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.
Question 11 :
What is the least possible value of (x2 - 1)/x, if x ≥ 1
(A) -1 (B) 0 (C) 3 (D) 3/4 (E) 2/3
To find the least possible value of (x2 - 1)/x, we have to simplify
(x2 - 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
Hence the least possible value for x is 0.
Question 12 :
What is the maximum number of points in which a circle and triangle can intersect ?
(A) 3 (B) 5 (C) 6 (D) 8 (E) ∞
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 ?
(A) 48 - 10π (B) 64 - 22π (C) 10π
(D) 48 - 6π (E) 16π
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 = πr2
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 ?
(A) 6 (B) 15 (C) 16 (D) 21 (E) 39
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 15 = 5
Number of purple ducks = 45 - (15 + 9 + 5)
= 45 - 29
Hence the number of purple ducks is 16.
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 ?
(A) 20° (B) 40° (C) 80° (D) 90° (E) 100°
Since AB and BC are equal, it forms same angle.
<ABC = 180 - (<BAC + <BCA)
= 180 - (30 + 30)
= 180 - 60
<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 ?
(A) 3 (B) 6 (C) 12 (D) 15 (E) 18
Since it is right triangle, we may apply the concept Pythagorean theorem.
302 = 242 + (12+y)2
900 = 576 + (144 + 24y + y2)
900 = 720 + 24y + y2
y2 + 24y + 720 - 900 = 0
y2 + 24y - 180 = 0
y2 + 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 ?
(A) 12 (B) 32 (C) 128 (D) 200 (E) 512
A painter needs 4 gallons of paint to paint each room.
Number of gallons of points needed to paint 8 rooms
= 32 gallons
1 gallon = 4 quats
Number of 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 ?
(A) 10π (B) 15π (C) 20π (D) 100π (E) 400π
AC is the diameter of the circle, then radius of the circle
= 10 inches
Area of circle = πr2
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 ?
(A) 2 gallons (B) 3 gallons (C) 5 gallons
(D) 20 gallons (E) 25 gallons
Number of gallons of gas filled by choosing unloaded gas
= 20 gallons
Number of gallons of gas filled by choosing regular gas
= 25 gallons
= 25 - 20
Required number of gallons = 5 gallons
Question 20 :
3[9 ÷ (-3)] + [-3 - (-8)] =
(A) -20 (B) -4 (C) -2 (D) 2 (E) 14
= 3[9 ÷ (-3)] + [-3 - (-8)]
= 3(-3) + (-3 + 8)
= -9 + 5
Hence the answer is -4.
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