A set of Math questions, with detailed solutions similar to the questions in the SAT math test.

If a^{2}  b^{2} = 30 and a  b = 5, then a =
A) 11/2
B) 5
C) 6
D) 55
E) 5/2

points A(8,0) and B(0,6) are points in the standard coordinate plane. Let a be the area, in squared units, of a circle that passes through A and B. Which of the following is the set of all possible values of a?
A) a < 25Pi
B) a > 48
C) a > 10
D) a ≥ 100Pi
E) a ≥ 25Pi

If 4x + y = 5 and 2x + 3y = 12, then 3x + 2y =
A) 5
B) 17
C) 12
D) 17/2
E) 2

The price x of a tshirt was first reduced by 10%. Then the new price was reduced by a further 20%. The price of the Tshirt after the two reductions is given by
A) x  0.3x
B) x  30
C) x  0.3x + 0.02x
D) x + 0.02x
E) x + 0.3x

If x + y = √22 and (x  y)^{2} = 10, then xy =
A) 3
B) 2√55
C) 10√22
D) 2√22
E) 10

ABCD is a parallelogram and MN is parallel to to DC. The length of BN is 1/3 of the length of BC. What is the ratio of the area of triangle BNM to the area of the parallelogram ABCD?
.
A) 18:1
B) 1:18
C) 1:9
D) 1:36
E) 1:6

If T = rR / (r + R), then R =
A) Tr  r
B) Tr
C) Tr / (r + T)
D) r / (r + T)
E) Tr / (r  T)

If 2< x <2, then 4  x^{2} / (x  2) =
A) 2  x
B) x + 2
C) x  2
D) 4  x
E) (x + 2)

For all real numbers x, x^{2}  1 =
A) x^{2}  1
B) x^{2} + 1
C) x^{2} + 1
D) x + 1
E) x^{2}  1

If 3/7 of the students in a school are girls, what is the ratio of boys to girls in this school?
A) 4/7
B) 4/3
C) 3/4
D) 7/4
E) 7/3

If 7/5 of a number is 6 more than 20% of the number, what is 11/10 of the number?
A) 5.5
B) 0.22
C) 1.54
D) 1.1
E) 0.22

What is the degree measure of the smaller angle formed by the hour and the minute hands of a clock at 2:50?
A) 14
B) 150
C) 24
D) 145
E) 50

AC is a diameter of the circle shown below and B is a point on the circle such that triangle ABC is isosceles. If the circle has a circumference of 8 Pi, what is the area of the shaded region?
.
A) 16  8Pi
B) 64
C) 8Pi  2
D) 4Pi + 1
E) 4(Pi  2)

ABCD is a square of side x feet. MCD is a triangle such that MC = x/3 feet. Find x so that the area of the trapezoid ABMD is equal to 30 square feet.
.
A) 6√10
B) √30
C) 6
D) √(135/2)
E) 6√3

The average (arithmetic mean) of 3 numbers is 42. The average of another 5 numbers is 50. What is the average of all 8 numbers grouped together?
A) 46
B) 47
C) 48
D) 49
E) 50

What is 5% of 6%?
A) 0.3
B) 3
C) 0.03
D) 0.0003
E) 0.00003

At a high school, where each student takes one foreign language only, 3/8 of the students take French and 1/5 of the remaining students take German. If all the other students study Italian, what percent of all students take Italian?
A) 50
B) 80
C) 10
D) 40
E) 30

On a certain day, a student spent 1/4 of his homework time reviewing his lessons, 7/12 of the time solving the assigned homework and the rest of the time revising for his coming tests. What is the ratio of the time spent revising for his tests to the time spent solving his assigned homework?
A) 1:7
B) 1:3
C) 2:7
D) 7:12
E) 7:4

From 2003 to 2004 the profits made by a company increased by 10%. A year later in 2005, the profits of this company decreased to their 2003 value. By what percent did the profits decrease from 2004 to 2005?
A) 10
B) 5
C) 1
D) 20
E) 9

In a bookshop, the sales of scientific books increased by 40% while the sales of engineering books decreased by 50% from 2001 to 2002. If R is the ratio of the number of scientific books to the number of engineering books in 2001 and r the same ratio in 2002, what is k if it is given by k = r/R?
A) 2.8
B) 1.25
C) 0.2
D) 1
E) 0.8

If f(x  2) = g(x + 1) + 1/x + 2, what does f(0) equal?
A) g(1) + 2
B) undefined
C) g(3) + 5/2
D) g(0) + 2
E) g(1)

Which of the following is not equivalent to 7/10?
A) 0.7
B) 35/50
C) (9/10)*(15/18)
D) 70%
E) 3/10 ÷ 3/7

If 3x  2 = 41, what is the value of √(3x + 6)?
A) √(43/3)
B) √49
C) √41
D) √43
E) √(41/43)

If n and m are integers such that n^{2} = √(m) / 2, which of the follwowing CANNOT be the value of m?
A) 4
B) 0
C) 64
D) 1024
E) 9

The system of equations
2x + y = 2 and x + ky = 5
does not have a solution if k =
A) 0
B) 1
C) 1/2
D) 1/2
E) 5

