SCAT ADVANCED MATH WORKSHEET

Question 1 :

A population of 42 fruit flies has increased by 150%. What is the total number of fruit flies after the increase?

(A) 57    (B) 63    (C) 105    (D) 192

Solution :

42 fruit flies  =  100%

100 + 150  ==>  250 %

=  250% of 42

=  2.5(42)

=  105

Question 2 :

Linda is performing an experiment using a random number generator. For each trial, the computer selects a whole number from 1 to 10. What is the probability that the whole numbers selected on the first two trials are both greater than 4?

(A) 1/10    (B) 9/25    (C) 3/5   (D) 7/10

Solution :

Sample space  =  {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

n(S)  =  10

Let A be the event of selecting a number greater than 4.

A  =  {5, ,6 ,7, 8, 9, 10}

n(A)  =  6

P(A)  =  n(A)/n(S)

P(A)  =  6/10  ==>  3/5

P(selecting number greater than 4 in two trails) 

=  (3/5) x (3/5)

=  9/25

So, the required probability is 9/25.

Question 3 :

The pattern shown can be folded into a polyhedron.

Which polyhedron would result from correctly folding the pattern?

Solution :

By observing the given net diagram, there is six faces. So the correct answer is C.

Question 4 :

A teacher awards test points according to the pattern shown in the table.

A student scored 128 points. How many correct answers did he provide? 

(A) 7    (B) 16    (C) 32    (D) 64

Solution :

128  =  2 x 2 x 2 x 2 x 2 x 2 x 2

128  =  2⁷

So, number of correct answers provided by him is 7.

Question 5 :

The large cube shown was built using smaller cubes.

How many small cubes were used to build the large cube?

(A) 32    (B) 48    (C) 64    (D) 96

Solution :

L  =  4 units, breadth  =  4 units and height  =  4 units.

Volume of cube  =  4 x 4 x 4

=  64 cubes.

So, 64 cubes are needed to make the given large cube.

Question 6 :

The swim team buys sweatshirts for $12.00 each, with an additional 5% sales tax added per shirt. A standard shipping fee is added to each order of sweatshirts. The table gives the total cost, including the shipping fee, for four separate orders.

What is the shipping charge per order?

(A) $4.00    (B) $4.60    (C) $12.00    (D) $12.60

Solution :

Cost price of 1 sweat shirt  =  $12.00

From the table, price of 1 sweat shirt  =  $16.60

cost price + 5% tax + shipping fee  =  16.60

5% tax + shipping fee  =  16.60- 12.00

=  4.60

5% of 12 + shipping fee  =  4.60

0.60 + shipping fee  =  4.60

shipping fee  =  4.60-0.60

=  $4.00

Question 7 :

On Monday, a student tells a secret to 3 people. On Tuesday, each of the 3 friends tells the secret to 3 different people, who in turn each tell the secret to 3 different people. The secret is repeated in the same pattern until Sunday. Which expression represents the number of people who will know the secret by the end of the day on Sunday?

(A) 1 + 3⁶

(B) 1 + 3⁷

(C) 3 + 3² + 3³ + 3⁴ + 3⁵ + 3⁶ + 3⁷

(D) 1 + 3 + 3² + 3³ + 3⁴ + 3⁵ + 3⁶ + 3⁷

Solution :

On Monday a student tells a secret to 3 people. So, number of student knows the truth on Monday 

=  4 that is (1+3)

On Tuesday, each of the 3 friends tells the secret to 3 different people.

So, number of student knows the truth on Tuesday  =  3² 

Number of student who knows the secret up to Sunday is

1 + 3 + 3² + 3³ + 3⁴ + 3⁵ + 3⁶ + 3⁷

Question 8 :

Elida scored an average of 10 points in each of the 5 rounds of a game. If her highest score was 18 and the range of her scores was 12, what was her lowest score?

(A) 2    (B) 5    (C) 6    (D) 7

Solution :

Range  =  Large value - Small value

L  =  18, R  =  12 

12  =  18 - Small value

Small value  =  18-12

Small value  =  6

Question 9 :

The students in Mr. Byrd’s class checked the hourly temperatures in their schoolyard and displayed the results on the graph shown.

What was the difference between the highest and lowest temperatures recorded?

