CLT Math 1 — Questions and Answers

Question 1: If x-y = 5 and a + b = 4, determine the value of (3x + 3y)(5a + 5b).

250
300 (Correct answer)
9
55

Correct answer: 300

To determine the value, we first factor the expression: (3x + 3y)(5a + 5b) simplifies to 3(x + y) * 5(a + b), which is 15(x + y)(a + b). Given the information x - y = 5 and a + b = 4, the expression as written cannot be solved because we don't have a value for (x + y). However, if the question intended (3x - 3y)(5a + 5b), then factoring would yield 3(x - y) * 5(a + b), which is 3(5) * 5(4) = 15 * 20 = 300. This suggests a likely typo in the original problem statement.

Question 2: Triangle ABC is comparable to triangle XYZ, with cos A = 0.98162718344 and sin A = 0.19080899537. Which of the following is the best approximation for tan X?

5.44
0.194 (Correct answer)
5.144
It cannot be determined.

Correct answer: 0.194

Since triangle ABC is similar (comparable) to triangle XYZ, their corresponding angles are equal, meaning angle A is equal to angle X. The tangent of an angle is defined as the ratio of its sine to its cosine (tan θ = sin θ / cos θ). Therefore, tan X = tan A = sin A / cos A. Dividing the given sin A (0.19080899537) by cos A (0.98162718344) yields approximately 0.19438, which rounds to 0.194.

Question 3: How many numbers from 60 to 130 inclusive fulfill both of the following statements?</br></br> Statement 1: The first digit of the number is even. Statement 2: The number is prime.

4 (Correct answer)
2
0
8

Correct answer: 4

We need to find prime numbers between 60 and 130 (inclusive) whose first digit is even. The numbers in this range with an even first digit are those starting with 6 or 8. The prime numbers starting with 6 are 61 and 67. The prime numbers starting with 8 are 83 and 89. Numbers starting with 7, 9, 10, 11, or 12 have an odd first digit, so they do not meet the criteria. Thus, there are exactly 4 numbers (61, 67, 83, 89) that fulfill both statements.

Question 4: Which of the following may be the next term in the arithmetic sequence below?</br></br> 2,5,8,11,7,...

14 (Correct answer)
18
12
26

Correct answer: 14

An arithmetic sequence is characterized by a constant difference between consecutive terms. In the initial part of the given sequence (2, 5, 8, 11), the common difference is 3 (e.g., 5-2=3). The term '7' disrupts this established arithmetic pattern. However, if we assume the question asks for the next term *if the arithmetic sequence were to continue from 11*, then adding the common difference of 3 to 11 yields 14.

Question 5: Which axis in the (x,y)-coordinate plane does the point at (-3,0) correspond to?

Neither the x-axis nor the y-axis
Both the x-axis and the y-axis
The y-axis
The x-axis (Correct answer)

Correct answer: The x-axis

A point lies on the x-axis in the (x,y)-coordinate plane when its y-coordinate is 0. For the point (-3,0), the x-coordinate is -3 and the y-coordinate is 0. Since the y-coordinate is zero, the point is located directly on the x-axis, specifically three units to the left of the origin.

Question 6: Which of the following is equal to 3(2-5) + 3x 7?

18
-42
12 (Correct answer)
22

Correct answer: 12

To evaluate the expression 3(2-5) + 3 x 7, we must follow the order of operations (PEMDAS/BODMAS). First, calculate the value inside the parentheses: (2-5) equals -3. Next, perform the multiplications: 3 * (-3) equals -9, and 3 * 7 equals 21. Finally, add the results: -9 + 21 equals 12.

Question 7: The sum of the perimeters of two congruent equilateral triangles equals 36 inches. What is the measurement of one of these triangles' sides?

6 inches (Correct answer)
9 inches
15 inches
24 inches

Correct answer: 6 inches

Since the two equilateral triangles are congruent, they must have identical perimeters. If the sum of their perimeters is 36 inches, then each individual triangle has a perimeter of 36 / 2 = 18 inches. An equilateral triangle has three sides of equal length, so to find the length of one side, divide its perimeter by 3: 18 / 3 = 6 inches.

Question 8: Each storage room in a storage facility has a maximum capacity of 80 boxes of a specific size. If a household has to keep 220 boxes of such size before moving, how many storage rooms will they require at that facility?

5
8
3 (Correct answer)
4

Correct answer: 3

To determine the number of storage rooms required, divide the total number of boxes by the capacity of a single room. 220 boxes divided by 80 boxes per room equals 2.75 rooms. Since a household cannot rent a fraction of a room and all boxes must be stored, the number of rooms must be rounded up to the next whole number, which is 3.

Question 9: Anna's English class had twenty percent more pupils than her social studies class. If her social studies class includes 20 pupils, how many are there in her English class?

42 students
24 students (Correct answer)
22 students
12 students

Correct answer: 24 students

To find the number of pupils in Anna's English class, first calculate 20 percent of her social studies class size. 20% of 20 pupils is found by multiplying 0.20 by 20, which equals 4 pupils. Since her English class has 20 percent *more* pupils, add this amount to the social studies class size: 20 + 4 = 24 pupils.

Question 10: Three congruent equilateral triangles are arranged to make an isosceles trapezoid. What is the perimeter of the trapezoid if one of its triangles has a perimeter of 24 inches?

54 in
28 in
32 in
40 in (Correct answer)

Correct answer: 40 in

An equilateral triangle with a perimeter of 24 inches has sides that are each 24 / 3 = 8 inches long. When three such congruent equilateral triangles form an isosceles trapezoid, the trapezoid's perimeter consists of five of these side lengths. Specifically, the top base is one side (8 inches), the bottom base is two sides (16 inches), and the two non-parallel sides are each one side (8 inches each). Therefore, the total perimeter is 8 + 16 + 8 + 8 = 40 inches.

Question 11: A circle's diameter is 12 centimeters. The circle's circumference is what?

144𝝿 cm
36𝝿 cm
12𝝿 cm (Correct answer)
24𝝿 cm

Correct answer: 12𝝿 cm

The circumference of a circle is calculated using the formula C = πd, where 'd' represents the diameter of the circle. Given that the circle's diameter is 12 centimeters, substitute this value into the formula. Therefore, the circumference is C = π * 12 cm, which simplifies to 12π cm.

CLT Math 1

If x-y = 5 and a + b = 4, determine the value of (3x + 3y)(5a + 5b).