Dat Quantitative Reasoning Questions

Front 1

1/6 + 3/8 - 5/12 =

A. 1/192

B. 5/24

C. 1/8

D. 23/24

E. -1/8

Back 1

Answer:
C: Key concept: To be able to solve this type of question you should have an understanding of addition/subtraction of fractions. The most important step in this process is finding a common denominator(number that is a common multiple of one or more numbers). Step one - In this question, 6, 8, and 12 are the denominators, and a common denominator of all three is 24. Step two - Now using this common denominator equivalent fractions are found. For example, the first fraction becomes 4/24, because 6 times 4 is 24. Step three - Now by substituting in the equivalent fractions, the numerators can be added or subtracted accordingly. ALWAYS PAY ATTENTION TO "+" OR "-".

Front 2

A farmer has a rectangular garden with a perimeter of 72 feet. If one side is 4 feet longer than the other, then what is the area of the garden?
A. 320 ft2

B. 1476 ft2

C. 1280 ft2

D. 324 ft2

E. 672 ft2

Back 2

Answer:
A: Key Concept: Knowledge of area, perimeter, and solving equations. Step one: It is always important to collect the data from a question and know what the question wants you to find. In this case, the question wants you to find the area: (L x W), and they give the perimeter: (2L + 2W = 72ft). Also we know that one side is 4 feet longer than the other(L = W + 4). Step two: Using the previous information, we simply substitute the value for length into the equation for the perimeter, and solve for Width (W). Step three: Length (L) is easily found knowing Width (W). Step four: Because the formula for area of a rectangle is length times width, the area is easily found by solving L x W.

Front 3

Which is the smallest?
A. 11/63

B. 5/46

C. 1/5

D. 2/9

E. 7/36

Back 3

Answer:
B: Key concept: Knowledge and quickness of fractions and long division. To answer these type of questions, your first step should be to approximate the fractions as below. For this question the answer becomes obvious after the first step, because 1/9 is less than 1/6 or 1/5. It is not always the case that these questions will work out this easily. Usually you will be able to narrow the answer choices to two or three and then perform long division from there, as is demonstrated (step two). Normally it does not require that you divide the anwswer out more than two numbers to the right of the decimal. The red circled value is three places to the right for demonstration.



Answer:
B: Key concept: Knowledge and quickness of fractions and long division. To answer these type of questions, your first step should be to approximate the fractions as below. For this question the answer becomes obvious after the first step, because 1/9 is less than 1/6 or 1/5. It is not always the case that these questions will work out this easily. Usually you will be able to narrow the answer choices to two or three and then perform long division from there, as is demonstrated (step two). Normally it does not require that you divide the anwswer out more than two numbers to the right of the decimal. The red circled value is three places to the right for demonstration.




Answer:
B: Key concept: Knowledge and quickness of fractions and long division. To answer these type of questions, your first step should be to approximate the fractions as below. For this question the answer becomes obvious after the first step, because 1/9 is less than 1/6 or 1/5. It is not always the case that these questions will work out this easily. Usually you will be able to narrow the answer choices to two or three and then perform long division from there, as is demonstrated (step two). Normally it does not require that you divide the anwswer out more than two numbers to the right of the decimal. The red circled value is three places to the right for demonstration.

Answer:
B: Key concept: Knowledge and quickness of fractions and long division. To answer these type of questions, your first step should be to approximate the fractions as below. For this question the answer becomes obvious after the first step, because 1/9 is less than 1/6 or 1/5. It is not always the case that these questions will work out this easily. Usually you will be able to narrow the answer choices to two or three and then perform long division from there, as is demonstrated (step two). Normally it does not require that you divide the anwswer out more than two numbers to the right of the decimal. The red circled value is three places to the right for demonstration.

Front 4

A young man works at a grocery store and is paid $10.00 an hour up to 40 hours. Then if he works more than 40 hours he is paid $15.00 per hour for the time he works over 40 hours. If the young man works 44 hours and 17 minutes, how much will he be paid?
A. $444.25

B. $460.50

C. $464.25

D. $660.75

E. $463.75

Back 4

Answer:
C: Key concept: Evaluating word problems involving money. For this type of problem it is important to first recognize what the question is asking and what values are given.(Step one) This step doesn't have to be written each time but it is helpful. Now that all the important values are known the problem can be solved.(Step two) Following the steps shown, the young man is paid $400 for the first 40 hours, $60 for the 4 hours over 40, and $4.25 for the 17 minutes. This last value had to be found by determining the pay per minute, which is $15 divided by 60 minutes, or $0.25/min. Then the pay for 17 minutes is 17 quarters, or $4.25. Finally in (step three) add all the values for the total of $464.25.

