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Inequalities Beginner-Intermediate Worksheet: Focus on common variations practice Inequalities BEGINNER INTERMEDIATE

Level up your Inequalities skills! You're at Worksheet 4 of 10 (33% through this series). This step-up challenge worksheet features 20 beginner-intermediate-level problems with a focus on common variations practice. Topics covered: inequalities for competitive exams, how to solve inequalities, inequalities tricks.

📝 Worksheet 4 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner Intermediate level

What you'll learn in this worksheet:
Your progress through Inequalities
Worksheet 4 of 10 (33% complete)

Question 1

Question: Is x > 0? Statement (1): x² > 0 Statement (2): x³ > 0
Statement (1): x² > 0 means x ≠ 0, but x could be positive or negative - insufficient. Statement (2): x³ > 0 means x must be positive - sufficient.

Question 2

Question: Is x > y? Statement (1): x² > y² Statement (2): x³ > y³
Statement (1): x² > y² means |x| > |y|, but x could be less than y if both negative - insufficient. Statement (2): x³ > y³ means x > y (cubing preserves inequality) - sufficient.

Question 3

Question: Is x > y? Statement (1): x² > y² Statement (2): x³ > y³
Statement (1): x² > y² means |x| > |y|, but x could be less than y if both negative - insufficient. Statement (2): x³ > y³ means x > y (cubing preserves inequality) - sufficient.

Question 4

Question: Is xy > 0? Statement (1): x > 0 Statement (2): y > 0
xy > 0 means x and y have same sign. Each alone insufficient, together they are both positive → product positive.

Question 5

Question: Is x > 0? Statement (1): x² > 0 Statement (2): x³ > 0
Statement (1): x² > 0 means x ≠ 0, but x could be positive or negative - insufficient. Statement (2): x³ > 0 means x must be positive - sufficient.

Question 6

Question: Is x > 0? Statement (1): x² > 0 Statement (2): x³ > 0
Statement (1): x² > 0 means x ≠ 0, but x could be positive or negative - insufficient. Statement (2): x³ > 0 means x must be positive - sufficient.

Question 7

Question: Is x > 0? Statement (1): x² > 0 Statement (2): x³ > 0
Statement (1): x² > 0 means x ≠ 0, but x could be positive or negative - insufficient. Statement (2): x³ > 0 means x must be positive - sufficient.

Question 8

Question: Is xy > 0? Statement (1): x > 0 Statement (2): y > 0
xy > 0 means x and y have same sign. Each alone insufficient, together they are both positive → product positive.

Question 9

Question: Is x > 0? Statement (1): x² > 0 Statement (2): x³ > 0
Statement (1): x² > 0 means x ≠ 0, but x could be positive or negative - insufficient. Statement (2): x³ > 0 means x must be positive - sufficient.

Question 10

Question: Is x > y? Statement (1): x² > y² Statement (2): x³ > y³
Statement (1): x² > y² means |x| > |y|, but x could be less than y if both negative - insufficient. Statement (2): x³ > y³ means x > y (cubing preserves inequality) - sufficient.

Question 11

Question: Is x > 0? Statement (1): x² > 0 Statement (2): x³ > 0
Statement (1): x² > 0 means x ≠ 0, but x could be positive or negative - insufficient. Statement (2): x³ > 0 means x must be positive - sufficient.

Question 12

Question: Is xy > 0? Statement (1): x > 0 Statement (2): y > 0
xy > 0 means x and y have same sign. Each alone insufficient, together they are both positive → product positive.

Question 13

Question: Is xy > 0? Statement (1): x > 0 Statement (2): y > 0
xy > 0 means x and y have same sign. Each alone insufficient, together they are both positive → product positive.

Question 14

Question: Is xy > 0? Statement (1): x > 0 Statement (2): y > 0
xy > 0 means x and y have same sign. Each alone insufficient, together they are both positive → product positive.

Question 15

Question: Is x > 0? Statement (1): x² > 0 Statement (2): x³ > 0
Statement (1): x² > 0 means x ≠ 0, but x could be positive or negative - insufficient. Statement (2): x³ > 0 means x must be positive - sufficient.

Question 16

Question: Is xy > 0? Statement (1): x > 0 Statement (2): y > 0
xy > 0 means x and y have same sign. Each alone insufficient, together they are both positive → product positive.

Question 17

Question: Is x > 0? Statement (1): x² > 0 Statement (2): x³ > 0
Statement (1): x² > 0 means x ≠ 0, but x could be positive or negative - insufficient. Statement (2): x³ > 0 means x must be positive - sufficient.

Question 18

Question: Is x > y? Statement (1): x² > y² Statement (2): x³ > y³
Statement (1): x² > y² means |x| > |y|, but x could be less than y if both negative - insufficient. Statement (2): x³ > y³ means x > y (cubing preserves inequality) - sufficient.

Question 19

Question: Is xy > 0? Statement (1): x > 0 Statement (2): y > 0
xy > 0 means x and y have same sign. Each alone insufficient, together they are both positive → product positive.

Question 20

Question: Is xy > 0? Statement (1): x > 0 Statement (2): y > 0
xy > 0 means x and y have same sign. Each alone insufficient, together they are both positive → product positive.
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