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CAT Quantitative Aptitude — practice questions

Explore 14 free Quantitative Aptitude questions in CAT Data Insights. Open each question or exercise to read its content, reference answers and available explanation.

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Quantitative Aptitude questions and exercises with answers

Showing questions 1–14 of 14.

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 →Determine $K$ so that one root of the equation $2x^2-5x+2=K$ is zero.Read the answer and worked solution →Find three consecutive positive integers such that the square of their sum exceeds the sum of their squares by 214.Read the answer and worked solution →The sum of a father's age and his son's age is 100 years. One-tenth of the product of their ages exceeds the father's age by 180. How old is the son?Read the answer and worked solution →Examine the nature of the roots of $x^2+8x+16=0$.Read the answer and worked solution →What is the discriminant of the quadratic equation $Ax^2+Bx+C=0$?Read the answer and worked solution →A system of two linear equations in two variables has infinitely many solutions when which condition is satisfied?Read the answer and worked solution →Solve the system by elimination: $x+y=7$ and $3x+2y=10$.Read the answer and worked solution →The sum of three consecutive integers is 24. What are the integers?Read the answer and worked solution →A number divided by 2 is 5 less than the number itself. What is the number?Read the answer and worked solution →Which of the following is a linear equation in one variable?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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