Q. Solve the inequality 5 - x ≥ 1.
-
A.
x ≤ 4
-
B.
x < 4
-
C.
x ≥ 4
-
D.
x > 4
Solution
5 - x ≥ 1 => -x ≥ -4 => x ≤ 4.
Correct Answer: A — x ≤ 4
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Q. Solve the inequality 5x - 7 > 3x + 1.
-
A.
x > 4
-
B.
x < 4
-
C.
x > 2
-
D.
x < 2
Solution
5x - 7 > 3x + 1 => 2x > 8 => x > 4.
Correct Answer: C — x > 2
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Q. Solve the inequality 6 - 2x > 4.
-
A.
x < 1
-
B.
x > 1
-
C.
x < 2
-
D.
x > 2
Solution
6 - 2x > 4 => -2x > -2 => x < 1.
Correct Answer: B — x > 1
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Q. Solve the inequality 6 - 2x > 4. What is the solution?
-
A.
x < 1
-
B.
x > 1
-
C.
x < 2
-
D.
x > 2
Solution
6 - 2x > 4 => -2x > -2 => x < 1.
Correct Answer: B — x > 1
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Q. Solve the inequality 6 - 2x ≤ 4.
-
A.
x ≥ 1
-
B.
x < 1
-
C.
x > 1
-
D.
x ≤ 1
Solution
6 - 2x ≤ 4 => -2x ≤ -2 => x ≥ 1.
Correct Answer: D — x ≤ 1
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Q. Solve the inequality 6 - 3x ≤ 0.
-
A.
x ≥ 2
-
B.
x < 2
-
C.
x > 2
-
D.
x ≤ 2
Solution
Subtract 6 from both sides: -3x ≤ -6. Then divide by -3 (reverse the inequality): x ≥ 2.
Correct Answer: A — x ≥ 2
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Q. Solve the inequality 6 - 3x ≥ 0. What is the solution?
-
A.
x ≤ 2
-
B.
x ≥ 2
-
C.
x < 2
-
D.
x > 2
Solution
6 - 3x ≥ 0 => -3x ≥ -6 => x ≤ 2.
Correct Answer: B — x ≥ 2
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Q. Solve the inequality 6x + 2 < 14.
-
A.
x < 2
-
B.
x < 3
-
C.
x > 2
-
D.
x > 3
Solution
6x + 2 < 14 => 6x < 12 => x < 2.
Correct Answer: B — x < 3
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Q. Solve the inequality 7 - 3x > 1.
-
A.
x < 2
-
B.
x > 2
-
C.
x < 3
-
D.
x > 3
Solution
7 - 3x > 1 => -3x > -6 => x < 2.
Correct Answer: B — x > 2
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Q. Solve the inequality 7 - 3x > 1. What is the solution?
-
A.
x < 2
-
B.
x > 2
-
C.
x ≤ 2
-
D.
x ≥ 2
Solution
7 - 3x > 1 => -3x > -6 => x > 2.
Correct Answer: B — x > 2
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Q. Solve the inequality 7 - 3x < 1. What is the solution?
-
A.
x < 2
-
B.
x > 2
-
C.
x < 3
-
D.
x > 3
Solution
7 - 3x < 1 => -3x < -6 => x > 2.
Correct Answer: B — x > 2
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Q. Solve the inequality 7 - x < 2.
-
A.
x > 5
-
B.
x < 5
-
C.
x > 7
-
D.
x < 7
Solution
7 - x < 2 => -x < -5 => x > 5.
Correct Answer: A — x > 5
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Q. Solve the inequality 7x + 2 < 3x + 10.
-
A.
x < 2
-
B.
x > 2
-
C.
x ≤ 2
-
D.
x ≥ 2
Solution
7x + 2 < 3x + 10 => 4x < 8 => x < 2.
Correct Answer: B — x > 2
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Q. Solve the inequality 7x - 4 < 2x + 11. What is the solution?
-
A.
x < 3
-
B.
x > 3
-
C.
x ≤ 3
-
D.
x ≥ 3
Solution
7x - 4 < 2x + 11 => 5x < 15 => x < 3.
Correct Answer: B — x > 3
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Q. Solve the inequality 7x - 5 < 2x + 10. What is the solution?
-
A.
x < 1
-
B.
x > 1
-
C.
x < 2
-
D.
x > 2
Solution
7x - 5 < 2x + 10 => 5x < 15 => x < 3.
Correct Answer: B — x > 1
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Q. Solve the inequality 8 - x > 3.
