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CAT Data Insights — practice by topic

Browse 103 questions across 29 Data Insights topics. Choose what you want to revise, then open a question to check its answer and worked solution.

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Data Insights topics

Averages and Mixtures (30)Descriptive Statistics (30)DI — Bar & Column Charts (26)DI — Pie Charts (26)DI — Tables (26)CAT DILR — Caselets (14)Quantitative Aptitude (14)Data Interpretation (9)Analogies (7)Analogy (7)Blood Relations (7)Calendar (7)Classification (7)Coding and Decoding (7)Dice And Cubes (7)Distance and Direction (7)Floor Puzzle (7)Inequalities (7)Logical Reasoning (7)Mirror And Water Images (7)Odd One Out (7)Reasoning & Aptitude (7)Seating Arrangements (7)Series (7)Sets and Venn Diagrams (7)Syllogisms (7)Venn Diagrams (7)Coding Decoding (3)Number Series, Coding and Decoding and Odd Man Out (3)

Try a Data Insights question

What is the difference between the roots of $x^2-14x+24=0$?Read the answer and worked solution →What is the quadratic equation whose sum and product of roots are 5 and 6 respectively?Read the answer and worked solution →Find the minimum value of $x^2-6x+10$ for real $x$.Read the answer and worked solution →Find $m$ if the equation $x^2+m^2-2mx+3x-5m+3=0$ has roots numerically equal but opposite in sign.Read the answer and worked solution →

Worked practice questions

What is the difference between the roots of $x^2-14x+24=0$?

  1. 2
  2. 4
  3. 10
  4. 14
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Correct answer: C. 10

For $x^2-14x+24=0$, the discriminant is $D=b^2-4ac=(-14)^2-4(1)(24)=196-96=100$. The roots are $\frac{14\pm\sqrt{100}}{2}=\frac{14\pm10}{2}$, so they are 12 and 2. Their difference is $10$.

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What is the quadratic equation whose sum and product of roots are 5 and 6 respectively?

  1. $x^2+5x+6=0$
  2. $x^2-5x+6=0$
  3. $x^2-6x+5=0$
  4. $x^2+6x+5=0$
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Correct answer: B. $x^2-5x+6=0$

If the sum of roots is $S$ and the product is $P$, the monic quadratic equation is $x^2-Sx+P=0$. Here $S=5$ and $P=6$, so the equation is $x^2-5x+6=0$.

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Find the minimum value of $x^2-6x+10$ for real $x$.

  1. 0
  2. 1
  3. 2
  4. 4
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Correct answer: B. 1

**Complete the square:** $x^2-6x+10=(x-3)^2+1$. Since $(x-3)^2\ge 0$ for all real $x$, the minimum value occurs when $(x-3)^2=0$, that is at $x=3$. **Therefore the minimum value is $1$.**

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How to practise

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