Digital SAT Math Questions and Answers (Part - 11)

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Question 1 :

A company ships medium and large refrigerators by using trucks of two different sizes. A large truck can carry 4 medium refrigerators and 5 large refrigerators. A small truck can carry 3 medium refrigerators and 2 large refrigerators. If a is the number of large trucks and b is the number of small trucks, which of the following represents the number of trucks of each size necessary to deliver an order for 20 medium refrigerators and 30 large refrigerators?

A) 4a + 3b ≥ 20

2a + 5b ≥ 30

B) 3a + 4b ≤ 20

5a + 2b ≤ 30

C) 4a + 3b ≥ 20

5a + 2b ≥ 30

D) 4a + 3b ≤ 30

5a + 2b ≤ 20

Answer :

Question 2 :

2x² – 10x + k = 0

The equation above, in which k is a constant, has two solutions m and n. If m > n and m – n = 9, what is the value of n?

A) -5

B) -2

C) 4

D) 7

Answer :

Question 3 :

In the figure above, the line ℓ intersects a regular pentagon. What is the value of a + b?

Answer :

Question 4 :

sin 24 = cos (3k + 6)

In the equation above, the angle measures are in degrees. If 0° < k < 90°, what is the value of k?

Answer :

Question 5 :

Traveling at an average speed of 40 miles per hour, a bus takes 3 hours to complete its morning route. At what average speed, in miles per hour, must the bus travel, if it is to complete its morning route in 2.5 hours?

Answer :

Question 6 :

(a – 2b)² + (b + 1)² + (c – 3a)² = 0

In the equation above, if a, b and c are real numbers, what is the value of (a + b + c) ?

Answer :

Question 7 :

For 5 consecutive even integers, the sum of the first and third integers is 20 less than 3 times the fourth integer. What is the fifth integer?

A) 12

B) 14

C) 16

D) 18

Answer :

Question 8 :

A) 1/4

B) 4

C) 5

D) 5/2

Answer :

Question 9 :

Answer :

Question 10 :

A) 1

B) 0

C) ½

D) -1

Answer :

Question 11 :

If a^x = b, b^y = c and c^z = a, then what is the value of xyz?

A) 0

B) 1

C) 2

D) 3

Answer :

Question 12 :

A) -1

B) 1

C) 0

D) 2

Answer :

Question 13 :

A clothing store carries red ties and blue ties. The number of red ties in stock is 40 less than three times the number of blue ties in stock. If there are 10 more red ties than blue ties in stock, how many blue ties are in stock?

Answer :

Question 14 :

Jonathan can edit at least 15 essays per day but no more than 18 essays per day. Which of the following could be the total number of essays he edits in a week?

A) 98

B) 102

C) 112

D) 130

Answer :

Question 15 :

According to the table, the model A car battery lasts how many times as long as the model D car battery?

A) 4

B) 8

C) 16

D) 32

Answer :

Question 16 :

Given :

(a - b)³ = a³ - 3ab(a - b) - b³

x = p^1/3 - p^-1/3

What is the value of x³ + 3x ?

A) p + 1/p

B) p - 1/p

C) p + 1

D) p - 1

Answer :

Question 17 :

Tickets to a concert are $40 for reserved seats and $15 for general admission seats. If a total of 1,200 tickets have been sold and x of them are for reserved seats, which of the following gives all possible values of x for which total ticket sales are at least $30,000?

A) x ≤ 480

B) x ≥ 480

C) x ≤ 520

D) x ≥ 520

Answer :

Question 18 :

A cable company surveyed a random sample of 400 subscribers to determine their favorite sport to watch. The results of the survey are shown in the table below.