CAT 2017 QA Questions: Slot 1 & Slot 2

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 2be 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 15a dozen and an equal number of different candies for Rs 12a 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 1pm and moves towards point $B$ at a uniform speed. A car leaves point $B$ at 2pm 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