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GRE Math Problem Solving Practice Test 05

1. Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $324 per week. How much does she earn in dollars per hour?

A. 11

B. 10

C. 9

D. 8

E. 7

2. ABCD is a parallelogram. BD = 2. The angles of triangle BCD are all equal. What is the perimeter of the parallelogram?

A. 12

B. 9√3

C. 9

D. 8

E. 3√3

3. 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

E. 6

4. If a positive integer n, divided by 5 has a remainder 2, which of the following must be true?

Select ALL such statements.

A. n is odd

B. n + 1 cannot be a prime number

C. (n + 2) divided by 7 has remainder 2

D. n + 3 is divisible by 5

5. A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2. How many of the smaller cubes have paint on exactly 2 sides?

A. 30

B. 24

C. 12

D. 8

E. 6

6. The slope of the line passing through the point (5,5) is 5/6. All of the following points could be on the line except

A. (2.5, 2)

B. (11, 10)

C. (8, 7.5)

D. (-1, 0)

E. (-7, -5)

7. In the figure above the square has two sides which are tangent to the circle. If the area of the circle is 4a²π, what is the area of the square?

A. 2a²

B. 4a

C. 4a²

D. 16a²

E. 64a²

8. A triangle has a perimeter 13. The two shorter sides have integer lengths equal to x and x + 1. Which of the following could be the length of the other side?

Select as many as are correct.

A. 4

B. 6

C. 8

9. A machine puts c caps on bottles in m minutes. How many hours will it take to put caps on b bottles?

A. 60bm/c

B. bm/60c

C. bc/60m

D. 60b/cm

E. b/60cm

10. Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts water. The painter has by mistake added water so that he has 6 litres of paint which is half water and half paint. What must he add to make the proportions of the mixture correct?

A. 1 litre paint

B. 1 litre water

C. ½ litre water and one litre paint

D. ½ litre paint and one litre water

E. ½ litre paint

1. Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $324 per week. How much does she earn in dollars per hour?

A. 11

B. 10

C. 9

D. 8

E. 7

2. ABCD is a parallelogram. BD = 2. The angles of triangle BCD are all equal. What is the perimeter of the parallelogram?

A. 12

B. 9√3

C. 9

D. 8

E. 3√3

3. 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

E. 6

4. If a positive integer n, divided by 5 has a remainder 2, which of the following must be true?

Select ALL such statements.

A. n is odd

B. n + 1 cannot be a prime number

C. (n + 2) divided by 7 has remainder 2

D. n + 3 is divisible by 5

5. A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2. How many of the smaller cubes have paint on exactly 2 sides?

A. 30

B. 24

C. 12

D. 8

E. 6

6. The slope of the line passing through the point (5,5) is 5/6. All of the following points could be on the line except

A. (2.5, 2)

B. (11, 10)

C. (8, 7.5)

D. (-1, 0)

E. (-7, -5)

7. In the figure above the square has two sides which are tangent to the circle. If the area of the circle is 4a²π, what is the area of the square?

A. 2a²

B. 4a

C. 4a²

D. 16a²

E. 64a²

8. A triangle has a perimeter 13. The two shorter sides have integer lengths equal to x and x + 1. Which of the following could be the length of the other side?

Select as many as are correct.

A. 4

B. 6

C. 8

9. A machine puts c caps on bottles in m minutes. How many hours will it take to put caps on b bottles?

A. 60bm/c

B. bm/60c

C. bc/60m

D. 60b/cm

E. b/60cm

10. Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts water. The painter has by mistake added water so that he has 6 litres of paint which is half water and half paint. What must he add to make the proportions of the mixture correct?

A. 1 litre paint

B. 1 litre water

C. ½ litre water and one litre paint

D. ½ litre paint and one litre water

E. ½ litre paint

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