ACT MATH PRACTICE QUESTIONS

Problem 1 :

If x = -2 and y = 3 then find the value of |2x - 3y|.

(A) 13     (B) -13     (C) 15

Solution :

= |2x - 3y|

Applying the values of x and y, we get

= |2(-2) - 3(3)|

= |-4 - 9|

= |-13|

= 13

So, 13 is the answer.

Porblem 2 :

Simplify : (8 + 5) x (35/5) + 6

(A) 169       (B) 50         (C) 97

Solution :

= (8 + 5) x (35/5) + 6

= 13 x 7 + 6

= 91 + 6

= 97

So, option C is correct.

Problem 3 :

Fill in the blank with any suitable digits.

54 _562. This number is divisible by 3. 

(A) 5      (B) 2     (C) 1

Solution :

If the number is divisible by 3, the sum of the digits must be divisible by 3.

Let x be the unknown digit.

= 5 + 4 + x + 5 + 6 + 2

= 22 + x

When we apply x as 2, then we will get the sum as 24 which is divisible by 3. So, option B is correct.

Problem 4 :

The weight of an empty bottle is 128.4 gram. It contains a syrup. The weight of the syrup is 156.8 gram. What is the weight of 24 bottles of syrup?

(A) 6844.8 grams    (B) 2232.5 grams    (C) 7128.7 grams

Solution :

Weight of bottle = 128.4 g

WEight of syrup = 156.8 g

total weight of bottle along with syrup = 128.4+156.8

= 285.2

Weight of 24 bottles = 24 x 285.2

= 6844.8 grams

Problem 5 :

 Factor : 4(a + b)² - 9.

Solution :

= 4(a + b)² - 9

= 2²(a + b)² - 3²

= [2(a + b)]² - 3²

= [2(a + b) + 3] [2(a + b) - 3]

Problem 6 :

Find the median of the data :

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

Solution :

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

To find the median, we have to find the exact middle term of the data set. n = 9

Step 1 :

Arrange the given numbers from smaller to greater.

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

Step 2 :

n = 9 (odd)

Median = (n + 1)/2 th term

= 5th term

= 54 is the median.

Problem 7 :

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

Solution :

Earning = $2400

Savings = 15% of salary

= 0.15 (2400)

= 360

So, his savings is $360.

Problem 8 :

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

Solution :

3x + 2y - 12  =  0

To convert the equation into slope intercept form, we have to convert the equation into the form of y = mx + b

2y = -3x + 12

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

y = (-3/2)x + 6

So, the slope is -3/2.

Problem 9 :

In a cricket team of 11 players, the average age of 4 players is 17,the average of 3 players is 18 and the average of 2 players is 19. The average age of the whole team is 18. One of the players is aged 22. Find the age of the last player.

Solution :

(A) 16 years     (B) 18 years      (C) 20 years

Total number of players = 11

Average of 4 players = 17

Sum of ages of 4 players / 4 = 17

Sum of ages of 4 players = 4(17)

= 68

Sum of ages of 3 players = 3(18)

= 54

Sum of ages of 2 players = 2(19)

= 38

Let x be the age of the last person.

Sum of ages of 4 players + Sum of ages of 3 players + Sum of ages of 2 players + 22 + x = 68 + 54 + 38 + 22 + x

68 + 54 + 38 + 22 + x = 18(11)

182 + x = 198

x = 198 - 182

x = 16

So, the 16 years is the answer, option A.

Problem 10 :

A fritterer spent $4000 in purchasing and transporting apples from kuku valley. He sold half of the stock of apples at a profit of 60% and remaining half of the apples at a profit of 50%. Find the sale price of all apples.

(A) 6200     (B) 1800     (C) 5750

Solution :

Total worth of stock = $4000

Half of the stock = $2000

60% of 2000 = 0.60(2000)

= 1200

Sales price with the profit of 60% = 2000 + 1200

= 3200

50% of 2000 = 0.50(2000)

= 1000

Sales price with the profit of 50% = 2000 + 1000

= 3000

Total sale price = 3200 + 3000

= $6200

Option A is correct.

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