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Question 1 :

Factorize

4(a+b)² - 9

Solution :

To factorize this we can write the given question in the form of square.

=  4(a+b)² - 9

=  2² (a+b)² - 3²

=  [2 (a + b)]² - 3²

a² - b²  =  (a+b) (a-b)

=  (2(a+b)+3) (2(a+b)-3)

Question 2 :

Find the median of the data

78, 56, 22, 34, 45, 54, 39, 68, 54, 84.

Solution :

To find the median first we have to arrange the numbers in ascending order. Arranging the data in the ascending order we get 

22, 34, 39, 45, 54, 54, 56, 68, 78, 84.

Here the total number of terms (n)  =  10, and even number

Median  =  [(n/2)^th term + ((n/2)+ 1)^th term]/2

n  =  10

=  [(10/2)^th term + ((10/2)+ 1)^th term]/2

=  (5^th term + 6^th term]/2

need to select the numbers from the ascending order.

5^th term  =  54 and 6^th term  =  54

=  (54 + 54)/2

=  108/2

=  54

Therefore the median is 54.

Question 3 :

A person earns $ 2,400 per month. He saves 15% of his salary. How much does he save?

Solution :

Earning of a person  =  $ 2,400

Since he is saving 15% of his salary.

His saving amount  =  15% of 2400

=  (15/100) x 2400

=  15 x 24

=  $360

So he is saving $ 360 per month.

Question 4 :

Find the slope of line 3x + 2y - 12  =  0.

Solution :

Slope (m)  =  -coefficient of x/coefficient of y

From the given equation the coefficient of x is 3 and the coefficient of y is 2.

m  =  -3/2

Therefore the required slope is -3/2.

Question 5 :

Seth has 4 plaid shirts and 5 solid-colored shirts hanging together in a closet. In his haste to get ready for work, he randomly grabs 1 of these 9 shirts. What is the probability that the shirt Seth grabs is plaid?

F. 1/5     G. 1/4     H. 4/9     J. 1/9      K. 4/5

Solution :

Total number of shirts = 4 plaid + 5 solid colored

= 9 shirts

Number of plaid shirts = 4

Required probability = 4/9

So, option H is correct.

Question 6 :

What is the slope of any line parallel to the line

2x −3y =7 ?

F. −3    G. −2/3        H. 2/3       J. 2      K. 3

Solution :

The lines will have slope if the lines are parallel.

2x - 3y = 7

3y = 2x - 7

y = (2/3) x - (7/3

Comparing with y = mx + b

Slope (m) = 2/3

Slope of the parallel line = 2/3

So, option H is correct.

Question 7 :

Andrew won a cash prize on a game show. Andrew paid taxes of 30% on the original cash prize and had $28,000 remaining. How much was the original cash prize?

A. $19,600 B. $28,300 C. $36,400 D. $40,000 E. $84,000

Solution :

Let x be the value of original cash prize.

70% of x = 28000

x = 28000/0.70

x = 40000

So, the worth of original prize is $40000.

Question 8 :

Melissa had 3 fewer apples than Marcia. Then, she gave 2 apples to Marcia. Now how many fewer apples does Melissa have than Marcia?

F. 0      G. 2      H. 3     J. 5      K. 7

Solution :

Let x be the number of apples Marcia has.

Number of apples Mellisa has = x - 3

After giving 2 apples to Marcia, then number of apples Mellisa has = x - 3 - 2

= x - 5

Now Marcia has x + 2 apples

Fewer number of apples Mellisa has = x + 2 - (x - 5)

= x + 2 - x + 5

= 7 apples

So, option K is correct.

Question 9 :

What is the 217th digit after the decimal point in the repeating decimal 0.3456........?

A. 0     B. 3     C. 4    D. 5    E. 6

Solution :

The given repeating decimal is 0.3456........

Here, the number of digits repeating is 4. To find the 217th digit of this repeating digits, we have to divide 217 by 4 and get the remainder. Then, we get 54 as quotient and 1 as remainder.

Here 54 means, this many times 3456 is repeating as a set. The corresponding digit of 1 is 3. So, option B is correct.

Question 10 :

The perimeter of a square is 48 centimeters. What is its area, in square centimeters?

F. 12      G. 96     H. 144     J. 192    K. 2,304

Solution :

Perimeter of square = 48

4(side length) = 48

Side length of square = 48/4

= 12

Area of square = side x side

= 12 x 12

= 144 square centimeters

Question 11 :

What is the product of the 2 solutions of the equation

x² +3x −21 =0?

A. −63     B. −21     C. −20    D. 20     E. 21

Solution :

Let a and b are the roots of the quadratic polynomial. Then

Sum of roots a + b = -Coefficient of x/coefficient of x²

Product of roots a b = Constant/coefficient of x²

Product of roots = -21/1

= -21

So, option B is correct.

Question 12 :

Which of the following expressions is a polynomial factor of a¹⁶ − 16?

F. a⁴ −4     G. a⁴ +4     H. a⁴ +2    J. a+2    K. a−2

Solution :

= a¹⁶ − 16

= (a⁸)² − 4²

Looks like a² − b² = (a + b)(a - b)

= (a⁸ + 4)(a⁸ - 4)

= (a⁸ + 4) ((a⁴)² - 2² )

= (a⁸ + 4) (a⁴ + 2) (a⁴ - 2)

So, option H is correct.

Question 13 :

When n = 1/4, what is the value of (2n − 5) / n ?

A. 18     B. 9     C. −3     D. −9     E. −18

Solution :

When n = 1/4

(2n − 5) / n

= [2(1/4) - 5]/(1/4)

= (1/2 - 5) / (1/4)

= (-9/2) / (1/4)

= -9/2 x (4/1)

= -9(2)

= -18

So, option E is correct.

Question 14 :

A proof reader can read 40 pages in one hour. How many pages can this proofreader read in 90 minutes?

F. 45     G. 60     H. 150     J. 360

Solution :

Number of pages read in one hour = 40

60 minutes = 40

1 minute = 40/60

= 2/3

Number of pages read in 90 minutes

= 90 x (2/3)

= 30(2)

= 60

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