**PSAT Math Worksheet :**

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

**Question 1 :**

The circle that is inscribed in the square below has a radius of 2. What is the length of diagonal of the square ?

(A) 2 (B) 4 (C) 16 (D) 4√2 (E) 2√2

**Solution :**

Side length of square = 4 Length of diagonal = √(4 = √32 = 4√2 |

**Question 2 :**

What is the absolute value of the difference between the number of integers between 0 and 5 inclusive and the number of integers between 1 and 6 exclusive ?

(A) 0 (B) 1 (C) 2 (D) 3 (E) 5

**Solution :**

Integers between 0 and 5 inclusive.

0, 1, 2, 3, 4, 5

There are 6 integers.

Integers between 1 and 6 exclusive.

2, 3, 4, 5

There are 4 integers.

Then,

= |6 - 4|

= 2 integers.

**Question 3 :**

Corey is walking on a path. Every three steps he takes, he makes a 30 degree rotation to counterclockwise, if he took 18 steps in total, how many full revolutions was he able to make altogether ?

(A) 0.25 (B) 0.5 (C) 1 (D) 2 (E) 5

**Solution :**

For every 3 steps, he takes 30 degree rotation. First let us find, how many 3 steps are in 18 steps.

= 18/3

= 6 times

In 6 times, he completes 180 degree.

So, he completes half of the rotation.The answer is 0.5.

**Question 4 :**

What is 20% of 20% of 20 ?

(A) 0.2 (B) 0.8 (C) 2 (D) 8 (E) 8000

**Solution :**

= 20 % of 20% of 20

= 20% of (20/100) x 20

= 20% of (400/100)

= 20% of 4

= (20/100) 4

= 0.8

**Question 5 :**

What is the difference between the largest and lowest integer in the sequence of consecutive odd integers whose sum is 15 ?

(A) 2 (B) 4 (C) 5 (D) 9 (E) 12

**Solution :**

Let us select three numbers 3, 5 and 7.

3 + 5 + 7 = 15

Difference between largest and lowest integer

= 7 - 3

= 4

Hence the answer is 4.

**Question 6 :**

The half life of a substance is the time it takes for a substance to decrease to half its initial amount. If John initially had 100 pounds of goo and ten days later, he only had 25 pounds of goo, what is the half life of the goo ?

(A) 10 days (B) 5 days (C) 7.5 days

(D) 20 days (E) 25 days

**Solution :**

In 10 days, the goo decreased by 2 half lives. So each life is 5 days.

**Question 7 :**

What is the value of (9^{4} - 8^{4}) / (9^{2} + 8^{2}) ?

(A) 1 (B) 16 (C) 17 (D) 18 (E) 155

**Solution :**

(9^{4} - 8^{4}) / (9^{2} + 8^{2}) = [(9^{2})^{2} - (8^{2})^{2}] / (9^{2} + 8^{2})

= [(9^{2} + 8^{2}) (9^{2} - 8^{2})] / (9^{2} + 8^{2})

= 9^{2} - 8^{2}

= 81 - 64

= 17

Hence the answer is 17.

**Question 8 :**

Jack fills a jug with water continuously. It takes him 2 minutes to fill up 50% of the empty space in the jug with water. After every 2 minutes, he puts a penny into a jar to celebrate. How many pennies will he have in the jar at the instant the jug has less than 30% empty space left ?

(A) 0 (B) 1 (C) 2 (D) 3 (E) 4

**Solution :**

At the first round, he fills 50% of empty space in the jug in 2 minutes and drop a penny.Now the jug contains 50% of empty space.

If he fills half of the 50% of empty space at that instant, the quantity of water will become 75%. But there will be 25% of empty space. Hence the condition will not satisfy, by filling water in the second round.

So, there is only 1 penny in the jar at the instant the jug has lesser than 30% of empty space.

**Question 9 :**

In the figure above, there are two balance beams that have triangles, circles and squares on them. Both beams are fully balanced. How many circles are needed to balance 70 squares ?

(A) 10 (B) 12 (C) 35 (D) 70 (E) 140

**Solution :**

From the above picture, we know that

1 square = 2 triangles ---(1)

4 triangles = 2 circles ----(2)

Divide by 2 on both sides

2 triangles = 1 circle -----(3)

(1) = (3)

1 square = 1 circle

70 squares = 70 circles.

So, 70 circles are needed to balance 70 squares.

**Question 10 :**

0.7 bar + (2/9) = 0.6 bar + ____

(A) 1/2 (B) 1/3 (C) 2/9 (D) 4/9 (E) 1

**Solution :**

**Let "x" be 0.7 bar**

**x = 0.77777........ ---(1)**

**Multiply both sides by 10x = 7.7777.......****---(2)**

**(2) - (1)**

10x - x = **7.7777....... - 0****.7777.......**

**9x = 7**

**x = 7/9**

**Let "y" be 0.6 bar**

**y = 0.66666........ ---(1)**

**Multiply both sides by 10y = 6.6666.......****---(2)**

**(2) - (1)**

10y - y = 6**.6666....... - 0****.6666.......**

**9y = 6**

**y = 6/9 = 2/3**

L.H.S : 7/9 + 2/9 = (7 + 2)/9 = 9/9 = 1 |
R.H.S : Let "t" be the missing value, which makes L.H.S and R.H.S equal. 1 = (2/3) + t t = 1 - (2/3) t = (3-2)/3 t = 1/3 |

Hence the answer is 1/3.

If you would like to have more questions on PSAT math, please click on the links given below.

**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**

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

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

HTML Comment Box 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**