SAT Math Multiple Choice Practice Test 12

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Question 22 questions

Time 26 minutes

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1. If , and , what is the value of x?

A.
B.
C.
D.
E.

2. Two positive integers are "compatible" if their greatest common factor is a prime number. For instance, 15 and 25 are compatible because their greatest common factor is 5, which is prime. If m and 98 are compatible, and m is an odd number, then what is the greatest common factor of m and 98?

A. 2
B. 5
C. 7
D. 14
E. 49

3. For how many integer values of k is ?

A. 17
B. 18
C. 19
D. 20
E. 21

4.

The figure above shows the graph of a quadratic function f that has a minimum value when . If , then which of the following could be the value of k?

A. -1
B. 1
C. 2
D. 3
E. 4

5. If m and n are integers and , what is the value of ?

A. 4
B. 8
C. 12
D. 16
E. 32

6. Amanda travels to work from home in 60 minutes. If, on her way home, she increases her average speed by 20% and she travels by the exact same route, how many minutes will it take her to get home?

A. 48
B. 50
C. 54
D. 60
E. 64

7. The number that is of 60 is what fraction of 80?

A.
B.
C.
D.
E.

8. If , then

A. 0.25
B. 0.5
C. 1
D. 2
E. 4

9. 29 apples, 21 pears, and 64 oranges are to be distributed among three baskets, with each basket getting an equal number of apples, each basket getting an equal number of pears, and each basket getting an equal number of oranges. If as much of the fruit as possible is distributed in this way, what fruit will remain undistributed?

A. 2 apples, 2 pears, and 1 orange
B. 2 apples, 1 pear, and 1 orange
C. 2 apples and 1 orange
D. 1 pear and 1 orange
E. 1 apple only

10. For all values of x and y, let x & y be defined by the equation . What is the value of 1 & 2?

A. 1
B. 2
C. 3
D. 4
E. 5

11. In ΔABC, and . Which of the following could not be the length of AC?

A. 5
B. 7
C. 9
D. 16
E. 22

12. What is the surface area of a cube that has a volume of 64 cubic centimeters?

A. 64 square centimeters
B. 96 square centimeters
C. 256 square centimeters
D. 288 square centimeters
E. 384 square centimeters

13. The average (arithmetic mean) of x, 2, 6, and 10 is 8. What is the median of x, 2, 6, and 10?

A. 4
B. 6
C. 7
D. 8
E. 9

14.

In the figure above, and . Which of the following expresses y in terms of x?

A.
B.
C.
D.
E.

15.

The graph above represents the set of all possible solutions to which of the following statements?

A.
B.
C.
D.
E.

16.

If a, b, and c represent different integers in the statements above, which of the following statements must be true?

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

17. How many different positive three-digit integers begin with an odd digit and end with an even digit?

A. 125
B. 180
C. 200
D. 225
E. 250

18.

A machine uses a laser beam to cut circles from a sheet of plastic, as shown in the figure above. The beam cuts at the rate of 3 cm per second. If circle A has an area of 64π square centimeters and circle B has an area of 16π square centimeters, how many more seconds will it take the machine to cut circle A than circle B?

A. 2π seconds
B.
C.
D. 8π seconds
E.

19.

In the figure above, the slope of AC is the opposite of the slope of CB. What is the value of k?

A. 9
B. 10
C. 12
D. 14
E. 15

20. If m is the product of all of the integers from 1 to 10, inclusive, and 2n is a factor of m, then what is the greatest possible value of n?

A. 2
B. 4
C. 8
D. 16
E. 32

21. An equilateral triangle with area square centimeters is divided into two triangles by the bisector of one of its angles. What is the sum of the perimeters of these two triangles?

A.
B.
C.
D.
E.

22. A culture of bacteria doubles in population every 2 hours. A sample of 100 bacteria grows to 1,000 bacteria by 4:00 p.m. At what time were there 250 bacteria in this sample?

A. 11:30 am
B. 12 noon
C. 12:30 pm
D. 1:00 pm
E. 2:00 pm