CAT Quantitative Aptitude MCQ Questions

Arun, Varun and Tarun, if working alone, can complete a task in 24, 21, and 15 days, respectively. They charge Rs 2160, Rs 2400, and Rs 2160 per day, respectively, even if they are employed for a partial day. On any given day, any of the workers may or may not be employed to work. If the task needs to be completed in 10 days or less, then the minimum possible amount, in rupees, required to be paid for the entire task is

Let $3\le x\le 6$ and $[x^2]=[x{]}^2$, where $[x]$ is the greatest integer not exceeding x. If set S represents all feasible values of x, then a possible subset of S is

For any natural number k, let $a_k=3^k$. The smallest natural number m for which $\{(a_1{)}^1\times (a_2{)}^2\times \dots \times (a_{20}{)}^{20}\}<\{a_{21}\times a_{22}\times \dots a_{20+m}\}$, is

In the set of consecutive odd numbers {1, 3, 5, ….., 57}, there is a number of k such that the sum of all the elements less than k is equal to the sum of all the elements greater than k. Then, k equals.

A value of c for which the minimum value of $f(x)=x^2-4cx+8c$ is greater than the maximum value of $g(x)=-x^2+3cx-2c$, is

If $a-6b+6c=4$ and $6a+3b-3c=50$, where a, b and c are real numbers, the value of $2a+3b-3c$ is

The (x, y) coordinates of vertices P, Q and R of a parallelogram PQRS are (-3, -2), (1, -5) and (9, 1), respectively. If the diagonal SQ intersects the x-axis at (a, 0), then the value of a is

A cafeteria offers 5 types of sandwiches. Moreover, for each type of sandwich, a customer can choose one of 4 breads and opt for either small or large sized sandwich. Optionally, the customer may also add up to 2 out of 6 available sauces. The number of different ways in which an order can be placed for a sandwich, is

At a certain simple rate of interest, a given sum amounts to Rs.13920 in 3 years, and to Rs 18960 in 6 years and 6 months. If the same given sum had been invested for 2 years at the same rate as before but with interest compounded every 6 months, then the total interest earned, in rupees, would have been nearest to

Five countries engage in trade with each other. Each country levies import tariffs on the other countries. The import tariff levied by Country X on Country Y is calculated by multiplying the corresponding tariff percentage with the total imports of Country X from Country Y.
The radar chart below depicts different import tariff percentages charged by each of the five countries on the others. For example, US (the blue line in the chart) charges 20%, 40%, 30%, and 30% import tariff percentages on imports from France, India, Japan, and UK, respectively. The bar chart depicts the import tariffs levied by each county on other countries. For example, US charged import tariff of 3 billion USD on UK.

Assume that imports from one country to another equals the exports from the latter to the former.
The trade surplus of Country X with Country Y is defined as follows Trade surplus = Exports from Country X to Country Y - Imports to Country X from Country Y.

A negative trade surplus is called trade deficit.

How much is Japan's export to India worth?

Shruti travels a distance of 224 km in four parts for a total travel time of 3 hours. Her speeds in these four parts follow an arithmetic progression, and the corresponding time taken to cover these four parts follow another arithmetic progression. If she travels at a speed of 960 meters per minute for 30 minutes to cover the first part, then the distance, in meters, she travels in the fourth part is

A container holds 200 litres of a solution of acid and water, having 30% acid by volume. Atul replaces 20% of this solution with water, then replaces 10% of the resulting solution with acid, and finally replaces 15% of the solution thus obtained, with water. The percentage of acid by volume in the final solution obtained after these three replacements, is nearest to

In a circle with center C and radius $6\sqrt{2}$ cm, PQ and SR are two parallel chords separated by one of the diameters. If $\angle PQC=45^{\circ }$, and the ratio of the perpendicular distance of PQ and SR from C is 3:2, then the area, in sq. cm, of the quadrilateral PQRS is

The number of distinct integers n for which ${\log }_{(1/4)}(n^2-7n+11)>0$, is

The ratio of the number of students in the morning shift and afternoon shift of a school was 13 : 9. After 21 students moved from the morning shift to the afternoon shift, this ratio became 19 : 14. Next, some new students joined the morning and afternoon shifts in the ratio 3 : 8 and then the ratio of the number of students in the morning shift and the afternoon shift became 5 : 4. The number of new students who joined is

Five countries engage in trade with each other. Each country levies import tariffs on the other countries. The import tariff levied by Country X on Country Y is calculated by multiplying the corresponding tariff percentage with the total imports of Country X from Country Y.
The radar chart below depicts different import tariff percentages charged by each of the five countries on the others. For example, US (the blue line in the chart) charges 20%, 40%, 30%, and 30% import tariff percentages on imports from France, India, Japan, and UK, respectively. The bar chart depicts the import tariffs levied by each county on other countries. For example, US charged import tariff of 3 billion USD on UK.

Assume that imports from one country to another equals the exports from the latter to the former.
The trade surplus of Country X with Country Y is defined as follows Trade surplus = Exports from Country X to Country Y - Imports to Country X from Country Y.

A negative trade surplus is called trade deficit.

Among France and UK, who has/have trade surplus(es) with US?

Five countries engage in trade with each other. Each country levies import tariffs on the other countries. The import tariff levied by Country X on Country Y is calculated by multiplying the corresponding tariff percentage with the total imports of Country X from Country Y.
The radar chart below depicts different import tariff percentages charged by each of the five countries on the others. For example, US (the blue line in the chart) charges 20%, 40%, 30%, and 30% import tariff percentages on imports from France, India, Japan, and UK, respectively. The bar chart depicts the import tariffs levied by each county on other countries. For example, US charged import tariff of 3 billion USD on UK.

Assume that imports from one country to another equals the exports from the latter to the former.
The trade surplus of Country X with Country Y is defined as follows Trade surplus = Exports from Country X to Country Y - Imports to Country X from Country Y.

A negative trade surplus is called trade deficit.

What is the trade surplus/trade deficit of India with UK?

Five countries engage in trade with each other. Each country levies import tariffs on the other countries. The import tariff levied by Country X on Country Y is calculated by multiplying the corresponding tariff percentage with the total imports of Country X from Country Y.
The radar chart below depicts different import tariff percentages charged by each of the five countries on the others. For example, US (the blue line in the chart) charges 20%, 40%, 30%, and 30% import tariff percentages on imports from France, India, Japan, and UK, respectively. The bar chart depicts the import tariffs levied by each county on other countries. For example, US charged import tariff of 3 billion USD on UK.

Assume that imports from one country to another equals the exports from the latter to the former.
The trade surplus of Country X with Country Y is defined as follows Trade surplus = Exports from Country X to Country Y - Imports to Country X from Country Y.

A negative trade surplus is called trade deficit.

Which among the following is the highest?