CMAT · Quantitative Techniques and Data Interpretation
Algebra, numbers and geometry
Equations, number properties, progressions, mensuration, probability.
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- In the exam pattern: CMAT, Quantitative Techniques and Data Interpretation: 20 questions, 80 marks (NTA brochure, 17 Oct 2025).
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Take a full mock →Q1 · Algebra, numbers and geometry · MEDIUM
A cylindrical tank of radius 3 m and height 2 m is full of water. The water is poured into a cuboid tank with a base of 6 m by 2 m. How high does the water stand in the cuboid tank? (Take pi = 3.14.)
Q2 · Algebra, numbers and geometry · EASY
If the roots of the quadratic equation x^2 - 6x + k = 0 are real and distinct, what is the maximum integer value of k?
Q3 · Algebra, numbers and geometry · MEDIUM
A number when divided by 7 leaves a remainder of 3. The same number when divided by 5 leaves a remainder of 2. What is the smallest positive integer that satisfies these conditions?
Q4 · Algebra, numbers and geometry · MEDIUM
Two taps A and B can fill a tank in 12 hours and 15 hours respectively. A leak at the bottom of the tank can empty the full tank in 20 hours. If all three are opened simultaneously, how long will it take to fill the empty tank?
Q5 · Algebra, numbers and geometry · HARD
In a geometric progression where all terms are positive, the second term is 18 and the fourth term is 2. What is the common ratio of the progression?