**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.

**Question 1 :**

[(2/3) + (1/4)] ÷ 2 =

(A) 22/12 (B) 1/12 (C) 11/24 (D) 1/3 (E) 12

**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 ?

(A) $287.00 (B) 266.00 (C) 295.47

(D) 300.60 (E) $301.98

**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 ?

(A) 20 (B) 21 (C) 23 (D) 30 (E) 60

**Solution :**

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

Total number of terms :

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

n = [(60 - 0)/3] + 1

n = (60/3) + 1

n = 20 + 1

n = 21

**Question 4 :**

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

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

**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

**Question 5 :**

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

(A) 6 (B) 9 (C) 12 (D) 15 (E) 27

**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 ?

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

**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 (number of boys)

Percentage of boys = (20/30) ⋅ 100

= 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)

(A) a^{2} + b^{2} (B) a - b (C) a^{2} + 3b^{2} + 3ab

(D) a^{2} - b^{2} (E) b^{2} + 3a

**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 ?

(A) 2^{3 }⋅ 48 (B) 2^{3 }⋅ 49 (C) 3^{3 }⋅ 49

(D) 2^{4 }⋅ 47 (E) 3^{4 }⋅ 47

**Solution :**

752 = 2^{4} ⋅ 47

**Question 9 :**

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

(A) -10 (B) -4 (C) 4 (D) 10 (E) ∞

**Solution :**

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

The least value may appear, when x = 0

= 4(0)^{2} - 10

= -10

Hence the answer is -10.

**Question 10 :**

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

(A) 2 (B) 3 (C) 6 (D) 7 (E) 8

**Solution :**

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

Total number of vehicles = 5

Let x be the number of bicycles

Let y be the number of tricycles.

Each bicycle will have 2 wheels and tricycle will have 3 wheels.

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 (Number of tricycles)

So, there are two tricycles.

**PSAT MATH ONLINE WORKSHEETS**

**PSAT online practice test math - Paper 1**

**PSAT online practice test math - Paper 2**

**PSAT online practice test math - Paper 3**

**PSAT online practice test math - Paper 4**

**PSAT online practice test math - Paper 5**

**PSAT online practice test math - Paper 6**

**PSAT online practice test math - Paper 7**

**PSAT online practice test math - Paper 8**

**PSAT online practice test math - Paper 9**

**PSAT online practice test math - Paper 10**

**PSAT online practice test math - Paper 11**

After having gone through the stuff given above, we hope that the students would have understood, how to solve questions in PSAT math.

Apart from the stuff given above, if you want to know more about , please use our google custom search here.

Widget is loading comments...

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

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**