CAT 2017 Slot 2 • Quantitative Aptitude

In a $10 \mathrm{~km}$ race. A, B, and C , each running at uniform speed, get the gold, silver, and bronze medals, respectively. If A beats B by $1 \mathrm{~km}$ and B beats C by $1 \mathrm{~km}$, then by how many metres does A beat C?

Bottle $1$ contains a mixture of milk and water in $7: 2$ ratio and Bottle $2$ contains a mixture of milk and water in $9: 4$ ratio. In what ratio of volumes should the liquids in Bottle $1$ and Bottle $2$ be combined to obtain a mixture of milk and water in $3: 1$ ratio?

Arun drove from home to his hostel at $60$ miles per hour. While returning home he drove half way along the same route at a speed of $25$ miles per hour and then took a bypass road which increased his driving distance by $5$ miles, but allowed him to drive at $50$ miles per hour along this bypass road. If his return journey took $30$ minutes more than his onward journey, then the total distance traveled by him is

Out of the shirts produced in a factory, $15 \%$ are defective, while $20 \%$ of the rest are sold in the domestic market. If the remaining $8840$ shirts are left for export, then the number of shirts produced in the factory is

The average height of 22 toddlers increases by 2 inches when two of them leave this group. If the average height of these two toddlers is one-third the average height of the original 22, then the average height, in inches, of the remaining 20 toddlers is

The manufacturer of a table sells it to a wholesale dealer at a profit of $10 \%$. The wholesale dealer sells the table to a retailer at a profit of $30\%$. Finally, the retailer sells it to a customer at a profit of $50\%$. If the customer pays Rs $4290$ for the table, then its manufacturing cost (in Rs) is

A tank has an inlet pipe and an outlet pipe. If the outlet pipe is closed then the inlet pipe fills the empty tank in $8$ hours. If the outlet pipe is open then the inlet pipe fills the empty tank in $10$ hours. If only the outlet pipe is open then in how many hours the full tank becomes half-full?

Mayank buys some candies for Rs $15$ a dozen and an equal number of different candies for Rs $12$ a dozen. He sells all for Rs $16.50$ a dozen and makes a profit of Rs $150$. How many dozens of candies did he buy altogether?

In a village, the production of food grains increased by $40 \%$ and the per capita production of food grains increased by $27\%$ during a certain period. The percentage by which the population of the village increased during the same period is nearest to

If $a, b, c$ are three positive integers such that a and b are in the ratio $3 : 4$ while $b$ and $c$ are in the ratio $2:1$, then which one of the following is a possible value of $(a + b + c)$?

A motorbike leaves point $A$ at $1$ pm and moves towards point $B$ at a uniform speed. A car leaves point $B$ at $2$ pm and moves towards point $A$ at a uniform speed which is double that of the motorbike. They meet at $3:40$ pm at a point which is $168 \mathrm{~km}$ away from $A$ . What is the distance, in km, between $A$ and $B$ ?

Amal can complete a job in $10$ days and Bimal can complete it in $8$ days. Amal, Bimal and Kamal together complete the job in $4$ days and are paid a total amount of Rs $1000$ as remuneration. If this amount is shared by them in proportion to their work, then Kamal's share, in rupees, is

Consider three mixtures - the first having water and liquid A in the ratio $1: 2$, the second having water and liquid B in the ratio $1: 3$, and the third having water and liquid $C$ in the ratio $1: 4$. These three mixtures of $A, B,$ and $C$, respectively, are further mixed in the proportion $4:3:2$. Then the resulting mixture has

Let $ABCDEF$ be a regular hexagon with each side of length $1$ cm. The area (in sq cm) of a square with $AC$ as one side is

The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths $10$ cm and $20$ cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is $12$ cm. If the height of the pillar is $20$ cm, then the total area, in sq cm, of all six surfaces of the pillar is

The points $(2, 5)$ and $(6, 3)$ are two end points of a diagonal of a rectangle. If the other diagonal has the equation $y = 3x + c$, then $c$ is

$$ABCD$ is a quadrilateral inscribed in a circle with centre O. If $\angle COD = 120$ degrees and $\angle BAC = 30$ degrees, then the value of $\angle BCD$ (in degrees) is

If three sides of a rectangular park have a total length $400 \mathrm{ft}$, then the area of the park is maximum when the length (in ft ) of its longer side is

Let $P$ be an interior point of a right-angled isosceles triangle $ABC$ with hypotenuse $AB$ . If the perpendicular distance of P from each of $A B, B C$, and $C A$ is $4(\sqrt{2}-1) \mathrm{cm}$, then the area, in sq cm, of the triangle $A B C$ is

If the product of three consecutive positive integers is $15600$ then the sum of the squares of these integers is

If $x$ is a real number such that $\log_3 5 = \log_5 (2 + x)$, then which of the following is true?

Let $f(x) = x^2$ and $g(x) = 2^x$, for all real $x$. Then the value of $f(f(g(x)) + g(f(x)))$ at $x = 1$ is

The minimum possible value of the sum of the squares of the roots of the equation $x^{2}+(a+3) x-(a+5)=0$ is

If $9^{x-\frac{1}{2}} - 2^{2x-2} = 4^x - 3^{2x-3}$, then x is