can be cut from this paper. There will be paper left over, since the dimensions of the paper are not exactly divisible by 5 cm. There will be only 7 rows of squares possible along the 38-cm side, because 38÷5=7.6. This is rounded to 7 because the .6 would only provide a 3 cm side and we need 5 cm sides. The 3 cm would be a leftover scrap, not useful for cutting another square. Similarly, there will be only 10 columns of squares possible along the 52-cm side, because 52÷5=10.4 or 10. (The extra 2 cm is also not enough for a square side.) 10⋅7=70 whole, 5 x 5 cm squares
Express 5.6 meters as a percentage of 8 meters. 75% 70% 4.48% 25%
70% Explanation: (5.6/8)⋅100=70%
In a competition, three teams, A, B and C, scored a total of 150 points. If A scored 40% of this total and B scored four times as many points as C, what were the number of points scored by B? 90 18 60 72
72 Explanation: 150-40% = 90 90/5 = 18 18(4) = 72
Which expression is equal to this one? 5x+2+(9(x-12)/3)-x 13x-7 7x-34 7x+38 8x+34
7x-34 Explanation: Simplify the fraction to get: 5x+2+3(x-12)-x Distribute the 3 to make it: 5x+2+3x-36-x Then combine like terms: (5x+3x+(-x))+(2+(-36)) to obtain the final result: 7x-34
The area of one face of a cube is 49 square centimeters. What is the total length of all its edges? 84 cm 112 cm 98 cm 48 cm
84 cm Explanation: A cube has 6 faces (sometimes called sides), all with equal areas, all square-shaped. A cube has 12 edges and all of these have equal lengths. (The edges are the borders of the square faces, so each would be the same length as one dimension of any face (7 cm).) A face has an area. This is the area of a face: (lengthofface)(lengthofface)=(lengthofface)2 49=(lengthofface)2 lengthofface=4-√9=7cm So, the total length of all edges: 7cm⋅12edges=84cm
What is the value of x in this equation? (x+3)/4=(2x−3)/5 -9 9 12 15
9 Explanation: (x+3)/4 = (2x-3)/5 Cross multiply 5x+15 = 8x-12 Solve for X 15+12 = 8x-5x 27 = 3x 9 = x
If 42.8 kg is divided into two parts, in a ratio of 7:2, how many kg is the smaller share? 21.4 kg 0.856 kg 12.22 kg 9.51 kg
9.51 kg Explanation: 7:2 → 7+2 = 9 (42.8/9)2 = 9.51
What is the value of the expression: 3+2(3+4)^2-6 95 19 239 38
95 Explanation: Remember, PEMDAS is the order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. Remember it by learning "Please Excuse My Dear Aunt Sally." Using PEMDAS, start inside the the parentheses: 3+2(7)^2-6 Next comes exponents 3+2(49)-6, followed by multiplication 3+98-6, with addition and subtraction in order coming last: (3+98)-6=101-6=95
What is the number of sides of a regular polygon whose interior angles are 156∘ each? (Remember, the sum of exterior angles of any polygon is 360∘.) 15 8 14 6
Explanation: The sum of exterior angles of any polygon is always equal to 360 degrees, hence: Exterior angle measurement in degrees x n = 360 where n is the number of angles (which is also the number of sides). Also, for a given interior angle, the exterior angle = 180 - interior angle In the problem: the exterior angle = 180 - 156 = 24 degrees From the formula given above and measurement of the exterior angle computed: 24n = 360 n=360÷24=15 The polygon has 15 angles and 15 sides.
Sam is now 5 times as old as his son Paul. Four years ago, the product of their ages was 52. Find their present ages. Sam: 5 years; Paul: 30 years Sam: 15 years; Paul: 2 years Sam: 60 years; Paul: 30 years Sam: 30 years; Paul: 6 years
Sam: 30 years; Paul: 6 years
Solve the inequality 17 - 2a < 10. a > 3.5 a < 3.5 a < 2.3 a > 5
a > 3.5 Explanation: Isolate the variable by undoing the operations performed on it to solve the inequality. Remember that multiplication or division of an inequality by a negative value switches the direction of the inequality sign. 17-2a<10 Subtract both sides by 17: −2a<−7 Divide both sides by −2, remembering to switch the direction of the inequality sign: a>3.5
Mary is x years old. She is 6 years older than her twin brothers Sam and Paul. What is the mean age of the three children? x−3 x+4 x−2 x−4
x−4 Explanation: Using the formula for mean: Mean=sum of the several given values÷number of values given [x+(x−6)+(x−6)]÷3 (x+x-6+x-6)÷3 (3x-12)÷3 3(x−4)÷3=x−4
