**PSAT Math Questions For Practice :**

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 Questions For Practice

**Question 1 :**

[(2/3) + (1/4)] ÷ 2 =

**Solution :**

** = [(2/3) + (1/4)] ÷ 2**

** = [(2/3) **⋅ (4/4)** + (1/4) **⋅ (3/3)**] ÷ 2**

** = [(8/12) ****+ (3/12)****] ÷ 2**

** = [(8 + 3)/12****] ÷ 2**

** = (11/12)**** ÷ (2/1)**

** = (11/12) **⋅ (1/2)

= 11/24

Hence the answer is 11/24.

**Question 2 :**

Michelle bought a dress that costs $103.00, a pair of shoes that costs $73.00 and a bag that costs $111.00. There is a 7% sales tax on all items priced at $90.00 and higher. There is no sales tax on items under $90.00. How much did Michelle spend on the following items, including tax ?

**Solution :**

Michelle bought three items.

A dress costs = $103.00

A pair of shoes costs = $73.00

A bag costs = $111.00

The cost of dress and bag are more than $90. So, we have to pay sales tax for those items.

Sales tax = 7%

107% of cost of dress = 1.07 (103.00) = 110.21

107% of cost of bag = 1.07(111.00) = 118.77

cost of shoes = 73

Total cost = 110.21 + 118.77 + 73

= 301.98

**Question 3 :**

How many terms are in the sequence 0, 3, 6.............57, 60?

**Solution :**

a = 3, d = 3 - 0 ==> 3 and l = 60

Total number of terms :

n = [(l - a)/d] + 1

n = [(60 - 3)/3] + 1

n = (57/3) + 1

n = 19 + 1

n = 20

**Question 4 :**

The larger of two consecutive even integers is two times the smaller. What is their sum ?

**Solution :**

Let "x" be a even number

Consecutive even number = x + 2

x + 2 = 2x

2x - x = 2

x = 2

So, the two even numbers are 2 and 4.

Their sum = 2 + 4 = 6

(A) 2 (B) 3 (C) 4 (D) 6 (E) 8

**Question 5 :**

3^{x} = 27 ^{a+b }and (a^{2} - b^{2}) /(a-b) = 5, what is x ?

**Solution :**

First, let us simplify (a^{2} - b^{2}) /(a-b)

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

5 = (a + b)

So, the value of a + b is 5.

3^{x} = 27^{5 }

3^{x} = (3^{3})^{5 }

3^{x} = 3^{15}

Hence the value of x is 15.

**Question 6 :**

In Mr.Farmer's class there are 30 kids. If there are twice as many boys as there are girls in the English club, then what percentage of the English club are boys ?

**Solution :**

Let "x" be the number of girls in English club

"2x" be the number of boys

x + 2x = 30

3x = 30

x = 10

2x = 20

20 = What percentage of 30 ?

20 = p% of 30

20 = (p/100) 30

20 ⋅ (10/3) = p

p = 66.6%

**Question 7 :**

a⊗b = a^{3}-3a^{2}b + 3ab^{2} - b^{3 }and a ⊕b = (a-b)(a+b), what is a⊗b/a ⊕b

**Solution :**

a⊗b = a^{3}-3a^{2}b + 3ab^{2} - b^{3 } = (a - b)^{3}

a ⊕ b = (a-b)(a-b) = (a-b)^{2}

a⊗b/a⊕b = (a - b)^{3}/ (a-b)^{2}

= (a - b)

**Question 8 :**

What is the prime factorization of 752 ?

**Solution :**

752 = 2^{4} ⋅ 47

**Question 9 :**

If x can be any integer, what is least possible value of the expression 4x^{2} - 10 ?

**Solution :**

By applying any negative value for x, we get positive value for 4x^{2}

The least value may appear, when x = 0

= 4(0)^{2} - 10

= -10

Hence the answer is -10.

**Question 10 :**

There are a total of 5 bicycles and tricycles in a park. There are 12 wheels.How many tricycles are there ?

**Solution :**

Let us use the concept system of equations to solve this problem.

Number of cycles = 5

Let "x" be the number of bicycles

Let "y" be the number of tricycles.

x + y = 5 -----(1)

2x + 3y = 12 -----(2)

(1) ⋅ 2 ==> 2x + 2y = 10

(1) - (2)

2x + 2y - (2x + 3y) = 10 - 12

-y = -2

y = 2

There are two tricycles, hence 6 wheels in two tricycles.

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