Q. If the product of two numbers is 48 and one of the numbers is 6, what can be inferred about the other number?
A.
It is 8.
B.
It is 12.
C.
It is 6.
D.
It is 4.
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Solution
If the product is 48 and one number is 6, then the other number must be 48 ÷ 6 = 8.
Correct Answer:
A
— It is 8.
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Q. If the product of two numbers is 48, which of the following pairs could represent these numbers?
A.
(2, 24)
B.
(3, 16)
C.
(4, 12)
D.
(All of the above)
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Solution
All pairs listed multiply to 48, hence they are valid pairs.
Correct Answer:
D
— (All of the above)
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Q. If the product of two numbers is 72 and one of the numbers is 8, what is the other number?
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Solution
The other number is 72 divided by 8, which equals 9.
Correct Answer:
A
— 6
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Q. If the product of two numbers is a multiple of 15, which of the following must be true?
A.
At least one of the numbers is a multiple of 3.
B.
At least one of the numbers is a multiple of 5.
C.
Both numbers are even.
D.
Both numbers are odd.
Show solution
Solution
For the product to be a multiple of 15, at least one of the numbers must be a multiple of 5.
Correct Answer:
B
— At least one of the numbers is a multiple of 5.
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Q. If the quadratic equation ax^2 + bx + c = 0 has roots p and q, which of the following is correct?
A.
p + q = -b/a and pq = c/a
B.
p + q = b/a and pq = -c/a
C.
p + q = c/a and pq = -b/a
D.
p + q = -c/a and pq = b/a
Show solution
Solution
According to Vieta's formulas, the sum of the roots p and q is -b/a and the product is c/a.
Correct Answer:
A
— p + q = -b/a and pq = c/a
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Q. If the quadratic equation x^2 + kx + 16 = 0 has real roots, what is the condition on k?
A.
k^2 >= 64
B.
k^2 < 64
C.
k > 16
D.
k < 16
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Solution
For real roots, the discriminant must be non-negative: k^2 - 4*1*16 >= 0, leading to k^2 >= 64.
Correct Answer:
A
— k^2 >= 64
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Q. If the quadratic equation x^2 - 4x + k = 0 has equal roots, what is the value of k?
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Solution
For equal roots, the discriminant must be zero: (-4)^2 - 4*1*k = 0, leading to k = 4.
Correct Answer:
B
— 4
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Q. If the quadratic equation x² - 4x + k = 0 has one real root, what must be the value of k?
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Solution
For the equation to have one real root, the discriminant must be zero. Thus, k must equal 4.
Correct Answer:
A
— 4
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Q. If the quadratic equation x² - 5x + 6 = 0 is factored, which of the following pairs of numbers represents the roots?
A.
2 and 3
B.
1 and 6
C.
0 and 6
D.
3 and 2
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Solution
Factoring the equation gives (x - 2)(x - 3) = 0, thus the roots are 2 and 3.
Correct Answer:
A
— 2 and 3
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Q. If the radius of a circle is increased by 50%, by what percentage does the area of the circle increase?
A.
25%
B.
50%
C.
75%
D.
100%
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Solution
The area of a circle is given by A = πr². If the radius is increased by 50%, the new radius is 1.5r. The new area is A' = π(1.5r)² = 2.25πr². The increase in area is (2.25 - 1) = 1.25 times the original area, which is a 125% increase.
Correct Answer:
C
— 75%
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Q. If the radius of a circle is increased by 50%, what happens to the area of the circle?
A.
It increases by 50%.
B.
It increases by 100%.
C.
It increases by 125%.
D.
It increases by 150%.
Show solution
Solution
If the radius increases by 50%, the new radius is 1.5r, and the area becomes (1.5r)² = 2.25r², which is a 125% increase.
Correct Answer:
C
— It increases by 125%.
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Q. If the radius of a sphere is halved, how does its volume change?
A.
It remains the same
B.
It doubles
C.
It halves
D.
It reduces to one-eighth
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Solution
Volume of a sphere = (4/3)πr³. If radius is halved, volume becomes (4/3)π(1/2)³ = (4/3)π(1/8) = (1/6)π, which is one-eighth of the original volume.
Correct Answer:
D
— It reduces to one-eighth
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Q. If the ranking of students is as follows: A is ranked 1st, B is ranked 2nd, C is ranked 3rd, and D is ranked 4th. If E is added and ranks 3rd, what will be the new ranking of C?
A.
2nd
B.
3rd
C.
4th
D.
5th
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Solution
If E is added and ranks 3rd, C will drop to 4th position.
Correct Answer:
C
— 4th
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Q. If the ratio of consecutive terms in a geometric series is constant, what can be inferred about the series? (2023)
A.
It is increasing.
B.
It is decreasing.
C.
It is exponential.
D.
It is linear.
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Solution
A constant ratio of consecutive terms indicates that the series is exponential.
Correct Answer:
C
— It is exponential.
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Q. If the ratio of consecutive terms in a geometric series is constant, what is this ratio called? (2023)
A.
Common difference
B.
Common ratio
C.
Term ratio
D.
Sequence ratio
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Solution
The constant ratio of consecutive terms in a geometric series is called the common ratio.