Front 5

If: x2 + 6x + 9 = (x+3). What is a value for x that makes this statement true?
A. -2

B. -1

C. 3

D. 1

E. 2

Back 5

Answer:
A: Key concept: Solving Algebraic Equations. To solve this problem you must be familiar with the FOIL method, or in this case the reverse of it.(Step one) demonstrates this, if you are still confused, type "FOIL method" in on any internet search engine. This problem requires the reverse of what is demonstrated. In (Step two), it must be recognized that (x + 3)2 = x2 + 6x + 9. From here, solve this algebraic equation for x giving answer a.

Front 6

Dick is driving on I-75 at 65 miles per hour for 24 minutes then slows down to 55 miles per hour for 30 minutes due to construction. How many miles did Dick travel in 54 minutes?
A. 58.5

B. 53.5

C. 60

D. 55.5

E. 50.5

Back 6

Answer:
B: Key concept: Knowledge of word problems involving speed and distances. In (Step one) record the important data that is found in the question. Now that we know what the question is looking for, and we have all the values we can solve the problem. (Step two) Determine the distance traveled at each speed. This is done by converting miles per hour to miles per minute. (Step three) shows a quick way to solve the equation by dividing 12 out of the top equation, and 30 out of the lower equation. This gives the total distance Dick traveled at each speed, and then addition of these two yields the total distance traveled - b.

Front 7

What is 8% of 4% of 2?
A. 64

B. 0.64

C. 0.064

D. 6.4

E. 0.0064

Back 7

Answer:
E: Key concept: knowledge of percentages. These are the questions that you are able to make up ground if you are behind on time. (Step one) Write out the equation for what the question asks. This is step can be skipped on some questions but not here. Once you do this, solve and you're done. Don't forget to move your decimal two places to the left for percentages - as seen below.

Front 8

If Chad has a 2 sided coin, what is the probability he will flip the coin on heads three times in a row?
A. 1/2

B. 1/4

C. 1/6

D. 1/8

E. 1/16

Back 8

Answer:
D: Key concept: knowledge of odds, and probability. Probability = # successes/# possibilities. Odds = # successes/failures. (Step one) Understanding the question write down what you know. (Step two) Understand that each event is separate, therefore on each flip there is a 1/2 chance of flipping heads. So on the first attempt the probability is 1/2. The probability of the second flip being heads is 1/2, and the probability of heads on the third flip is 1/2. The probability of flipping the coin on heads consecutively three times in a row is 1/2(first flip) x 1/2(second flip) x 1/2(third flip). So the probability is 1/8.

Front 9

Brandon shoots freethrows at a ration of 3:2 for made to missed respectively. If he misses 150 shots then how many freethrows did he make?
A. 450

B. 150

C. 300

D. 320

E. 225

Back 9

Answer:
E: Key concept: knowledge of ratios, and word problems. (Step one) Understand that a ratio of 3:2 is 3 made shots and 2 missed shots, or as a fraction he makes 3/5 of his shots and misses 2/5 of his shots. (Step two) Now using this information we can create an equation with the information we know. Because he misses 2/5 of all his shots, and he missed 150 shots we created this equation solving for total shots taken. (Step three) Now using total shots taken and the fraction for shots made we can find the number of shots made.

