SAT MATH QUESTIONS WITH ANSWERS - 6

Question 1 :

Stephen wins the lottery and decides to donate 30% of his winnings to charity. Then he decides to give 20% of what he has left to his mother. What percent of his winnings does Stephen have for left for himself?

(A)  67%

(B)  56%

(C)  54%

(D)  50%

Answer :

Let $100 be won by Stephen in lottery.

Given : 30% of the winnings is donated to charity.

Amount of money donated to charity :

= 30% of $100

= 0.3 ⋅ $100

= $30

Given : After donated to charity, Stephen gives 20% of what he has left to his mother.

Amount of money given to Stephen's mother :

= 20% of ($100 - $30)

= 0.2 ⋅ $70

= $14

Amount of money Stephen has left for himself :

= $100 - ($30 + $14)

= $100 - $44

= $56

$56 is 56% of the winnings $100.

Stephen has left 56% of the winnings for himself.

Therefore, the correct answer is option (B).

Question 2 :

If x³ = y, then what is the difference between x⁶ and x³ in terms y?

(A)  y³

(B)  y²

(C)  y(y - 1)

(D)  2y - y

Answer :

x⁶ - x³ = (x³)² - x³

x⁶ - x³ = y² - y

x⁶ - x³ = y(y - 1)

Therefore, the correct answer is option (C).

Question 3 :

What is the sum of the measures of the marked angles in the figure above?

(A)  1080°

(B)  900°

(C)  720°

(D)  540°

Answer :

When know that the sum of the three interior angles of any type triangle is equal to 180°.

The easisest way to handle this problem is to assume the given triangle as equilateral triangle. 

Sum of the measures of the marked angles :

= 3(120° + 60° + 120°)

= 3(300°)

= 900°

Therefore, the correct answer is option (B).

Question 4 :

If 2x + 3y = 11, what is the value of 4^x8^y?

(A)  2¹⁵

(B)  2¹¹

(C)  2⁹

(D)  2⁸

Answer :

= 4^x8^y 

= (2²)^x(2³)^y

= (2^2x)(2^3y)

= 2^{2x + 3y}

= 2¹¹

Therefore, the correct answer is option (B).

Question 5 :

If x > 4, which of the following is equivalent to the above expression?

Answer :

Therefore, the correct answer is option (A).

Question 6 :

In a certain office, there are c chairs and d desks, and e employees. Five desks are not occupied and all other desks are occupied by exactly one employee. All but two of the employees have two chairs at their desks, and all other desks, whether they are occupied or not, have one chair. If e > 2, then which of the following expression is equal to c?

(A)  2(d - 5) + e

(B)  2(d - e)

(C)  2(d - 2)

(D)  2e + 3

Solution :

number of chairs = c

number of desks = d

number of employees = e

Given : Five desks are not occupied and all other desks are occupied by exactly one employee.

So, there are 5 more desks than employees.

d = e + 5

Given : All but two of the employees have two chairs at their desks, and all other desks, whether they are occupied or not, have one chair .

c = d + (e - 2)

Substitute d = e + 5.

c = e + 5 + (e - 2)

c = e + 5 + e - 2

c = 2e + 3

Therefore, the corrrect answer is option (D).

Question 7 :

Shira keeps both dogs and cats as pets; she has 7 pets in total. A dog eats 4 pounds of food per day and a cat eats 1 pound of food per day. If Shira uses 16 pounds of food per day to feed her pets, how many dogs does she have? 

(A)  2

(B)  3

(C)  4

(D)  5

Solution :

Let d be the number of dogs and c be the number of cats.

Given : The total number of pets is 7.

d + c = 7

c = 7 - d

Given : A dog eats 4 pounds of food per day and a cat eats 1 pound of food per day and Shira uses 16 pounds of food per day to feed her pets.

4d + c = 16

Substitute c = 7 - d.

4d + (7 - d) = 16

4d + 7 - d = 16

3d + 7 = 16

3d = 9

d = 3

Shira has 3 dogs.

Therefore, the corrrect answer is option (B).

Question 8 :

Rex is carnivorous dinosaur who lives on an island that is also inhabited by people. He eats one fourth of the people on his island on Monday, 13 of them on Tuesday and half as many he ate on Monday on Wednesday. If there are 22 people left on the island on Thursday and nobody came to the island or left in a way other than being eaten in that time period, how many people were on the island before Rex's rampage? 

(A)  56

(B)  64

(C)  68

(D)  74

Solution :

Let x be the totsl number of people in the island before Rex's rampage.

From the given information, number of people eaten by Rex on Monday, Tuesday and Wednesday :

Monday ----> (¼)x = ˣ⁄₄

Tuesday ----> 13

Wednesday ----> (½)(ˣ⁄₄) = ˣ⁄₈

Total number of people eaten by Rex on these three days :

= ˣ⁄₄ + 13 + ˣ⁄₈

= ²ˣ⁄₈ + ¹⁰⁴⁄₈ + ˣ⁄₈

= ⁽³ˣ ⁺ ¹⁰⁴⁾⁄₈

Given : 22 people left on the island on Thursday.

x - ⁽³ˣ ⁺ ¹⁰⁴⁾⁄₈ = 22

Multiply both sides by 8.

8[x - ⁽³ˣ ⁺ ¹⁰⁴⁾⁄₈] = 8(22)

8x - 8[⁽³ˣ ⁺ ¹⁰⁴⁾⁄₈] = 176

8x - (3x + 104) = 176

8x - 3x - 104 = 176

5x - 104 = 176

Add 104 to both sides.

5x = 280

Divide both sides by 5.

x = 56

There were 56 people on the island before Rex's rampage.

Therefore, the corrrect answer is option (A).

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