-
A.
x < 5
-
B.
x > 5
-
C.
x < 3
-
D.
x > 3
Solution
8 - x > 3 => -x > -5 => x < 5.
Correct Answer: A — x < 5
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Q. Solve the inequality x/3 + 2 > 1. What is the solution?
-
A.
x > -3
-
B.
x < -3
-
C.
x > 3
-
D.
x < 3
Solution
x/3 + 2 > 1 => x/3 > -1 => x > -3.
Correct Answer: C — x > 3
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Q. Solve the inequality x/3 - 2 > 1. What is the solution set?
-
A.
x < 9
-
B.
x > 9
-
C.
x < 3
-
D.
x > 3
Solution
x/3 - 2 > 1 => x/3 > 3 => x > 9.
Correct Answer: B — x > 9
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Q. Solve the inequality x/3 - 2 ≤ 1. What is the solution?
-
A.
x ≤ 9
-
B.
x ≥ 9
-
C.
x ≤ 3
-
D.
x ≥ 3
Solution
x/3 - 2 ≤ 1 => x/3 ≤ 3 => x ≤ 9.
Correct Answer: A — x ≤ 9
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Q. Solve the inequality x/4 - 1 < 0.
-
A.
x < 4
-
B.
x > 4
-
C.
x ≤ 4
-
D.
x ≥ 4
Solution
x/4 - 1 < 0 => x/4 < 1 => x < 4.
Correct Answer: A — x < 4
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Q. Solve the inequality: 4x + 1 ≥ 3.
-
A.
x ≥ 0.5
-
B.
x ≤ 0.5
-
C.
x ≥ 1
-
D.
x ≤ 1
Solution
4x + 1 ≥ 3 => 4x ≥ 2 => x ≥ 0.5.
Correct Answer: A — x ≥ 0.5
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Q. Solve the inequality: 6 - x ≤ 2.
-
A.
x ≥ 4
-
B.
x ≤ 4
-
C.
x ≥ 6
-
D.
x ≤ 6
Solution
6 - x ≤ 2 => -x ≤ -4 => x ≥ 4.
Correct Answer: B — x ≤ 4
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Q. Some birds can fly. All sparrows are birds. Therefore, some sparrows can fly. Is this conclusion valid? (2023)
-
A.
Yes
-
B.
No
-
C.
Only if all birds can fly
-
D.
Only if some birds are sparrows
Solution
The conclusion is valid. Since all sparrows are birds and some birds can fly, it follows that some sparrows can fly.
Correct Answer: A — Yes
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Q. Some cars are red. All red things are fast. Therefore, some cars are fast. (2023)
-
A.
True
-
B.
False
-
C.
Cannot be determined
-
D.
None of the above
Solution
The conclusion logically follows from the premises.
Correct Answer: A — True
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Q. Some cars are red. All red things are fast. Therefore, some cars are fast. Is this conclusion valid? (2023)
-
A.
Yes
-
B.
No
-
C.
Only if all cars are red
-
D.
Only if some fast things are cars
Solution
The conclusion is valid. If some cars are red and all red things are fast, then it follows that some cars are fast.
Correct Answer: A — Yes
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Q. Some fruits are apples. All apples are sweet. Therefore, some fruits are sweet. (2023)
-
A.
True
-
B.
False
-
C.
Cannot be determined
-
D.
None of the above
Solution
The conclusion logically follows from the premises.
Correct Answer: A — True
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Q. Some students are diligent. All diligent people succeed. Therefore, some students succeed. Is this conclusion valid? (2023)
-
A.
Yes
-
B.
No
-
C.
Only if all students are diligent
-
D.
Only if some diligent people are students
Solution
The conclusion is valid. If some students are diligent and all diligent people succeed, then it follows that some students succeed.
Correct Answer: A — Yes
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Q. Some students are diligent. All diligent people succeed. Therefore, some students succeed. (2023)
-
A.
True
-
B.
False
-
C.
Cannot be determined
-
D.
None of the above
Solution
The conclusion logically follows from the premises.
Correct Answer: A — True
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Q. Spot the error in this sentence: 'The informations provided were helpful.'
-
A.
The
-
B.
informations
-
C.
provided
-
D.
were
Solution
'informations' should be 'information' as it is an uncountable noun.
Correct Answer: B — informations
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Q. Spot the error in this sentence: She sings good. (2021)
-
A.
A) She
-
B.
B) sings
-
C.
C) good
-
D.
D) .
Solution
The correct word should be 'well' instead of 'good' as 'well' is the adverb that modifies the verb 'sings'.
Correct Answer: C — C) good
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