Front 10

If the average of a and b is 5 and c = 10. What is the average of a, b, and c?
A. 10

B. 20/3

C. 5

D. 7.5

E. 6

Back 10

Answer:
B: Key concept: Knowledge of word problems, and averages. (Step one) Write everything out so that you can see it clearly. (Step two) Setup an equation that represents the question, and solve.
C=10
(A+B)/2 = 5 so A+B=10
(A+B)+C /3 = 20/3

Front 11

A few years back Kevin bought a new car for $30,000 but since then it has depreciated by half. Now Kevin is again buying a new car with his trade in worth 25% of the new car. What is the value of the new car?
A. $30,000

B. $15,000

C. $18,000

D. $45,000

E. $60,000

Back 11

Answer:
E: Key concept: knowledge of word problems involving interest/depreciation. (Step one) Organize all of the information in the question. (Step two) Setup an equation, and solve.
original car = new car
30,000x50% = y x25%
15,000 = y x(1/4)
4 x 15000 = y
60000 = y

Front 12

If a + b > a - b, then which of the following must be true?
A. b ≤ 0

B. a - b > b - a

C. a > 0

D. a = 0

E. None of the above.

Back 12

Answer:
E: Key concept: Understanding/Comprehension of inequalities. The key to ruling answer choices out is that they must always be true according to the stipulations of the question. Therefor rule out answer choices in a stepwise fashion until only one is left. Start with the answer choices that only have one variable in them - (A,C, & D).

Front 13

what is the square root of (.25 x 2.25)?

A. 2

B. 0.75

C. 0.5

D. 20

E. 75

Back 13

Answer:
B: Key concept: Experience with square roots. This problem should become simple with practice. But care must be taken with the decimal points. The most important step is knowing the rules about square roots
take the square of each term, then multiply those together. You can do that with division, too- but not addition or subtraction.

Front 14

A rectangle with a perimeter of 68 inches has one side that is 4 inches longer than the other. What is the area of this rectangle?
A. 225 in2

B. 361 in2

C. 285 in2

D. 165 in2

E. 300 in2

Back 14

Answer:
C: Key concept: Knowledge of area/perimeter. (Step one) Write down all of the data that is given in the question. (Step two) Formulate an equation using the information in step one. (Step three) Don't forget to finish answering the question. Now that you have solved for "x", find the total area of the rectangle.

Front 15

1/2 +1/3 + 1/4 +1/5+ 1/6 =
A. 3/2

B. 82/60

C. 91/60

D. 5/2

E. 87/60

Back 15

Answer:
E: Key concept: To be able to solve this type of question you should have an understanding of addition/subtraction of fractions. The most important step in this process is finding a common denominator. Step one - In this question, as you can see it is difficult to determine a least common denominator in this fashion. Because the answer must be a multiple of 5 or 6, you can use this in the process of finding a common denominator. Here 5 x 6 = 30, but this doesn't work with all of the other numbers. Try 5 x 6 x 2 = 60. The reason to do this is that the next number both 5 and 6 divide into[60] is 2 x 5 x 6 versus 1 x 5 x 6 = [30]. Step two - Now using this common denominator equivalent fractions are found. Step three - Now by substituting in the equivalent fractions, the numerators can be added to find the answer.

Front 16

What is the median number of the following group? {1, 2, 3, 5, 9}.
A. 1

B. 3

C. 5

D. 9

E. 7/3

Back 16

Answer:
B: Key concept: Knowledge of median, mean, and mode.

Front 17

(x^2 -3) / (x-1) = 1 / (x-1)
what is the value for x that makes this statement true?
A. 3, -3

B. -4, 4

C. -6, 6

D. 0, 1

E. 2, -2

Back 17

Answer:
E: Key concept: knowledge of solving algebraic equations, and FOIL method. (Step one) step back from the question. This allows you to see that by multiplying each side by (x - 1), you will receive x2 - 3 = 1. (Step two) Now solve to solve this equation you must recognize that x2 - 4 = (x + 2)(x - 2). This means that there are two numbers that will satisfy the equation. If all else fails, plug the numbers from the answers into the equation until they work.

Front 18

If 1 inch equals 2.5 centimeters them how many centimeters is 25 feet?
A. 10 cm

B. 100 cm

C. 1000 cm

D. 750 cm

E. 500 cm

Back 18

Answer:
D: Key concept: knowledge of conversions. (Step one) write down all of the information given. (Step two) Set up equation and solve.
25 ft x (12 in/1ft) x (2.5cm/1in) =750cm

Front 19

Which value is the largest?
A. 2sin(0)

B. 2sin(π/6)

C. sin(π/4)

D. 2sin(π/2)

E. sin(π/3)

Back 19

Answer:
D: Key concept: knowledge of trigonomtry values. (You must know (learn/memorize) these values).

