CAT Inequalities & modulus Questions

Inequalities describe ranges rather than single values. Modulus measures distance from zero, so expressions involving absolute values are often easiest to solve interval by interval.

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Key concepts

• Sign charts and critical points
• Absolute value as distance
• Open and closed interval endpoints

CAT inequalities & modulus practice questions

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Common mistakes

• Keeping the inequality direction unchanged after multiplying by a negative number.
• Ignoring points where a denominator is zero.

Practical solving approaches

• Find zeros and undefined points before constructing a sign chart.
• Split modulus expressions at their sign-change points and validate each result within its interval.

Inequalities & modulus FAQs

Can I square both sides of an inequality?

Only after checking their signs and whether the operation preserves equivalence. Squaring expressions of unknown sign can change the solution set.

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CAT Inequalities & modulus Questions

Inequalities describe ranges rather than single values. Modulus measures distance from zero, so expressions involving absolute values are often easiest to solve interval by interval.

6 free practice questions

Key concepts

• Sign charts and critical points
• Absolute value as distance
• Open and closed interval endpoints

CAT inequalities & modulus practice questions

Question 1Multiple choiceMEDIUM

Question 1

Select the correct alternative from the given choices.

Answer the questions independently of each other.

Given that –1 < v < 1, –2 < u < –0.5 and –2 < z < –0.5 and w = vz/u, then which of the following is necessarily true?

Choose an answer

A.–0.5 < w < 2B.–4 < w < 4C.–4 < w < 2D.–2 < w < –0.5

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Question 2Multiple choiceHARD

Question 2

Select the correct alternative from the given choices.

Answer the questions independently of each other.

Each family in a locality has at most two adults, and no family has fewer than 3 children. Considering all families together, there are more adults than boys, more boys then girls, and more girls than families. Then minimum possible number of families in the locality is

Choose an answer

A.4B.5C.2D.3

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Question 3Multiple choiceMEDIUM

Question 3

Select the correct alternative from the given choices.

Answer the questions independently of each other.

In the X-Y plane, the area of the region bounded by the graph |x + y| + |x – y| = 4 is

 

Choose an answer

A.8B.12 C.16 D.20

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Question 4Multiple choiceMEDIUM

Question 4

Select the correct alternative from the given choices

Choose an answer

A.10B.15C.20D.Cannot be determined

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Question 5Type in the answerMEDIUM

Question 5

Enter your response (as an integer) using the virtual keyboard in the box provided.

Your answer

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Question 6Multiple choiceMEDIUM

Question 6

Select the correct alternative from the given choices

Choose an answer

A.15B.0C.16D.10

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Common mistakes

• Keeping the inequality direction unchanged after multiplying by a negative number.
• Ignoring points where a denominator is zero.

Practical solving approaches

• Find zeros and undefined points before constructing a sign chart.
• Split modulus expressions at their sign-change points and validate each result within its interval.

Inequalities & modulus FAQs

Can I square both sides of an inequality?

Only after checking their signs and whether the operation preserves equivalence. Squaring expressions of unknown sign can change the solution set.

More Algebra practice

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• Quadratic equations & expressions →
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