CAT Quantitative Aptitude — practice questions
90 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice CAT Quantitative Aptitude in the app →Which of the following statements about fractions is correct?In the figure, the whole strip is divided into 8 equal parts and 3 of them are shaded. Which fraction is repreIf @$(A,B)$ denotes the average of $A$ and $B$, /$(A,B)$ denotes the product of $A$ and $B$, and $\times(A,B)$If $A \# B$ denotes the average of $A$ and $B$, $A\$B$ denotes subtraction of $B$ from $A$, and $A im B$ denotGiven that $ qrt[3]{3^x}=5^{1/4}$ and $ qrt[4]{5^y}= qrt{3}$, what is the value of $2xy$?A student claims that $\dfrac{1}{x^b}\times \dfrac{1}{x^c}\times \dfrac{1}{x^a}\times \dfrac{1}{x^b}\times \dfWhat is the simplified form of $\left\{(x^m)^{\frac{1}{m}}\right\}^{\frac{1}{m+1}}$?Simplify $\left(\dfrac{x^a}{x^b}\right)^{a+b}\cdot \left(\dfrac{x^a}{x^{a-b}}\right)^{\frac{a^2}{b}}$.If $(xyz)^4$ is divided by $(x^{-2}y^3)^{-3}(z^{1/2})^6$, what is the simplified result for nonzero $x,y,z$?What least number should be subtracted from 5634 so that the result becomes a perfect square?By what least number should 9900 be multiplied so that the product becomes a perfect square?A piece of land is an isosceles right triangle whose longest side is $98.2\,\mathrm{m}$. What is its perimeterIf $a+\dfrac{1}{a}=5$ for a nonzero real number $a$, then the value of $a^2+\dfrac{1}{a^2}$ isWhich identity is correct?Using prime factorisation, what is the positive square root of $1764$?Which statement correctly distinguishes $ qrt{16}$ from $\pm qrt{16}$?If $N$ is a perfect square, which one of the following cannot be the remainder when $N$ is divided by 4?A natural number greater than 1 is a perfect square. Which of the following remainders is impossible when it iUsing Pascal's triangle, what is the coefficient of $x^2a^3$ in the expansion of $(x+a)^5$?
$ is also a prime, then $x$ can have$P$ is a prime number greater than 5. What is the remainder when $P$ is divided by 6?If 17 is added to the product of two consecutive whole numbers, the result is always a/anS and L are the smallest and the largest $n$-digit natural numbers respectively. $L-S$ is always divisible byOn the number line shown, which one of the marked numbers is irrational?
![](https://qallery.app/diagrams/v2_With the help of the classification tree shown, which of the following statements is correct?
![](https://qalIn a car race, two-third of B's rate is equal to three-fourth of A's rate. If the distance is 1080 km and the Two trains start at the same time from Aligarh and Delhi and proceed towards each other at the rate of $16$ kmA train $150$ m long, travelling at $75$ km per hour overtakes another train travelling in the same direction Two trains start at the same time from two stations and proceed towards each other at the rate of $20$ km/hr aThe distance between two cities A and B is 80 km. A motorcycle rider starts from A towards B at 7 am at a speeIf a train of length $L_1$ km running at a speed of $X$ km/hr crosses a bridge of length $L_2$ km, the time taA train, $140$ metres long, moves at the rate of $36\,\mathrm{kmph}$. How long will it take to pass a certain When two bodies move in the same direction, their relative speed is equal toA train has $320\,\mathrm{km}$ to run. After going $\tfrac{1}{5}$ of the distance, the engine breaks down and Two persons A and B can complete a work in 10 and 15 days respectively, working separately. If they work togetA and B could do a piece of work in 12 days. B and C together do it in 15 days. If A is twice as good a workmaA and B can do a piece of work in 24 days, B and C in 30 days, and C and A in 40 days. How long would all threA can do a piece of work in 10 days, B in 12 days and C in 15 days. They all start the work together, but A leIf three men A, B and C can complete a work in $P$, $Q$ and $R$ days respectively while working alone, then thRam and Shyam together can finish a piece of work in 8 days. Both started the work together. After 3 days, RamA can build a wall in the same time in which B and C together can do it. If A and B together could do it in 10Amar can finish a piece of work alone in 12 days. Atul alone can finish the same work in 24 days. If both of tA can do a piece