CAT Modulus Practice Questions With Solutions

Updated By Nidhi Bahl on 20 Aug, 2025 13:18

Registration Starts On August 01, 2025

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CAT Modulus Practice Questions with Solutions

With regard to the CAT Quant Modulus Practice Test is about enhancing a candidate's problem-solving skills pertaining to the modulus concept, an important topic in the Quantitative Aptitude section of the CAT. Modulus questions test your capability to work with absolute values, understand positive and negative ranges, and solve equations or inequalities involving modulus. The set of CAT Modulus Practice Questions with Solutions on this page aims at further cementing the solution concept so that you apply it to different scenarios and avoid common mistakes.

From solving modulus equations, modulus inequalities, properties of modulus, graphical interpretation, and application-type problems in algebra-the questions can be anything. These practice tests will show you step-by-step how to break down modulus expressions into various cases, carry out substitution accordingly, and reach the right answer within the stipulated time. The modulus questions also require logic along with calculation speed in the CAT. Hence, with enough CAT Modulus Practice Questions with Solutions solved, you shall be able to build your speed and accuracy. 

In general, you may expect 1–2 questions from modulus in the CAT Quant section. To score well, candidates should spend the first few seconds understanding the nature of the modulus problem, identify the range splits, and then apply the relevant case analysis. Practicing regularly will ensure you can solve these questions with confidence during the exam.

CAT Quant Modulus Practice Questions

VARCDILR

Question 1.

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Let 0ax1000 \leq a \leq x \leq 100 and f(x)=xa+x100+xa50f(x) = \mid x - a \mid + \mid x - 100 \mid + \mid x - a - 50\mid. Then the maximum value of f(x) becomes 100 when a is equal to

Question 2.

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The largest real value of a for which the equation x+a+x1=2\mid x + a \mid + \mid x - 1 \mid = 2 has an infinite number of solutions for x is

Question 3.

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The number of integers n that satisfy the inequalities n60<n100<n20\mid n - 60 \mid < \mid n - 100 \mid < \mid n - 20 \mid is

Question 4.

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If r is a constant such that x24x13=r\mid x^2 - 4x - 13 \mid = r has exactly three distinct real roots, then the value of r is

Question 5.

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For a real number x the condition 3x20+3x40=20\mid3x-20\mid+\mid3x-40\mid=20 necessarily holds if

Question 6.

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If 3x+2y+y=73x+2\mid y\mid+y=7 and x+x+3y=1x+\mid x \mid+3y=1 then x+2yx+2y is:

Question 7.

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In how many ways can a pair of integers (x , a) be chosen such that x22x+a2=0x^{2}-2\mid x\mid+\mid a-2\mid=0 ?

Question 8.

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The product of the distinct roots of x2x6=x+2\mid x^2 - x - 6 \mid = x + 2 is

Question 9.

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The shortest distance of the point (12,1)(\frac{1}{2},1) from the curve y = I x -1I + I x + 1I is

Question 10.

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Let f(x)=2x5f(x) =2x-5 and g(x)=72xg(x) =7-2x. Then |f(x)+ g(x)| = |f(x)|+ |g(x)| if and only if

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