# PSAT MATH QUESTIONS PRACTICE

Question 1 :

Given that 0 < x < 1, and set A = {x, x2, x3, x4}, what is the smallest value in set A ?

(A)  x  (B)  x2  (C)  x3  (D)  x

(E)  cannot be determined

Solution :

Let  x = 0.5

x2  =  0.25

x3  =  0.125

x4  =  0.0625

When the power is being increased, the answer get decreased. Hence the smallest value of the given set is x4

Question 2 :

Sammy has a faulty clock. Every 15 degrees that one of the hands moves, 5 minutes passes. If a hand is initially 5 : 35 PM, in how long will be the hand be at that same position ?

(A)  65  minutes  (B)  2 hours  (C)  1 hour

(D)  45 minutes   (E)  1 hour and 15 minutes

Solution :

There are 360 degree that the hands must move to complete a full revolution and to be at the same time of 5 :35, if every 15 degree, 5 minutes passes, then (24 ⋅5) minutes will have passed by the time it is 5 : 35 again. This is 2 hours.

Question 3 :

If (x - 2) (x + 2)  =  ax2 + bx + c, what is the sum of a, b and c ?

(A)  -4  (B)  -3  (C)  0  (D)  1  (E)  5

Solution :

ax2 + bx + c  =  (x - 2)(x + 2)

=  x2 - 2x + 2x - 4

=  x2 - 0x - 4

a = 1, b = 0 and c = -4

a + b + c = 1 + 0 + (-4)

a + b + c  =  -3

Question 4 :

Natalie walks in a special way. After every 2 steps she takes, she takes 1 step in the opposite direction. She starts at point A and walks forward. When she is 7 steps away from the point A, she has reached her destination point B. How many steps in total did she take to get from point A to B.

(A)  7  (B)  8  (C)  17  (D)  15  (E)  18

Solution : When she takes two steps forward, she has to go 1 step back ward.

From the picture given above, she has taken 3 steps.

 1st time landing in step 2 and going back to step 1 3 steps taken. 2nd time landing in step 3 and going back to step 2 6 steps taken. 3rd time landing in step 4 and going back to step 3 9 steps taken. 4th time landing in step 5 and going back to step 4 12 steps taken. 5th time landing in step 6 and going back to step 5 15 steps taken. 6th time landing in step 7, reached destination 17 steps taken.

Question 5 :

If Cmn  =  C(m + n), for what value of n is Cmn neither positive nor negative ?

(A)  -C  (B)  -m  (C)  2m  (D)  0  (E)  1/m

Solution :

We must pick value of n that makes the expression O, since O neither positive nor negative. This occurs when n is the negative of m.

Hence the value of n is -m.

Question 6 :

Two sides of a triangle at 6 and 8. What is the length of the third side ?

(A)  2  (B)  4  (C)  5  (D)  10  (E)  Cannot be determined

Solution :

The sum of length of 2 sides will be greater than the other side. But we could not say the exact length of third side.

Hence, we cannot determine.

Question 7 :

2 + (1/3)  =  14/b, what is b ?

(A)  3  (B)  6  (C)  7  (D)  9  (E)  28

Solution :

2 + (1/3)  =  14/b

(6 + 1)/3  =  14/b

7/3  =  14/b

b  =  14 (3)/7

b  =  6

Question 8 :

The radius of circle A is x and the radius of circle B is 2. If the circumference of circle A is two times the circumference of the circle B, find the value of x.

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

Solution :

2πx  =  2[2π(2)]

2πx  =  2(4π)

2πx  =  8π

Divide each side by 2π.

x  =  4

Question 9 :

In the formula V = r2h, if h is doubled and r is tripled, then V is multiplied by ?

(A)  6  (B)  9  (C)  12  (D)  18  (E)  36

Solution :

h = 2h, r = 3r

V = r2h

V = (3r)2(2h)

V = 9r2(2h)

V = 18r2h

Question 10 :

Max A returns the largest value in the set A, min A returns the lowest value in the set A. For example, max {1, 2, 3} = 3 and min {0, 4, 5} = 0. What is max {min{x, 2x, 3x}, max{x/2, x/4,x/8}} ?

(A)  x   (B)  2x  (C)  x/2  (D)  3x

(E)  cannot be determined.

Solution :

The answer cannot be uniquely determined, since we do not know if x is negative or positive. Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

You can also visit the following web pages on different stuff in math.

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