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Absolute Values - Intermediate Level: tricky scenarios handling Absolute Values INTERMEDIATE

This expert challenge 📈 worksheet focuses on Absolute Values - a key topic in Data Sufficiency. You'll solve 20 intermediate-level problems (Worksheet 5 of 10). The primary focus is on tricky scenarios handling. Master how to solve absolute values, absolute values tricks, and absolute values shortcut methods through systematic practice.

📝 Worksheet 5 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Absolute Values
Worksheet 5 of 10 (44% complete)

Question 1

Question: What is the value of x? Statement (1): |x| = 5 Statement (2): x² = 25 and x > 0
Statement (1): |x| = 5 → x = 5 or x = -5. NOT sufficient alone (two values).
Statement (2): x² = 25 → x = 5 or x = -5, but x > 0 → x = 5 uniquely. SUFFICIENT alone.
Therefore, only Statement (2) alone is sufficient.

Question 2

Question: What is the value of x? Statement (1): |x| = 5 Statement (2): x² = 25 and x > 0
Statement (1): |x| = 5 → x = 5 or x = -5. NOT sufficient alone (two values).
Statement (2): x² = 25 → x = 5 or x = -5, but x > 0 → x = 5 uniquely. SUFFICIENT alone.
Therefore, only Statement (2) alone is sufficient.

Question 3

Question: What is the value of x? Statement (1): |x| = 5 Statement (2): x² = 25 and x > 0
Statement (1): |x| = 5 → x = 5 or x = -5. NOT sufficient alone (two values).
Statement (2): x² = 25 → x = 5 or x = -5, but x > 0 → x = 5 uniquely. SUFFICIENT alone.
Therefore, only Statement (2) alone is sufficient.

Question 4

Question: What is the value of x? Statement (1): |x| = 5 Statement (2): x² = 25 and x > 0
Statement (1): |x| = 5 → x = 5 or x = -5. NOT sufficient alone (two values).
Statement (2): x² = 25 → x = 5 or x = -5, but x > 0 → x = 5 uniquely. SUFFICIENT alone.
Therefore, only Statement (2) alone is sufficient.

Question 5

Question: What is the value of x? Statement (1): |x| = 5 Statement (2): x² = 25 and x > 0
Statement (1): |x| = 5 → x = 5 or x = -5. NOT sufficient alone (two values).
Statement (2): x² = 25 → x = 5 or x = -5, but x > 0 → x = 5 uniquely. SUFFICIENT alone.
Therefore, only Statement (2) alone is sufficient.

Question 6

Question: What is the value of x? Statement (1): |x| = 5 Statement (2): x² = 25 and x > 0
Statement (1): |x| = 5 → x = 5 or x = -5. NOT sufficient alone (two values).
Statement (2): x² = 25 → x = 5 or x = -5, but x > 0 → x = 5 uniquely. SUFFICIENT alone.
Therefore, only Statement (2) alone is sufficient.

Question 7

Question: What is the value of x? Statement (1): |x| = 5 Statement (2): x² = 25 and x > 0
Statement (1): |x| = 5 → x = 5 or x = -5. NOT sufficient alone (two values).
Statement (2): x² = 25 → x = 5 or x = -5, but x > 0 → x = 5 uniquely. SUFFICIENT alone.
Therefore, only Statement (2) alone is sufficient.

Question 8

Question: What is the value of x? Statement (1): |x| = 5 Statement (2): x² = 25 and x > 0
Statement (1): |x| = 5 → x = 5 or x = -5. NOT sufficient alone (two values).
Statement (2): x² = 25 → x = 5 or x = -5, but x > 0 → x = 5 uniquely. SUFFICIENT alone.
Therefore, only Statement (2) alone is sufficient.

Question 9

Question: What is the value of x? Statement (1): |x| = 5 Statement (2): x² = 25 and x > 0
Statement (1): |x| = 5 → x = 5 or x = -5. NOT sufficient alone (two values).
Statement (2): x² = 25 → x = 5 or x = -5, but x > 0 → x = 5 uniquely. SUFFICIENT alone.
Therefore, only Statement (2) alone is sufficient.

