**PSAT Math Practice Questions :**

Here we are going to see some sample questions for PSAT exams. For each and every questions, you will have solutions with step by step explanation.

Each question paper will contain set of 20 questions.

PSAT Math Practice Questions

**Question 11 :**

What is the least possible value of (x^{2} - 1)/x, if x ≥ 1

**Solution :**

To find the least possible value of (x^{2} - 1)/x, we have to simplify

(x^{2} - 1)/x = (x + 1)(x - 1)/x

Since the value of x is greater than or equal to 1, we may apply x = 1.

= (1 + 1) (1 - 1)/2

= 0/2

= 0

**Question 12 :**

What is the maximum number of points in which a circle and triangle can intersect ?

**Solution :**

Let us draw a circle and triangle to intersect each other at maximum points.

From the picture, there are 6 points can intersect both circle and triangle.

**Question 13 :**

What is the area of the shaded region ?

**Solution :**

In order to find the area of shaded region, we have to subtract the areas of two circles from the area of rectangle.

Area of circle = πr^{2}

Radius of larger circle = 3, radius of small circle = 1

Area of shaded region

= Area of rectangle - Areas of circles

= length ⋅ width - [π(3)^{2} + π(1)^{2}]

= 8 ⋅ 6 - π [9 + 1]

= 48 - 10π

**Question 14 :**

There are 45 plastic ducks in a bag. If there are black, green, blue and purple plastic ducks and 1/3 of the plastic ducks are black, 1/5 of the plastic ducks are blue, one third of the number of black plastic ducks are green, then how many purple plastic ducks are in the bag ?

**Solution :**

There are 4 colors of plastic ducks, black, green, blue and purple.

Number of black ducks = (1/3) of 45 = 15

Number of blue ducks = (1/5) of 45 = 9

Number of green ducks = (1/3) of 45 = 15

Number of purple ducks = 45 - (15 + 9 + 15)

= 45 - 39

= 6

Hence the number of purple ducks is 6.

**Question 15 :**

In the figure above, point B is on the line segment DC. IF AB = BC, what is the measure of the angle ABE ?

**Solution :**

Since AB and BC are equal, it forms same angle.

<ABC = 180 - (<BAC + <BCA)

= 180 - (30 + 30)

= 180 - 60

= 120

<DBE + <EBA + <ABC = 180

4x + 2x + 120 = 180

6x = 180 - 120

6x = 60 ==> x = 10

2x = 2(10) = 20°

**Question 16 :**

According to the figure above, what is the value of y?

**Solution :**

Since it is right triangle, we may apply the concept Pythagorean theorem.

30^{2} = 24^{2} + (12+y)^{2}

900 = 576 + (144 + 24y + y^{2})

900 = 720 + 24y + y^{2}

y^{2} + 24y + 720 - 900 = 0

y^{2} + 24y - 180 = 0

y^{2} + 30y - 6y - 180 = 0

y(y + 30) - 6(y + 30) = 0

(y - 6) (y + 30) = 0

y = 6 (or) y = -30

The negative values is not possible. Hence the value of y is 6.

**Question 17 :**

A painter needs 4 gallons of paint to paint each room. If a house has 8 rooms in total, how many quarts of paint is he going to need ?

**Solution :**

1 gallon = 4 quats

A painter needs 4 gallons of paint to paint each room.

Gallons of points needed to paint 8 rooms

= 8(4)

= 32 gallons

quats of paint needed to paint = 32 (4) = 128 quats

**Question 18 :**

A rectangle is inscribed in a circle. The rectangle is tangent at the points A, B, C and D. If the diagonal of the rectangle is 20 inches long. What is the area of the circle ?

**Solution :**

AC is the diameter of the circle, then radius of the circle

= 10 inches

Area of circle = πr^{2}

= π(10)^{2}

= 100π

**Question 19 :**

The prices in the table given below show the different types of gas offered at a gas station and the prices of gas per gallon. If Emily has $50, what is the least amount of gas, in gallons, she can purchase subtracted from the greatest amount of gas, in gallons, she can purchase ?

**Solution :**

Number of gallons of gas filled by choosing unloaded gas

= 50/2.50

= 20 gallons

Number of gallons of gas filled by choosing regular gas

= 50/2

= 25 gallons

= 25 - 20

Required number of gallons = 5 gallons

**Question 20 :**

3[9 ÷ (-3)] + [-3 - (-8)] =

**Solution :**

= 3[9 ÷ (-3)] + [-3 - (-8)]

= 3(-3) + (-3 + 8)

= -9 + 5

= -4

Hence the answer is -4.

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