Q. Given two parallel lines cut by a transversal, if one of the same-side interior angles is 40 degrees, what is the measure of the other same-side interior angle?
A.
40 degrees
B.
140 degrees
C.
180 degrees
D.
90 degrees
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Solution
Same-side interior angles are supplementary. Therefore, if one angle is 40 degrees, the other must be 180 - 40 = 140 degrees.
Correct Answer:
B
— 140 degrees
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Q. How many different ways can you arrange 5 different colored balls in a row?
A.
60
B.
120
C.
240
D.
720
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Solution
The number of arrangements of 5 balls is 5! = 5 × 4 × 3 × 2 × 1 = 120.
Correct Answer:
D
— 720
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Q. How many different ways can you arrange the letters in the word 'MATH'?
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Solution
The number of arrangements of 4 letters is 4! = 4 × 3 × 2 × 1 = 24.
Correct Answer:
C
— 24
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Q. How many different ways can you arrange the letters in the word 'SCHOOL'?
A.
120
B.
360
C.
720
D.
840
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Solution
The number of arrangements of the letters in 'SCHOOL' is 6! / 2! = 360.
Correct Answer:
B
— 360
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Q. How many different ways can you choose 4 toppings from a selection of 10?
A.
210
B.
120
C.
100
D.
90
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Solution
The number of combinations of 10 toppings taken 4 at a time is C(10, 4) = 210.
Correct Answer:
A
— 210
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Q. How many sides does a hexagon have?
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Solution
A hexagon is defined as a polygon with six sides.
Correct Answer:
C
— 6
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Q. How many ways can you arrange 3 books on a shelf?
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Solution
The number of arrangements of 3 books is 3! = 3 × 2 × 1 = 6.
Correct Answer:
B
— 6
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Q. How many ways can you arrange 5 books on a shelf?
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Solution
The number of arrangements of 5 books is 5! = 5 × 4 × 3 × 2 × 1 = 120.
Correct Answer:
A
— 120
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Q. How many ways can you arrange the letters in the word 'BOOK'?
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Solution
The number of arrangements is 4! / 2! = 12, since 'O' repeats.
Correct Answer:
C
— 16
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Q. How many ways can you choose 2 items from a set of 5?
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Solution
C(5,2) = 5! / (2!(5-2)!) = 10.
Correct Answer:
B
— 10
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Q. How many ways can you choose 3 items from a set of 10?
A.
120
B.
720
C.
10
D.
100
Show solution
Solution
The number of combinations is calculated as 10! / (3!(10-3)!) = 120.
Correct Answer:
A
— 120
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Q. How many ways can you choose 3 items from a set of 5 items?
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Solution
C(5,3) = 5! / (3!(5-3)!) = 10
Correct Answer:
A
— 10
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Q. How many ways can you choose 3 items from a set of 5?
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Solution
The number of ways to choose 3 items from 5 is calculated using combinations: C(5,3) = 5! / (3!(5-3)!) = 10.
Correct Answer:
A
— 10
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Q. How many ways can you choose 3 students from a group of 10?
A.
120
B.
210
C.
100
D.
30
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Solution
The number of combinations is calculated as 10C3 = 10! / (3!(10-3)!) = 120.
Correct Answer:
B
— 210
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Q. How many ways can you select 1 card from a standard deck of 52 cards?
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Solution
The number of ways to select 1 card from 52 is simply 52.
Correct Answer:
B
— 52
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Q. How many ways can you select 2 students from a class of 8?
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Solution
The number of combinations of 8 students taken 2 at a time is C(8, 2) = 8! / (2!(8-2)!) = 28.
Correct Answer:
A
— 28
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Q. How many ways can you select 3 students from a group of 8?
A.
56
B.
84
C.
112
D.
128
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Solution
The number of combinations of 3 students from 8 is C(8, 3) = 8! / (3!(8-3)!) = 56.
Correct Answer:
B
— 84
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Q. If -x + 6 > 2, what is the solution for x?
A.
x < 4
B.
x > 4
C.
x < 6
D.
x > 6
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Solution
Step 1: Subtract 6 from both sides: -x > -4. Step 2: Multiply by -1 (reverse inequality): x < 4.
Correct Answer:
B
— x > 4
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Q. If 2(x + 3) = 10, what is x?
A.
x = 1
B.
x = 2
C.
x = 3
D.
x = 4
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Solution
Divide by 2: x + 3 = 5. Subtract 3: x = 2.
Correct Answer:
B
— x = 2
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Q. If 2(x + 3) = 14, what is x?
A.
x = 4
B.
x = 5
C.
x = 6
D.
x = 7
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Solution
Step 1: Divide both sides by 2: x + 3 = 7. Step 2: Subtract 3 from both sides: x = 4.
Correct Answer:
A
— x = 4
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Q. If 2(x + 3) = 16, what is x?
A.
x = 4
B.
x = 5
C.
x = 6
D.
x = 7
Show solution
Solution
Divide by 2: x + 3 = 8. Subtract 3: x = 5.
Correct Answer:
B
— x = 5
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Q. If 2x + 3 > 11, what is the solution for x?
A.
x > 4
B.
x < 4
C.
x > 3
D.
x < 3
Show solution
Solution
Step 1: Subtract 3 from both sides: 2x > 8. Step 2: Divide by 2: x > 4.
Correct Answer:
A
— x > 4
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Q. If 2x + 3 > 7, what is the solution for x?
A.
x > 2
B.
x < 2
C.
x > 3
D.
x < 3
Show solution
Solution
Subtract 3 from both sides: 2x > 4. Divide by 2: x > 2.
Correct Answer:
A
— x > 2
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Q. If 2x + 3 > 7, what is the solution set for x?
A.
x > 2
B.
x < 2
C.
x > 3
D.
x < 3
Show solution
Solution
Subtract 3 from both sides: 2x > 4. Divide by 2: x > 2.
Correct Answer:
A
— x > 2
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Q. If 2x + 3y = 12 and y = 2, what is the value of x?
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Solution
Step 1: Substitute y = 2 into the equation: 2x + 6 = 12. Step 2: Subtract 6: 2x = 6. Step 3: Divide by 2: x = 3.
Correct Answer:
C
— 2
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Q. If 2x + 5 > 3x - 1, what is the solution for x?
A.
x < 6
B.
x > 6
C.
x < -6
D.
x > -6
Show solution
Solution
Step 1: Subtract 2x from both sides: 5 > x - 1. Step 2: Add 1: 6 > x, or x < 6.
Correct Answer:
D
— x > -6
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Q. If 2x + 5 = 3x - 1, what is the value of x?
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Solution
Rearranging gives: 5 + 1 = 3x - 2x, thus x = 6.
Correct Answer:
A
— -6
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Q. If 2x - 5 = 3x + 1, what is x?
A.
x = -6
B.
x = -4
C.
x = 4
D.
x = 6
Show solution
Solution
Step 1: Subtract 2x from both sides: -5 = x + 1. Step 2: Subtract 1 from both sides: x = -6.
Correct Answer:
B
— x = -4
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Q. If 2x^2 - 8 = 0, what is the value of x?
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Solution
Add 8 to both sides: 2x^2 = 8. Divide by 2: x^2 = 4. Taking the square root gives x = ±2.
Correct Answer:
C
— 2
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Q. If 2x^2 - 8 = 0, what is x?
A.
x = 2
B.
x = -2
C.
x = 4
D.
x = -4
Show solution
Solution
Add 8: 2x^2 = 8. Divide by 2: x^2 = 4. Take square root: x = 4 or x = -4.
Correct Answer:
C
— x = 4
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