PSAT MATH PRACTICE ONLINE

Question 1 :

If 2000/2x  =  10, then what is √x?

(A)  √10  (B)  10  (C)  √1000  (D)  100  (E)  1000

Solution :

2000/2x  =  10

1000/x  =  10

x  =  1000/10  

 x  =  100 

Taking square roots on both sides, we get

√x  =  √100

√x  =  10

Question 2 :

If x = 9, y = -9 and z = -1, what is the value of yz + √x + yz - √x ?

(A)  -24  (B)  -18  (C)  0  (D)  18  (E)  24

Solution :

First let us simplify

  yz + √x + yz - √x 

=  2yz

By applying the value of y and z, we get

  =  2(-9) (-1)

  =  18

Question 3 :

1 dollar  =  0.5 pillets

4 coss  =  1 dollar

Lindsey has $20 to spend. She needs to buy exactly 2 pillets. She spends the remaining amount buying coss. How many coss does Lindsey purchase ?

(A)  4  (B)  5  (C)  64  (D)  72  (E)  76

Solution :

1 dollar  =  0.5 pillets ----(1)

2 pillets  =  4 dollar

She is spending 4 dollar to purchase 2 pillets. So, the remaining amount that she has  =  20 - 4  =  16 dollar

For this 16 dollars, she has to buy coss.

Give n that :

1 dollar  =  4 coss

16 dollar  =  4 (16) coss 

16 dollar  =  64 coss 

Hence, she has to purchase 64 coss.

Question 4 :

√100 ÷ √25  =  

(A) √2  (B)  2  (C)  4  (D)  10  (E)  1/2

Solution :

  =  √100 ÷ √25

  =  √(100/25)

  =  √4

  =  2

Question 5 :

If x  =  -8, what is the value of (1/2) |4x - 4|?

(A)  -18  (B)  -14  (C)  -8  (D)  14  (D)  14  (E)  18

Solution :

  =  (1/2) |4x - 4|

Applying the value of x in the expression, we get

  =  (1/2) |4(-8) - 4|

  =  (1/2) |-32-4|

  =  (1/2) (36)

  =  18

Hence the answer is 18.

Question 6 :

Triangle NPQ is an equilateral triangle. If its perimeter is 27, what is the length of NP + NQ ?

(A)  16  (B)  18  (C)  4  (D)  32  (E)  0

Solution :

To find the perimeter of the triangle, we have to find the sum of all the sides.

NP + NQ + PQ  =  27

x + x + x  =  27

3x  =  27

x  =  27/3  =  9

NP + PQ  =  9 + 9  =  18

Question 7 : 

If 40% of x is 160, what is x ?

(A)  0.0025  (B)  4  (C)  64  (D)  360  (E)  400

Solution :

40% of x  =  160

(40/100) ⋅ x  =  160

x  =  160 (100/40)

x  =  400

Question 8 :

When d is divided by 7, the remainder is 5, what is the remainder when d + 1 is divided by 7 ?

(A)  0  (B)  1  (C)  4  (D)  5  (E)  6

Solution :

Let d = 12

Here we choose 12, because it is greater than 7, when we divide 12 by 7, we get the remainder 5.

Then d + 1  =  12 + 1  =  13

By dividing this d + 1 by 7, we get 6(5 + 1) as remainder.

Hence the answer is 6.

Note : The number chosen should be 5 more than the multiple of 7.

Question 9 :

In the figure above, O is the center of the square. What is the area of the square ?

(A)  8  (B) 16  (C)  32  (D)  64  (E)  256

Solution :

Side length of square is 8 units.

Area of square  =  a²

  =  8²

  =  64  square units.

Question 10 :

If O is the midpoint of PW, then what is the distance of OE ?

(A)  10  (B)  11  (C)  12  (D)  13  (E)  17

Solution :

P (-13, 0)  W (-3, 0)   

O is the midpoint of PW

  =  (x₁ + x₂)/2, (y₁ + y₂)/2

  =  (-13-3)/2, (0+0)/2

  =  O (-8, 0)

E (3, 0)

OE  =  √(x₂ - x₁)² + (y₂ - y₁)²

OE  =  √(-8-3)² + (0-0)²

OE  =  √(-11)²

   =  11

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