# PSAT MATH WORKSHEET

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  =  4Length of diagonal   =  √(42 + 42)   =  √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

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 (94 - 84) / (92 + 82) ?

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

Solution :

(94 - 84) / (92 + 82)  =  [(92)2 - (82)2] / (92 + 82)

=  [(92 + 82) (92 - 82)] / (92 + 82)

=  92 - 82

=  81 - 64

=  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) + tt  =  1 - (2/3)t  =  (3-2)/3t  =  1/3 Apart from the stuff given above, if you need any other stuff in math,  please use our google custom search here.

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

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6

Featured Categories

Math Word Problems

SAT Math Worksheet

P-SAT Preparation

Math Calculators

Quantitative Aptitude

Transformations

Algebraic Identities

Trig. Identities

SOHCAHTOA

Multiplication Tricks

PEMDAS Rule

Types of Angles

Aptitude Test 