Front 20

Brant is x feet tall. At what angle must the sun be at for his shadow to equal his height?
A. sin 1

B. cos 1

C. arcsin 1

D. arccos 1

E. arctan 1

Back 20

Answer:
E: Key concept: knowledge of trig values. Know 'em yet? There is a pneumonic here to help you remember sin, cos, and tan. This question requires tan, as well as arctan.
SOH CAH TOA
tan(theta) = opp/adj
tan(theta) = x/x because shadow equals height
tan(theta) = 1
theta = arctan1

Front 21

0.4 is 30% of x. What is x = ?
A. 12/10

B. 4/3

C. 40/3

D. 10/3

E. 8/5

Back 21

Answer:
B: Key concept: knowledge of percentages and fraction.

Front 22

Jen is building a playground with a perimeter of 280 feet. If the length is 10 feet less than twice the width, then what is the area?
A. 7295 feet2

B. 17475 feet2

C. 11545 feet2

D. 654 feet2

E. 4500 feet2

Back 22

Answer:
E: Key concept: knowledge of area, perimeter, and seting up equations. (Step one) Write down all of the data given in the question. (Step two) combine equations as shown, and find width. (Step three) Find Length using width. (Step four) Solve for area.

Front 23

(8 x 105) x (5 x 10-2) = ?
A. 4.0 x 103

B. 4.0 x 10-10

C. 4.0 x 1011

D. 4.0 x 10-7

E. 4.0 x 104

Back 23

Answer:
E: Key concept: knowledge of scientific notation. Remember scientific notation has one number to the left of the decimal.

Front 24

y = (x+5) / (x-9)
represent this in the form of x=
A. (9y - 9)/(y + 5)

B. (9y + 5)/y

C. (9y + 5)/(y - 1)

D. (y + 5)/(y - 9)

E. 9y/(y - 1)

Back 24

C: Key concept: Knowledge of solving equation.
this one involves factoring out stuff after you've gotten all x on one side and all y on the other.

Front 25

sq rt (x^2 - 9) / sq rt (x-3) = 4
for what value of x is this statement true?
A. 3

B. 13

C. 23

D. 4

E. 14

Back 25

Answer:
B: Key concept: knowledge of the FOIL method, and properties of squares.

Front 26

Danny caught a fish that weighed 5 pounds 8 ounces, Glen caught a fish that weighed 6 pounds 2 ounces, and Michael caught a fish that weighed 4 pounds 8 ounces. What is the average weight of these fish?
A. 5 lbs. 0 oz.

B. 5 lbs. 5 2/3 oz.

C. 5 lbs. 6 oz.

D. 5 lbs. 6 2/3 oz.

E. 5 lbs. 5 oz.

Back 26

Answer:
C: Key concept: knowledge of conversions of weights and averages. (Step one) Convert each fishes' weight to ounces in order to (step two) find the averages. Then (step three) reconvert back to pounds. The remainder is the ounces.

Front 27

If a and b are prime numbers and a = x/b then which of the following could x = ?
A. 20

B. 24

C. 33

D. 36

E. 40

Back 27

Answer:
C: Key concept: knowledge of prime numbers. A prime number is one that can only be divided by itself and one. One way to solve this type of problem is to write out the multiples of each number. However this is time consuming. You may have to do this mentally.

Front 28

Jacob is one fourth the age of his dad. In three and a half years he will be one third the age of his dad. How old is Jacob now?
A. 4

B. 5

C. 6

D. 7

E. 8

Back 28

Answer:
D: Key concept: knowledge of word problems involving age. (Step one) Set up the equation. Jacob is 1/4 his dad's age. In 3 1/2 years Jacob = 1/3 his dad's age. (Step two) The following shows how to substitute one equation into another, in this case 4J = D into J + 3 1/2 = 1/3(D + 3 1/2). (Step three) Now because there is only one variable in the equation we can solve for Jacob's age now.

Front 29

At Adam's graduation there were 224 seniors graduating. If the ratio of girls to boys was 7 to 9 then how many girls were graduating with Adam?
A. 98

B. 177

C. 128

D. 130

E. 110

Back 29

Answer:
A: Key concept: knowledge of ratios. Ratio is the number of one thing to another. In this case girls to boys. 224 seniors. A 7 to 9 girls to boys ratio. Fractionally this means that 7/16 of the students are girls and 9/16 of the students are boys.