(A) 8°    (B) 12°    (C) 22°    (D) 24°

Solution :

Highest temperature  =  80°, lowest temperature  =  58°

Difference  =  80-58

=  22°

Question 10 :

If P = 2 × (L + W), what is P when L is 18 inches and W is 10 inches? 

(A) 28 inches    (B) 36 inches

(C) 46 inches    (D) 56 inches

Solution :

P  =  2 × (L + W)

P  =  2 × (18+10)

P  =  2 × (28)

P  =  56 inches

Question 11 :

A very hungry goat can eat 10 square feet of grass in three minutes. How long will it take the goat to eat all of the grass in the diagram below ?

A) 1,000 minutes    B) 300 minutes     C) 30 minutes

D) 100 minutes

Solution :

Find the area of the rectangle :

Area = length x width

= 50 x 20

= 1000 square feet

Every 10 square feet can graze in every 3 minutes

Finding number of 10 square feet in 1000.

= 1000/10

= 100

Time taken to graze it completely = 100 x 3

= 300 minutes

Question 12 :

What is the mean for the following number set?

13, 5, 22, 19, 7, 8, 14, 42

A) 16.25   B) 15     C) 17.75    D) 15.5

Solution :

Mean is the average,

mean = sum of all numbers / total number of terms

= (13 + 5 + 22 + 19 + 7 + 8 + 14 + 42)/8

= 130/8

= 16.25

so, option A is correct.

Question 13 :

The correct expanded form of forty-five thousand four hundred and fifty-nine will be ___________.

a. 40,000 + 5,000 + 40 + 59  b. 45,000 + 400 + 50 + 9

c. 45,000 + 5,000 + 400 + 50 + 9

d. 40,000 + 5,000 + 400 + 50 + 9

Solution :

Converting forty-five thousand four hundred and fifty-nine into number, we get

= 45, 459

Writing in expanded form, we get

=  4 x 10,000 + 5 x 1000 + 4 x 100 + 5 x 10 + 9 x 1

=  40,000 + 5,000 + 400 + 50 + 9

So, option d is the correct answer.

Question 14 :

Amy's monthly income is 36,000 cents. Two-thirds of it is used for paying house rent and one-fourth is used for household expenditure. How much money is left with him?

a) 3,000 cents   b) 3,500 cents   c) 4,000 cents

d) 5,000 cents

Solution :

Monthly income = 36000 cents

Amount spent for rent = 2/3

Amount spent for household expenditure = 1/4

Amount remaining = 1 - [(2/3) + (1/4)]

= 1 - [(8 + 3)/12]

= (12 - 11)/12

= 1/12

So, 1/12 of the money is remaining 

Remaining amount = 1/12 of 36000

= (1/12) x 36000

= 3000 cents

So, option a is correct.

Question 15 :

Which of the following correctly represents all the factors of 64?

a) 1, 2, 3, 4, 8, 16, 64   b) 1, 2, 4, 8, 16, 64

c) 1, 2, 4, 8, 16, 32, 64    d) 1, 2, 3, 4, 16, 32, 64

Solution :

Factors of 64

Every number and 1 are factors of number itself. Since it is even number it is divisible by 2. Sum of the digits is not multiple of 3, then it is not divisible by 3.

1, 2, 4, 8, 16, 32 and 64 are factors of 64.

Question 16 :

Seren bought 5 kg of fruit. His neighbour borrowed three-fifths of the fruits from him. What amount of fruit was borrowed? 

a) 2 kg 500 g   b) 3 kg   c) 3 kg 250 g    d) 3 kg 500 g

Solution :

Quantity of fruit Seren bought = 5 kg

Quantity of fruit his neighbour borrowed = 3/5 of 5 kg

= 3/5 x 5

= 3 kg

So, 3 kg fruit is borrowed by his neighbour.

Question 17 :

Sam's mother gave her 100 cents for the school canteen. She spent one-fifth of the amount in buying a burger and one-fourth of the amount in buying a Coke can. How much money is left with her?

a) 35 cents     b) 45 cents      c) 55 cents        d) 65 cents

Solution :

Amount gave by Sam's mother = 100 cents

Amount spent for burger = 1/5

amount spent for cake = 1/4

Part of the amount left over = 1 - [(1/5) + (1/4)]

= 1 - [(4 + 5)/20]

= 1 - 9/20

= 11/20

Finding 11/20 of 100

= (11/20) x 100

= 11 (5)

= 55 cents

So, option c is correct.

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