CSAT › Quantitative Aptitude – UPSC Prelims PYQs

Amit starts from a point A, walks to another point B and then returns from B to A by his car, taking a total time of 6 hours 45 minutes. If he had driven both ways in his car, he would have taken 2 hours less. How long would it take for him to walk both ways?

A watch showed a time of fourteen minutes past nine (9 hrs 14 minutes). The positions of the hour-hand and the minute-hand of the watch are exactly interchanged. The new time shown by the watch is closest to which one of the following?

Each of 8 identical balls is to be placed in the squares shown in the figure given above in a horizontal direction such that one horizontal row contains 6 balls and the other horizontal row contains 2 balls. In how many maximum different ways can this be done?

In a tournament each of the participants was to play one match against each of the other participants. 3 players fell ill after each of them had played three matches and had to leave the tournament. What was the total number of participants at the beginning, if the total number of matches played was 75 ?

A box contains 5 sets of balls while there are 3 balls in each set. Each set of balls has one colour which is different from every other set. What is the least number of balls that must be removed from the box in order to claim with certainty that a pair of balls of the same colour has been removed?

3 digits are chosen at random from 1, 2, 3, 4, 5, 6, 7, 8 and 9 without repeating any digit. What is the probability that their product is odd?

In a question paper, there are four multiple-choice questions. Each question has five choices with only one choice for its correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?

Each of the persons A, B, C, D and E possesses unequal number (<10) of similar items. A, B and C possess 21 items in all, while C, D and E possess 7 items in all. How many items do A and B possess in all?

There are three parallel straight lines. Two points A and B are marked on the first line, points C and D are marked on the second line, and points E and F are marked on the third line. Each of these six points can move to any position on its respective straight line. Consider the following statements:

1. The minimum number of triangles that can be formed by joining these points is zero.
2. The maximum number of triangles that can be formed by joining these points is twenty.

Which of the statements given above is/are correct?

A mixed doubles tennis game is to be played between two teams (each team consists of one male and one female). There are 4 married couples. No team is to consist of a husband and his wife. What is the maximum number of games that can be played?

How many numbers are there in all 6000 to 6999 (both 6000 and 6999 included) having at least one of their digits repeated?

Each of 2 women and 3 men is to occupy one chair out of 8 chairs, each of which is numbered from 1 to 8. First, women are to occupy any two chairs from those numbered 1 to 4; and then 3 men would occupy any three chairs out of the remaining 6 chairs. What is the maximum number of different ways in which this can be done?

Left pan of a faulty balance weighs 100 gram more than its right pan. A shopkeeper keeps the weight measure in the left pan while buying goods but keeps it in the right pan while selling his goods. He uses only 1 kg weight measure. If he sells his goods at the listed cost price, what is his gain?

On a railway route between two places A and B, there are 10 stations on the way. If 4 new stations are to be added, how many types of new tickets will be required if each ticket is issued for a one-way journey?

Aryan runs at a speed of 40 metre/minute. Rahul follows him after an interval of 5 minutes and runs at a speed of 50 metre/minute. Rahul’s dog runs at a speed of 60 metre/minute and starts along with Rahul. The dog reaches Aryan and then comes back to Rahul, and continues to do so till Rahul reaches Aryan. What is the total distance covered by the dog?

A big rectangular plot of area 4320 m² is divided into 3 square-shaped smaller plots by fencing parallel to the smaller side of the plot. However some area of land was still left as a square could not be formed. So, 3 more square-shaped plots were formed by fencing parallel to longer side of the original plot such that no area of the plot was left surplus. What are the dimensions of the original plot?

2 men and 1 woman board a bus in which 5 seats are vacant. One of these five seats is reserved for ladies. A woman may or may not sit on the seat reserved for ladies but a man can not sit on the seat reserved for ladies. In how many different ways can the five seats be occupied by these three passengers?

A square is divided into 9 identical smaller squares. Six identical balls are to be placed in these smaller squares such that each of the three rows gets at least one ball (one ball in one square only). In how many different ways can this be done?

There are 6 persons – A, B, C, D, E and F. They are to be seated in a row such that B never sits anywhere ahead of A. In how many different ways can this be done?

300 persons are participating in a meeting, out of which 120 are foreigners and the rest are Indians. Out of the Indians there are 110 men who are not judges; 160 are men judges, and 35 are women judges. There are no foreign judges. How many Indian women attended the meeting?

Ten identical particles are moving randomly inside a closed box. What is the probability that at any given point of time all ten particles will be lying in the same half of the box?

An equilateral triangular plate is to be cut into a number of identical small equilateral triangular plates.

Which one of the following can be a possible value of n?

There are 10 identical coins and each one of them has ‘H’ engraved on one face and ‘T’ engraved on the other face. These 10 coins are lying on a table and each one of them has the ‘H’ face as the upper face. In one attempt, exactly four (neither more nor less) coins can be turned upside down. What is the minimum number of attempts in which the ‘T’ faces of all the 10 coins can be brought to be the upper faces?

