PSAT ONLINE PRACTICE TEST MATH

Question 1 :

The perimeter of a square is four times the circumference of a circle with radius of 1 m. What is the area of the square ?

(A)  4π  (B)  8π  (C)  4π²  (D)  8π²  (E)  16π²

Solution : 

Perimeter of square  =  4 Circumference of circle

Radius of circle  =  1 m

4a  =  4(2π r)

4a  =  8π(1)

a  =  8π/4  ==>  2π

Area of square  =  a²

  =  (2π)²

  =  4π²

Question 2 :

(A)  24  (B)  66  (C)  67  (D)  68  (E)  1120

Solution :

Since the given shapes are similar, we may equate the corresponding angles.

<a  =  4, <b  =  5, <c  =  7 and <d  =  8

bc + ad  =  5(7) + 4(8)

  =  35 + 32

  =  67

Question 3 :

Convert 3/40 to a decimal.

(A)  0.0075  (B)  0.075  (C)  0.06  (D)  0.75  (E)  7.5

Solution :

To present the given fraction in decimal form, we have to convert the denominator as 10, 100 or 1000 etc.

When we multiply 40 by 25, we get 1000.

  =  (3/40) ⋅ (25/25)

=  75/1000

=  0.075

Question 4 :

For what value of q is 6(q + 3)  =  2(q + 4) ?

(A)  -1/2  (B)  -4/9  (C)  -5/2  (D)  -3  (E)  -2/5

Solution :

6(q + 3)  =  2(q + 4) 

6q + 18  =  2q + 8

6q - 2q  =  8 - 18

4q  =  -10

q  =  -10/4

q  =  -5/2

Question 5 :

What is angle x of the circle O?

(A)  45 degree  (B)  60 degree (C)  75 degree 

(D)  150  degree  (E)  90 degree

Solution :

OA  =  OB  =  r

OA  =  OB (Equal sides makes an equal angle) 

The sum of the angles in a triangle.

x + x + 30  =  180

2x + 30  =  180

2x  =  180 - 30

2x  =  150

x  =  150/2  =  75

Question 6 :

For how many values of x is -3x²/4 > 0

(A)  0  (B)  1   (C)  3  (D)  5  (E)  6

Solution :

For all positive and negative values of x, x² will be positive, but in front 3x²/4 we have negative sign. For no values of x, we will have negative.

Hence the answer is 0.

Question 7 :

x is 40% of y and y is the square of x, which is x ?

(A)  √x  (B)  0.4√x  (C)  0.4x²  (D)  x²  (E)  0.4 x

Solution :

x  =  40% of y  ----(1)

y  =  x² -----(2)

Applying the value of y in (1), we get

x  =  40% of x²

x  =  0.4 x²

Hence the answer is 0.4 x².

Question 8 :

If x  =  7 and 4x (3y - 2x)  =  112, what is the value of y ?

(A)  4  (B)  6  (C)  7  (D)  28  (E)  84

Solution :

By applying x  =  7, we get

4x (3y - 2x)  =  112

4(7) [3y - 2(7)]  =  112

28 (3y - 14)  =  112

3y - 14  =  112/28

3y  - 14  =  4

3y  =  4 + 14 

3y  =  18

y  =  18/3  =  6

Hence the value of y is 6.

Question 9 :

If x ⟩ y  =  (x + y)/(x - y), what is a ⟩ (a - b) ?

(A)  2a/b  (B)  (2a - b)/2a  (C)  (2a - b)/b 

(D)  (2a - b)/2b  (E)  (a + b)/(a - 2b)

Solution :

Given that :

  x ⟩ y  =  (x + y)/(x - y)

We need to find, a ⟩ (a - b).

Here, x  =  a and y  =  a - b

 a ⟩ (a-b)  =  (a + a - b)/(a - (a - b))

=  (2a - b)/(a - a + b)

=  (2a - b)/b

Question 10 :

What is the value of √25 + √64?

(A)  10  (B)  13  (C)  14  (D)  89  (E)  100

Solution :

√25 + √64  =  √(5 ⋅ 5) + √(8 ⋅ 8)

  =  5 + 8

  =  13

Question 11 :

On a certain map that is drawn to scale, 1.5 centimeters is equivalent to 2 miles. If two cities are 35 miles apart, how many centi-meters apart should they be on this map? 

(A) 24.75     (B) 26.00   (C) 26.25   (D) 45   (E) 46.33

Solution :

1.5 cm = 2 miles

Dividing by 1.5 on both sides, we get 

1 cm = 2/1.5

= 1.3 miles

Distance between two cities= 35 miles

Let x be the distance in centimeters in the map.

1.5 : 2 = x : 35

1.5/2 = x/35

x = 1.5(35)/2

= 26.25

So, the required distance is 26.25 centimeter.

Question 12 :

Jose needs a 5/8-meter length of copper pipe to complete a project. Which of the following lengths of pipe can be cut to the required length with the least length of pipe left over?

(A) 9/16 meter      (B) 3/5 meter     (C) 3/4 meter

(D) 4/5 meter       (E) 5/6 meter

Solution :

Since comparing decimals is easier than comparing fractions, it’s probably best to convert all the fractions to decimals with your calculator. 

Since the project requires 5/8 = .625 meter of pipe, the correct answer must be no less than .625. To minimize the waste, we must find the smallest length that is greater than .625. “Decimalizing” the choices gives

(A) .5625     (B) .6     (C) .75     (D) .8 and

(E) .83. The smallest length greater than .625 is (C) .75.

So, option C is correct.

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