CAT 2017 PYQsQuantitative Ability. Free, no login required.

The numbers $1, 2,..., 9$ are arranged in a $3 \times 3$ square grid in such a way that each number occurs once and the entries along each column, each row, and each of the two diagonals add up to the same value.

If the top left and the top right entries of the grid are $6$ and $2$, respectively, then the bottom middle entry is

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

If $\log (2^a \times 3^b \times 5^c)$ is the arithmetic mean of $\log (2^2 \times 3^3 \times 5)$, $\log (2^6 \times 3 \times 5^7)$, and $\log (2 \times 3^2 \times 5^4)$, then a equals

Let $a_1, a_2, a_3, a_4, a_5$ be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with $2a_3$.

If the sum of the numbers in the new sequence is $450$, then $a_5$ is

How many different pairs $(a, b)$ of positive integers are there such that $a ≤ b$ and $\frac{1}{a} + \frac{1}{b} = \frac{1}{9}$

In how many ways can $8$ identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least $1$ pen, Bimal gets at least $2$ pens, and Kamal gets at least $3$ pens?

How many four digit numbers, which are divisible by $6$, can be formed using the digits $0, 2, 3, 4, 6$, such that no digit is used more than once and $0$ does not occur in the left-most position?

If $f(ab) = f(a)f(b)$ for all positive integers $a$ and $b$, then the largest possible value of $f(1)$ is

Let $f(x) = 2x – 5$ and $g(x) = 7 – 2x$. Then $|f(x) + g(x)| = |f(x)| + |g(x)|$ if and only if

An infinite geometric progression $a_1, a_2, a_3,...$ has the property that $a_n = 3(a_{n+1} + a_{n+2} +....)$ for every $n \ge 1$. If the sum $a_1 + a_2 + a_3 +..... = 32$, then $a_5$ is

If $\mathrm{a}_{1}=\frac{1}{2 \times 5}, \mathrm{a}_{2}=\frac{1}{5 \times 8}, \mathrm{a}_{3}=\frac{1}{8 \times 11}$, then $\mathrm{a}_{1,}+\mathrm{a}_{2,}+\mathrm{a}_{3,}+\ldots . . \mathrm{a}_{100}$ is