Recent questions tagged cat2017-1

Arun's present age in years is $40\%$ of Barun's. In another few years, Arun's age will be half of Barun' s. By what percentage will Barun's age increase during this peri...

If a seller gives a discount of $15\%$ on retail price, she still makes a profit of $2\%$. Which of the following ensures that she makes a profit of $20\%$?Give a discoun...

Ravi invests $50\%$ of his monthly savings in fixed deposits. Thirty percent of the rest of his savings is invested in stocks and the rest goes into Ravi's savings bank a...

A man leaves his home and walks at a speed of $12$ km per hour, reaching the railway station $10$ minutes after the train had departed. If instead he had walked at a spee...

A person can complete a job in $120$ days. He works alone on Day $1$. On Day $2$, he is joined by another person who also can complete the job in exactly $120$ days. On D...

A man travels by a motor boat down a river to his office and back. With the speed of the river unchanged, if he doubles the speed of his motor boat, then his total travel...

A class consists of $20$ boys and $30$ girls. In the mid-semester examination, the average score of the girls was $5$ higher than that of the boys. In the final exam, how...

In a market, the price of medium quality mangoes is half that of good mangoes. A shopkeeper buys $80$ kg good mangoes and $40$ kg medium quality mangoes from the market a...

A stall sells popcorn and chips in packets of three sizes: large, super, and jumbo. The numbers of large, super, and jumbo packets in its stock are in the ratio $7: 17: 1...

The number of girls appearing for an admission test is twice the number of boys. If $30\%$ of the girls and $45\%$ of the boys get admission, the percentage of candidates...

Suppose, $\text{C1, C2, C3, C4}$, and $\text{C5}$ are five companies. The profits made by $\text{C1, C2}$, and $\text{C3}$ are in the ratio $9: 10: 8$ while the profits m...

Let $\text{ABC}$ be a right-angled triangle with $\text{BC}$ as the hypotenuse. Lengths of $\text{AB}$ and $\text{AC}$ are $15$ km and $20$ km, respectively. The minimum ...

Let $\text{ABC}$ be a right-angled isosceles triangle with hypotenuse $\text{BC}$. Let $\text{BQC}$ be a semi-circle, away from A, with diameter $\text{BC}$. Let $\text{B...

A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio $1: 1:8: 27: 27$. The percentage by which the sum of the surface areas of these fi...

The area of the closed region bounded by the equation $\mid x \mid+\mid y \mid= 2$ in the two-dimensional plane is $4\pi$$4$$8$$2\pi$

A ball of diameter $4$ cm is kept on top of a hollow cylinder standing vertically. The height of the cylinder is $3$ cm, while its volume is $9\pi \;\text{cm}^{3}$. Then ...

For how many integers $n$, will the inequality $\left ( n-5 \right )\left ( n-10 \right )-3\left ( n-2 \right )\leq 0$ be satisfied?$10$$11$$12$$9$

If $9^{2x-1}-81^{x-1}= 1944$ then $x$ is$3$$9/4$$4/9$$1/3$

The value of $\log_{0.008}\sqrt{5}+\log_{\sqrt{3}}81-7$ is equal to$1/3$$2/3$$5/6$$7/6$

If $x+1= x^{2}$ and $x 0$, then $2x^{4}$ is$6+4\sqrt{5}$$3+5\sqrt{5}$$5+3\sqrt{5}$$7+3\sqrt{5}$

Suppose, $\log_{3}x= \log_{12}y= a$, where $x, y$ are positive numbers. If $\text{G}$ is the geometric mean of $x$ and $y$, and $\log_{6}\text{G}$ is equal to$\sqrt{a}$$2...

In how many ways can $7$ identical erasers be distributed among $4$ kids in such a way that each kid gets at least one eraser but nobody gets more than $3$ erasers? $16$$...

The shortest distance of the point $\left ( \frac{1}{2}, 1 \right )$ from the curve $y=\mid x-1 \mid+\mid x+1 \mid$ is $1$$0$$\sqrt{2}$$\sqrt{\dfrac{3}{2}}$

Let $\text{AB, CD, EF, GH}$, and $\text{JK}$ be five diameters of a circle with center at $\text{O}$. In how many ways can three points be chosen out of $\text{A, B, C, D...

If $a, b, c$ and $d$ are integers such that $a+b+c+d=30$ , then the minimum possible value of $( a-b )^{2}+( a-c )^{2}+( a-d)^{2}$ is $1$$2$$5$$6$

If $f_{1}\left ( x \right )=x^{2}+11x+n$ and $f_{2}\left ( x \right )=x$, then the largest positive integer $n$ for which the equation $f_{1}\left ( x \right )=f_{2}\left...

If the square of the $7^{\text{th}}$ term of an arithmetic progression with positive common difference equals the products of the $3^{\text{rd}}$ and $17^{\text{th}}$ ter...

If $f( x)=\dfrac{5x+2}{ 3x-5}$ and $g( x )=x^{2}-2x-1,$ then the value of $g( f( f( 3 ) ) )$ is $2$$1/3$$6$$2/3$

Let $a_{1}, a_{2},\ldots, a_{3n}$ be an arithmetic progression with $a_{1} = 3$ and $a_{2}=7$. If $a_{1}+ a_{2}+\ldots +a_{3n}=1830$, then what is the smallest positive...