Front 30

If two x's and four o's are placed in a bag, then what is the probability that two draws from the bag at random, without replacement, will yield two x's?
A. 3/11

B. 2/15

C. 1/15

D. 1/10

E. 1/9

Back 30

9

Answer:
C: Key concept: knowledge of probability, odds. Probability = # successes/# possibilities. Odds = # successes/failures. So the number of successes on the first draw are 2 and the number of possibilities is 6. On the second draw there is one success, and 5 possibilities. Therefor the probability of two consecutive draws without replacement is 1/15 .
2/6 x 1/5 = 2/30 = 1/15

Front 31

Brian receives 6 magazines at the begining of each month. If he wants to read 2 magazines, then how many combinations of 2 could he select?
A. 12

B. 6

C. 15

D. 11

E. 36

Back 31

Answer:
C: Key concept: knowledge of combinations. There are two rules to follow for almost any question like this. Combinations and Permutations
this involves factorials. yuk.

Front 32

What is the distance between the two points (2, 6) and (-1, 3) on a graph?
A. 3sqrt2
B. 6
C. 9sqrt2
D. 18
E. 4

Back 32

Answer:
A: Key concept: knowledge of the distance formula. You have to know this formula. Once you do this question is a breeze.
Distance = sqrt((x1-x2)^2 + (y1 - y2)^2)
plug n chug

Front 33

3x + 2y is what percent of 6x2 + y, if x = 2 and y = 6?
A. 30%

B. 35%

C. 37%

D. 43%

E. 60%

Back 33

Answer:
E: Key concept: knowledge of percentages and substitution of values. (Step one) write out what question is asking. (Step two) Plug in values and solve.

Front 34

What percent of 54/3 is 56/4 + 48/8 - 24/3 ?
A. 12

B. 18

C. 33.3

D. 66.6

E. 50

Back 34

Answer:
D: Key concept: Knowledge of percentages and fractions. (Step one) Here this involves determining what the question is asking. (Step two) involves reducing each fraction to a number that's easier to work with. (Step three) involves solving the question.

Front 35

A dog kennel has 220 dogs. The ratio of Labrador Retrievers to German Shepherds is 6 to 9. How many Labrador Retrievers are at this kennel?
A. 132

B. 147

C. 88

D. 15

E. 98

Back 35

Answer:
C: Key concept: knowledge of ratios. Ratio is the number of one thing to another. In this case labrador retrievers to german shepherds. 220 dogs. A 6 to 9 lab to shepherd ratio. Fractionally this means that 6/15 of the dogs are labs and 9/15 of the dogs are shepherds.

Front 36

Which is the smallest?
A. 17/23

B. 31/33

C. 9/11

D. 41/43

E. 34/39

Back 36

Answer:
A: Key concept: Knowledge and quickness of fractions and long division. To answer these type of questions, your first step should be to approximate the fractions as below. For this question the answer becomes reasonably apparent after the first step, because 3/4 is less than the other by quite a bit. It is not always the case that these questions will work out this easily. Let's say you were able to narrow the answer choices to A and C. Then just perform long division from there, as is demonstrated (step two). Normally it does not require that you divide the anwswer out more than two numbers to the right of the decimal.

Front 37

A bicyclist pedals at an average speed of 20 mph his first lap around a circle. His second lap was at an average speed of 30 mph. What was his average speed for the entire trip?
A. 25

B. 22

C. 24

D. 26

E. 30

Back 37

Answer:
C: Key concept: understanding of speed and averages. A bicyclist does lap one at 20mph. He does lap two at 30mph. Following the steps below, you can see that the average time for the total trip is the total distance (2d) divided by the total time of the two laps d/20 + d/30. This gives an answer of 24 mph. To conceptualize this the bicyclist will be traveling at 20 mph for a longer period of time than he will at 30 mph, because he covers the same distance faster at 30 mph. This is why the average is 24 mph rather than 25 mph.

Front 38

27 X 756 - 30 X 756 = ?
A. 20412

B. 22680

C. -2268

D. -22680

E. 2268

Back 38

Answer:
C: Key concept: Knowledge of mathematical principles. Simply put the test taker must recognize that there is a group of 27 (756's) minus another group of 30 (756's). Therefor a similar statement is (27 - 30) x 756. Now all that has to be done is multiply (-3) x 756 which equals -2268.

