GRE Math Problem Solving Practice Test 08

1. 3x + y = 19 , and x + 3y = 1.
Find the value of 2x + 2y

A. 20
B. 18
C. 11
D. 10
E. 5

2. The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 20 per cent. The two reductions together are equal to a single reduction of

A. 45%
B. 40%
C. 35%
D. 32.5%
E. 30%

3. x and y are integers
x + y < 11 , and x > 6
What is the smallest possible value of x - y ?

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

4. If x⁵y⁴z² <0 , which of the following must be true?

Select ALL such statements.

A. xy < 0
B. yz < 0
C. xz < 0
D. x < 0
E. x⁵ < 0

5. BCD is a line segment and Angle BAC = ¼ Angle ACB ; Angle ACD = ?

A. 140
B. 100
C. 120
D. 60
E. it cannot be determined from the information given

6. If x ¤ y = (x + y)² - (x - y)²
Then √5 ¤ √5 =

A. 0
B. 5
C. 10
D. 15
E. 20

7. In a certain village, m litres of water are required per household per month. At this rate, if there are n households in the village, how long (in months) will p litres of water last?

A. p /mn
B. mn / p
C. mp / n
D. np / m
E. npm

8. In the figure below, what is the slope of line l ?

A. - 3
B. - 1/3
C. 0
D. 1/3
E. 3

9. What digit appears in the units place in the number obtained when 2³²⁰ is multiplied out?

A. 0
B. 2
C. 4
D. 6
E. 8

10. Radius of circle center O is 3 times the radius of circle center C.

Angle ACB = Angle POQ

A. 6
B. 12
C. 18
D. 36
E. 3/2