Question 10

Question: What is the value of x? Statement (1): |x| = 5 Statement (2): x² = 25 and x > 0
Statement (1): |x| = 5 → x = 5 or x = -5. NOT sufficient alone (two values).
Statement (2): x² = 25 → x = 5 or x = -5, but x > 0 → x = 5 uniquely. SUFFICIENT alone.
Therefore, only Statement (2) alone is sufficient.

Question 11

Question: What is the value of x? Statement (1): |x| = 5 Statement (2): x² = 25 and x > 0
Statement (1): |x| = 5 → x = 5 or x = -5. NOT sufficient alone (two values).
Statement (2): x² = 25 → x = 5 or x = -5, but x > 0 → x = 5 uniquely. SUFFICIENT alone.
Therefore, only Statement (2) alone is sufficient.

Question 12

Question: What is the value of x? Statement (1): |x| = 5 Statement (2): x² = 25 and x > 0
Statement (1): |x| = 5 → x = 5 or x = -5. NOT sufficient alone (two values).
Statement (2): x² = 25 → x = 5 or x = -5, but x > 0 → x = 5 uniquely. SUFFICIENT alone.
Therefore, only Statement (2) alone is sufficient.

Question 13

Question: What is the value of x? Statement (1): |x| = 5 Statement (2): x² = 25 and x > 0
Statement (1): |x| = 5 → x = 5 or x = -5. NOT sufficient alone (two values).
Statement (2): x² = 25 → x = 5 or x = -5, but x > 0 → x = 5 uniquely. SUFFICIENT alone.
Therefore, only Statement (2) alone is sufficient.

Question 14

Question: What is the value of x? Statement (1): |x| = 5 Statement (2): x² = 25 and x > 0
Statement (1): |x| = 5 → x = 5 or x = -5. NOT sufficient alone (two values).
Statement (2): x² = 25 → x = 5 or x = -5, but x > 0 → x = 5 uniquely. SUFFICIENT alone.
Therefore, only Statement (2) alone is sufficient.

Question 15

Question: What is the value of x? Statement (1): |x| = 5 Statement (2): x² = 25 and x > 0
Statement (1): |x| = 5 → x = 5 or x = -5. NOT sufficient alone (two values).
Statement (2): x² = 25 → x = 5 or x = -5, but x > 0 → x = 5 uniquely. SUFFICIENT alone.
Therefore, only Statement (2) alone is sufficient.

Question 16

Question: What is the value of x? Statement (1): |x| = 5 Statement (2): x² = 25 and x > 0
Statement (1): |x| = 5 → x = 5 or x = -5. NOT sufficient alone (two values).
Statement (2): x² = 25 → x = 5 or x = -5, but x > 0 → x = 5 uniquely. SUFFICIENT alone.
Therefore, only Statement (2) alone is sufficient.

Question 17

Question: What is the value of x? Statement (1): |x| = 5 Statement (2): x² = 25 and x > 0
Statement (1): |x| = 5 → x = 5 or x = -5. NOT sufficient alone (two values).
Statement (2): x² = 25 → x = 5 or x = -5, but x > 0 → x = 5 uniquely. SUFFICIENT alone.
Therefore, only Statement (2) alone is sufficient.

Question 18

Question: What is the value of x? Statement (1): |x| = 5 Statement (2): x² = 25 and x > 0
Statement (1): |x| = 5 → x = 5 or x = -5. NOT sufficient alone (two values).
Statement (2): x² = 25 → x = 5 or x = -5, but x > 0 → x = 5 uniquely. SUFFICIENT alone.
Therefore, only Statement (2) alone is sufficient.

Question 19

Question: What is the value of x? Statement (1): |x| = 5 Statement (2): x² = 25 and x > 0
Statement (1): |x| = 5 → x = 5 or x = -5. NOT sufficient alone (two values).
Statement (2): x² = 25 → x = 5 or x = -5, but x > 0 → x = 5 uniquely. SUFFICIENT alone.
Therefore, only Statement (2) alone is sufficient.

Question 20

Question: What is the value of x? Statement (1): |x| = 5 Statement (2): x² = 25 and x > 0
Statement (1): |x| = 5 → x = 5 or x = -5. NOT sufficient alone (two values).
Statement (2): x² = 25 → x = 5 or x = -5, but x > 0 → x = 5 uniquely. SUFFICIENT alone.
Therefore, only Statement (2) alone is sufficient.
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