Front 39

A square's perimeter is 24 feet. What is the area?
A. 16 ft2

B. 26 ft2

C. 36 ft2

D. 10 ft2

E. 40 ft2

Back 39

Answer:
C: Key concept: Knowledge of area/perimeter. You must first recognize that a square has all sides of equal value. That's it. There are 4 equal sides to a square with a perimeter of 24 feet, so each side is 6 feet. Now that you have solved for "x", find the total area of the square

Front 40

( (.3)^2 (sqrt.36) (10) ) / .6 =
A. 90

B. 9

C. 0.9

D. 0.09

E. 0.009

Back 40

Answer:
C: Key concept: Practice. These should come easy to you with practice. These are very straight forward. Just make sure to watch your decimal point.

Front 41

If x = y/4 + z, and x = 14/13, and y = 35/70, what does z equal?
A. -8/13

B. 99/104

C. 0

D. 125/104

E. 8/13

Back 41

Answer:
B: Key concept: knowledge of fractions and solving equations. (Step one) input the values into the equation. (Step two) solve the equation for "z"

Front 42

John buys a paper everyday for 26 weeks. If he pays $0.50 daily for the paper, then how much would he have saved if he bought weekly subscriptions at $2.10?
A. $54.60

B. $36.40

C. $3.64

D. $34.50

E. $91.00

Back 42

Answer:
B: Key concept: knowledge of word problems involving money. (Step one) To solve this problem, determine how much John paid over 26 weeks at $.50/day, and (Step two) determine how much John would have paid over 26 weeks at $2.10/week. Then (Step three) subtract daily from weekly

Front 43

What is 2% of 15% of 12?
A. 2.4

B. 0.36

C. 0.018

D. 0.036

E. 0.24

Back 43

Answer:
D: Key concept: knowledge of percentages. (Step one) Write out the equation for what the question asks. This is step can be skipped on some questions but not here. Once you do this, solve and you're done. Don't forget to move your decimal two places to the left for percentages

Front 44

Which of the following is equivalent to cos (π/3)?
A. sin(π/4)

B. cos(2π/3)

C. -sin(π/6)

D. sin(π/3)

E. -cos(2π/3)

Back 44

Answer:
E: Key concept: knowledge of trig values. (Step one) To solve this problem you must first know the value of cos (π/3). (Step two) Now find the values of the answer choices to find an equivalent one.

Front 45

If: x2 + 7x + 1 = -x - 15. Which of the following is a solution for x = ?
A. 0

B. -4

C. 7

D. 4

E. 1

Back 45

Answer:
B: Key concept: Knowledge of solving equations, and FOIL method. (Step one) step back from the question. This allows you to see that by getting all of the terms on one side of the equation you can more easily solve for x. (Step two) Now solve to solve this equation you must recognize that x2 + 8x + 16 is a square. In this case (x + 4)2. Now solving this equation for zero we find the answer to be -4. If all else fails, plug the numbers from the answers into the equation until one of them works.

Front 46

Each side of a square is increased by 5 inches which increases the area of the square by 65 square inches. What was the area of the original square?
A. 81 in2

B. 64 in2

C. 49 in2

D. 16 in2

E. 25 in2

Back 46

Answer:
D: Key concept: Knowledge of area, perimeter, and setting up equations. (Step one) Write out the data from the question, what does the question want? (Step two) Use this data to combine equations that allow you to solve for one variable, (Step three) Now that you have the new values of the square solve for area.

Front 47

If: 3x - 4 > -(x + 6), then a solution for "x" that would make the statement true is which of the following?
A. x < -2

B. x < -1

C. x > -1/2

D. x < -4

E. x < -8

Back 47

Answer:
C: Knowledge of greater than/lesser than sign. This question is straight forward. Solve for x as shown.

Front 48

Hose A fills a trough in 12 minutes and hose B fills the same trough in 24 minutes. How long does it take to fill the trought with both hose A and B going at the same time?
A. 10

B. 8

C. 12

D. 16

E. 6

Back 48

Answer:
B: Key concept: Knowledge of word problems involving work/time. (Step one) To solve this you need to setup an equation that relates the work done by each person and the amount of time each person takes. (Step two) Now that you have this equation solve.
set up fractions with common denominators for time, add them together to equal total time.