Correct Answer:
B
— Common ratio
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Q. If the ratio of consecutive terms in a geometric series is constant, what is this constant called? (2023)
A.
Common difference
B.
Common ratio
C.
Term factor
D.
Sequence multiplier
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Solution
The constant ratio of consecutive terms in a geometric series is called the common ratio.
Correct Answer:
B
— Common ratio
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Q. If the ratio of the ages of A and B is 5:3 and the sum of their ages is 64 years, what is A's age?
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Solution
Let A's age be 5x and B's age be 3x. Then, 5x + 3x = 64, which gives 8x = 64. Therefore, x = 8, and A's age is 5x = 40 years.
Correct Answer:
A
— 40
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Q. If the ratio of the lengths of two sides of a triangle is 7:5 and the perimeter is 48 cm, what is the length of the longer side?
A.
28 cm
B.
20 cm
C.
24 cm
D.
16 cm
Show solution
Solution
Let the lengths of the sides be 7x and 5x. Then, 7x + 5x = 48, which gives 12x = 48. Thus, x = 4, and the longer side is 7x = 28 cm.
Correct Answer:
A
— 28 cm
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Q. If the ratio of the number of cats to dogs in a shelter is 2:3 and there are 30 dogs, how many cats are there?
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Solution
The ratio of cats to dogs is 2:3. If there are 30 dogs, the number of cats can be calculated as (2/3) * 30 = 20 cats.
Correct Answer:
A
— 20
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Q. If the roots of the equation x^2 - 5x + 6 = 0 are p and q, what is the value of p + q?
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Solution
According to Vieta's formulas, the sum of the roots p + q is equal to -(-5) = 5.
Correct Answer:
A
— 5
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Q. If the roots of the quadratic equation ax^2 + bx + c = 0 are p and q, which of the following is correct?
A.
p + q = -b/a and pq = c/a
B.
p + q = c/a and pq = -b/a
C.
p - q = -b/a and pq = c/a
D.
p * q = -b/a and p + q = c/a
Show solution
Solution
According to Vieta's formulas, the sum of the roots p + q = -b/a and the product pq = c/a.
Correct Answer:
A
— p + q = -b/a and pq = c/a
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Q. If the roots of the quadratic equation x² + px + q = 0 are both negative, which of the following must be true?
A.
p > 0 and q > 0
B.
p < 0 and q < 0
C.
p < 0 and q > 0
D.
p > 0 and q < 0
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Solution
For both roots to be negative, the sum (p) must be positive and the product (q) must also be positive.
Correct Answer:
A
— p > 0 and q > 0
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Q. If the sales of Product A in Q1 were 200 units, what was the percentage increase in sales by Q2?
A.
50%
B.
100%
C.
25%
D.
75%
Show solution
Solution
The sales increased to 350 units in Q2, which is a 75% increase from Q1.
Correct Answer:
D
— 75%
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Q. If the sales of Product A in Q3 are 300 units, what is the percentage increase from Q2?
A.
50%
B.
100%
C.
75%
D.
25%
Show solution
Solution
The percentage increase from Q2 (200 units) to Q3 (300 units) is 50%.
Correct Answer:
C
— 75%
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Q. If the sales of Product A in Q4 are projected to be 20% higher than in Q3, and Q3 sales were 300 units, what will be the projected sales for Q4?
A.
360
B.
320
C.
300
D.
280
Show solution
Solution
Projected sales for Q4 would be 300 + (20% of 300) = 300 + 60 = 360 units.
Correct Answer:
A
— 360
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Q. If the sales of Product B in Q3 are projected to increase by 20% from Q2, what will be the new sales figure?
A.
600 units
B.
720 units
C.
800 units
D.
900 units
Show solution
Solution
If Product B sold 600 units in Q2, a 20% increase would result in 720 units in Q3.
Correct Answer:
B
— 720 units
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Q. If the sales of Product B in Q3 were to decrease by 20%, what would be the new sales figure?
A.
400
B.
450
C.
480
D.
500
Show solution
Solution
If Product B sold 600 units in Q3, a 20% decrease would result in 480 units.
Correct Answer:
C
— 480
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Q. If the sales of Product B in Q4 are projected to be 600 units, what will be the total sales for Product B over the four quarters?
A.
1800
B.
1600
C.
1400
D.
1200
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Solution
The total sales for Product B over the four quarters would be 1600 units (400 + 500 + 400 + 600).
Correct Answer:
B
— 1600
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Q. If the sales of Product B in Q4 are projected to be 600 units, what would be the total sales for the year? (2000)
A.
2000
B.
2200
C.
2400
D.
2600
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Solution
Adding the projected Q4 sales of 600 to the previous quarters gives a total of 2200 units for the year.
Correct Answer:
B
— 2200
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Q. If the sales of Product B in Q4 were 600 units, what was the percentage increase from Q3 if Q3 sales were 500 units?
A.
20%
B.
25%
C.
30%
D.
15%
Show solution
Solution
The percentage increase from Q3 to Q4 is ((600 - 500) / 500) * 100 = 20%.
Correct Answer:
B
— 25%
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