of work in 25 days and B can do it in 20 days. They work together for 5 days and then A goes An article costs Rs.200, is marked 25% above cost price, and is then sold at a discount of 10% on the marked pA fruit vendor sells apples at cost price but uses a false weight of 960 gm instead of 1 kg. What is his gain A shopkeeper sells two articles at the same selling price. He gains 10% on one and loses 10% on the other. WhaA vessel is full of wine. Ten gallons are drawn off and replaced with water. The operation is repeated once moUsing the alligation diagram shown, what proportion of the three wheat varieties priced at 127 p, 129 p, and 1Two alloys contain zinc and tin in the ratios $3:2$ and $2:3$ respectively. If 7 kg of the first alloy and 21 A mixture of 70 litres of wine and water contains 10% water. How much water must be added so that water becomeSugar costing Rs.14 per kg and Rs.17 per kg is mixed and the mixture is sold at Rs.18 per kg to earn a profit A grocer wants to mix tea costing Rs.40 per kg with tea costing Rs.45 per kg so that the mixture costs Rs.41.5A sector has arc length $l$ and radius $r$. Which expression gives its area?If the radius of a circle is doubled, how do its circumference and area change?A sector is cut from a circle of radius 21 cm with central angle $150^\circ$. What is the length of its arc? TThe minute hand of a clock is 7 cm long. What area does it sweep in 10 minutes? Take $\pi=\dfrac{22}{7}$.For a sector of a circle with radius $r$ and central angle $\theta$ in degrees, which formula gives the lengthIn the figure shown, what forms the boundary of the shaded region?
![](https://qallery.app/diagrams/v2_14fb3eIn the figure shown, which description correctly matches the shaded region?
![](https://qallery.app/diagrams/A circle has circumference $30\pi$ cm. What is its area?If the area of a circle is $25\pi$ sq ft, what is its circumference?A triangle has sides in the ratio $1: qrt{2}: qrt{3}$. If the smallest angle is $\alpha^{\circ}$, what are tIn the given figure, two parallel lines are intersected by a transversal. Find the measure of angle $y$.
![](In the figure, lines $a$ and $b$ are parallel and are cut by a transversal. Which pair is an alternate interioWhich statement about lines in the same plane is correct?If two adjacent angles form a linear pair, which statement is always true?
![](https://qallery.app/diagrams/vIf one angle measures $57^{\circ}$, what is its supplement?Two angles are adjacent if they share the same vertex and a common side, and additionally which condition mustIn the figure, which pair of angles are vertical angles?
![](https://qallery.app/diagrams/v2_14fb3e380ef3/imgWhat is the name of the part of a line that has one endpoint and extends infinitely in one direction?What is the difference between the roots of $x^2-14x+24=0$?What is the quadratic equation whose sum and product of roots are 5 and 6 respectively?Find the minimum value of $x^2-6x+10$ for real $x$.Find $m$ if the equation $x^2+m^2-2mx+3x-5m+3=0$ has roots numerically equal but opposite in sign.Determine $K$ so that one root of the equation $2x^2-5x+2=K$ is zero.Mr. Iyer distributed Rs. 24 amongst his grandchildren. Had there been 4 grandchildren fewer, each would have rFind three consecutive positive integers such that the square of their sum exceeds the sum of their squares byThe sum of a father's age and his son's age is 100 years. One-tenth of the product of their ages exceeds the fA number of two digits is equal to three times the product of its digits. The digit in the ten's place is 2 leExamine the nature of the roots of $x^2+8x+16=0$.What is the discriminant of the quadratic equation $Ax^2+Bx+C=0$?A system of two linear equations in two variables has infinitely many solutions when which condition is satisfSolve the system by elimination: $x+y=7$ and $3x+2y=10$.Using the graph of $3x+2y=12$ and $-x+y=3$, what is the solution of the system?
![](https://qallery.app/diagrFor the pair of linear equations $3x+2y=12$ and $-x+y=3$, what does the graphical solution represent?
![](httThe sum of three consecutive integers is 24. What are the integers?A number divided by 2 is 5 less than the number itself. What is the number?Which of the following is a linear equation in one variable?