Front 49

If 25mm is 1in then how many feet is 0.48 meter?
A. 1

B. 1.6

C. 1.5

D. 1.3

E. 2

Back 49

Answer:
B: Key concept: Knowledge of conversions of units (measurements). You need to know how to convert not just lengths, but weights, and volumes etc. (Step one) Write out all of the values given, and any you might need to know. (Step two) set up an equation and solve. Don't forget to solve for feet, not just inches.

Front 50

If y = (3+4)/(x+6), then which of the following represents x?
A.x= (3-6y)/(y-4)

B. x=(6y-4)/(y-3)

C. x=(6-4y)/(3-y)

D. x=(3y-4)/(6-y)

E. x=(4-6y)/(y-3)

Back 50

Answer:
E: Key concept: Knowledge of solving equations.

Front 51

What is the probability of rolling two 6 sided dice simultaneously and receiving a value of seven?
A. 1/7

B. 7/36

C. 1/6

D. 1/18

E. 1/3

Back 51

Answer:
C: Key concept: knowledge of probability, odds. Probability = # successes/# possibilities. Odds = # successes/failures. So the number of successes is 6 and the number of possibilities is 36. Therefore the probablility is 6/36 or 1/6. Successes is found, because there are 6 ways to roll a seven - 1-6, 2-5, 3-4, 4-3, 5-2, 6-1. The number of possibilities is found because 6 sides x 6 sides = 36 possibilities.

Front 52

For the following statement to be true which of the variables can not be zero? 24x2(y-z)[(9+b)]a = 13.
A. x

B. y

C. z

D. a

E. b

Back 52

Answer:
A: Key concept: Knowledge of polynomial expressions. If x were 0 the statement would = 0 not 13. Any of the other answer choices could equal zero and the statement could still be true.

Front 53

Mackenzie is 1/3 the age of her mother. In 8 years she will be 1/2 the age of her mother. How old is Mackenzie's mother now?
A. 8

B. 16

C. 12

D. 24

E. 32

Back 53

Answer:
D: Key concept: knowledge of word problems involving age. (Step one) Set up the equation. Mackenzie is 1/3 her mom's age. In 8 years Mackenzie = 1/2 her mom's age. (Step two) The following shows how to substitute one equation into another, in this case 3M = P into M + 8 = 1/2(P + 8). (Step three) Now we solve for Mackenzie's age, and use this in (Step four) to find her mom's age.

Front 54

Which of the following expressions is equivalent to: (6a2b5)(4a3b)-2 ?
A. (a5b6)/10

B. (3b3)(8a4)-1

C. (3a4)(b3)

D. (3b2)(8a3)-1

E. 24a6b10

Back 54

Answer:
B: Key concept: Knowledge of working with powers. If a power is raised to a power, then you multiply. But when a variable raised to a power is multiplied by the same variable raised to a power, you add the exponents.

Front 55

What is the value of sqrt(.64/.0016)?
A. 200

B. 20

C. 2

D. 0.2

E. 0.02

Back 55

Answer:
B: Key concept: Experience with square roots.

Front 56

If the bottom of a vase is a circle with an area of 49π, then which of the following represents the circles circumference?
A. 49

B. 14π

C. 7π

D. 25π

E. 10π

Back 56

Answer:
B: Key concept: Knowledge of area, diameter, and circumference of circles. You should know that the area of a circle is πr2. Also you should know the formula for circumference of a circle is 2π. From here you can solve for circumference

Front 57

[3,5,3,7,8,5,3]. In this group of numbers what is the mode?
A. 5

B. 7

C. 3

D. 6

E. 8

Back 57

Answer:
C: Key concept: Knowledge of median, mean, and mode.

Front 58

On one buffet bar there are 7 different meats, and on another buffet bar there are 6 different vegetables. People are allowed to chose one item from each bar. How many combinations of one meat and one vegetable can be chosen?
A. 42

B. 49

C. 21

D. 36

E. 25

Back 58

Answer:
A: Key concept: knowledge of combinations. [For one meat and one vegetable] : The number of meats x number of vegetables.

Front 59

(2/a) / (c/4)
Evaluate this expression if a= 4/10 and c = 5/23
A. 100/23

B. 1/2

C. 2

D. 5

E. 92

Back 59

Answer:
E: Key concept: knowledge of fractions and solving equations. (Step one) input the values into the equation. (Step two) organize the equation so that it is easier to work with. (Step three) solve equation

Front 60

Which of the following equations of lines is parallel to y = 5x + 4?
A. y = (1/3)x + 4

B. y = (1/5)x + 4

C. y = (1/5)x - 4

D. y = 5x -1

E. y = 10x - 2

Back 60

Answer:
D: Key concept: Knowledge of linear equations. y = 5x + 4 is an equation of a line with a slope of 5(rise/run) and it crosses the x-axis at 4. Therefore a parallel line to this line would have the same slope no matter where it crosses the x-axis.

Front 61

If: f(x) = 6x - x2, then what does f(3) = ?
A. 6

B. 9

C. 7

D. 8

E. 10

Back 61

Answer:
B: Key concept: Knowledge of graphic functions. f(x) = 6x - x2 is an equation for a parabola seen below. It doesn't matter what shape it makes though. All you need to know is that you substitute 3 from f(3) in for x as seen below. This gives the point (3, 9) on the curve

Front 62

If: -4a + 8 > 12, then which of the following must be true?
A. a > -1

B. a > 1

C. a = 0

D. a < -1

E. a = 1

Back 62

Answer:
D: Knowledge of greater than/lesser than sign. This question is straight forward. You must remember that if you multiply or divide a negative number to another side of a "< or >" sign you must reverse the sign.

Front 63

On a coordinate graph what is the distance between (3, 4) and (0, 8)?
A. 5
B. sqrt89
C. 7
D. 2sqrt5
E. 8sqrt3

Back 63

Answer:
A: Key concept: knowledge of the distance formula. You have to know this formula. Once you do this question is a breeze.

Front 64

What are four consecutive odd numbers that when added together equal 64?
A. {7,9,11,13}

B. {9,11,13,15}

C. {11,13,15,17}

D. {13,15,17,19}

E. {15,17,19,21}

Back 64

Answer:
D: Key concept: Knowledge of the consecutive number formula. (Step one) Recognize that (n) and (n + 2) are two consecutive (odd or even) numbers. (Step two) Using this knowledge create a formula for 4 consecutive odd numbers that when added equal 64. (Step three) Solve for n. (Step four) Determine all four consecutive odd numbers

Front 65

Dayne has a gallon of orange juice. For breakfast he drinks 13 fluid ounces of the gallon. How many fluid ounces of the gallon remain?
A. 96

B. 115

C. 99

D. 84

E. 117

Back 65

Answer:
B: Key concept: knowledge of conversions of volumes. These must also be known(learned/memorized). (Step one) write out what is given in the question. (Step two) Convert the original gallon to fluid ounces. Once this is done, (step three) subtract the 13 fluid ounces from the 128 fluid ounces of the gallon.
1gallon = 4 quarts = 8 pints
1 pint = 16 fluid ounces

Front 66

Which of the following is equivalent to (sec x)(sin x)?
A. sin x

B. cos x

C. tan x

D. csc x

E. cot x

Back 66

Answer:
C: Key concept: knowledge of trig values. SOH CAH TOA. (Step one) To solve this problem you must first know the value of (sec x), and (sin x) individually. (Step two) Then the expression must be reduced as seen below and find an equivalent value from the answer choices.

Front 67

What is the value of x if: 8y = 2x + 4 and 3y + 8 = x?
A. 10

B. 10

C. 24

D. 36

E. 38

Back 67

Answer:
E: Key concept: knowledge of substituting equations. (Step one) Write out what is given in the question. (Step two) (There are many different ways of solving this question, so you may have gone about this differently). By substituting x = 3y + 8 into 8y = 2x + 4 you can solve for "y" as seen below. Then (Step three) you can input "y" into either equation to find the value for "x".

Front 68

What is the radius of a circle with the given area = (x2 + 4x + 4)π ?
A. x + 2

B. 2

C. 4

D. x + 4

E. 8

Back 68

Answer:
A: Key concept: knowledge of FOIL and area of a circle. This question is a little tricky but if you understand the concept you will be fine. You know the area of a circle is πr2, so somewhere there in the (x2 + 4x + 4) is (r)2. This is demonstrated below. If all else fails look to the answer choices for guidance.