Two cars X and Y start from two places A and B respectively which are 700 km apart at 9 a.m. Both the cars run at an average speed of 60 km/hr. Car X stops at 10 a.m. and again starts at 11 a.m. while the other car Y continues to run without stopping. When do the two cars cross each other?

In a question of a test paper, there are five items each under List-A and List-B. The examinees are required to match each item under List-A with its corresponding correct item under List-B. Further, it is given that

1. No examinee has given the correct answer
2. Answers of no two examinees are identical

What is the maximum number of examinees who took this test?

A and B start from the same point and in the same direction at 7 a.m. to walk around a rectangular field 400 m × 300 m. A and B walk at the rate of 3 km/hr and 2.5 km/hr respectively.

How many times shall they cross each other if they continue to walk till 1 and 2.30 p.m.?

Nine different letters are to be dropped in three different letter boxes. In how many different ways can this be done?

How many three-digit even numbers are there such that 9 comes as a succeeding digit in any number only when 7 is the preceding digit, and 7 is the preceding digit only when 9 is the succeeding digit?

In how many different ways can six players be arranged in a line such that two of them, Ajit and Mukherjee, are never together?

50 men or 80 women can finish a job in 50 days. A contractor deploys 40 men and 48 women for this work, but after every duration of 10 days, 5 men and 8 women are removed till the work is completed. The work is completed in

Three students are picked at random from a school having a total of 1000 students. The probability that these three students will have identical date and month of their birth is

Three flags, each of different colour, are available for a military exercise. Using these flags, different codes can be generated by waving i) a single flag of different colours, or ii) any two flags in a different sequence of colours, or iii) three flags in a different sequence of colours. The maximum number of codes that can be generated is

A car travels the first one-third of a certain distance with a speed of 10 km/hr, the next one-third distance with a speed of 20 km/hr and the last one-third distance with a speed of 60 km/hr. The average speed of the car for the whole journey is

‘A’ walks around a circular field at the rate of one round per hour while ‘B’ runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at

Four different candles, which can last for 5 hours, 4 hours, 3 hours and 2 hours of burning, respectively, are lit in a room at the same instant and allowed to burn till such time that the three candles in the room get extinguished. The cost of burning each one of these candles is 75 paise per hour. The cost involved is:

A two-member committee comprising of one male and one female member is to be constituted out of five males and three females. Amongst the females, Ms. A refuses to be a member of the committee in which Mr. B is taken as the member. In how many different ways can the committee be constituted?

Three bells toll at intervals of 9, 12 and 15 minutes respectively. All three begin to toll at 8 a.m. At what time will they first toll together again?

Total time taken by a person in going to a place by walking and returning on cycle is 5 hours 45 minutes. He would have gained 2 hours by cycling both ways. The time taken by him to walk both ways is

‘A’ and ‘B’ are two fixed points in a field. A cyclist C moves such that ACB is always a right angle. In this context, which one of the following statements is correct?

A complete cycle of a traffic light takes 60 seconds. During each cycle the light is green for 25 seconds, yellow for 5 seconds and red for 30 seconds. At a randomly chosen time, the probability that the light will not be green is

A trader fixed the price of an article in such a way that by giving a rebate of 10 % on the price fixed he made a profit of 15 %. If the cost of the article is Rs 72, the price fixed on it is

Consider the volumes of the following:

1. A parallelepiped of length 5 cm, breadth 3 cm and height 4 cm
2. A cube of each side 4 cm
3. A cylinder of radius 3 cm and length 3 cm
4. A sphere of radius 3 cm The volumes of these in the decreasing order is

A train of length 150 metres, moving at a speed of 90 km/hr can cross a 200-metre bridge in

The age of a man is three times the sum of the ages of his two sons. Five years hence, his age will be double the sum of the ages of his sons. The father’s present age is

The length of the longest pole that can be placed in a room 12 m long and 9 m wide and 8 m high is

In a company 60 % of the employees are men. Of these, 40 % are drawing more than Rs 50,000 per year. If 36 % of the total employees of the company draw more than Rs 50,000 per year, what is the percentage among women who are drawing less than Rs 50,000 per year?

A bus is moving at 30 km/h, and a car is coming from behind at 50 km/h. How far apart are they if it takes 15 minutes for the car to catch up with the bus?

Two ladies simultaneously leave cities A and B connected by a straight road and travel towards each other. The first lady travels 2 km/hr faster than the second lady and reaches B one hour before the second lady reaches A. The two cities A and B are 24 km apart. How many kilometres does each lady travel in one hour?

Amit started a business by investing Rs 30,000. Rahul joined the business after some time and invested Rs 20,000. At the end of the year, profit was divided in the ratio of 2 :

1. After how many months did Rahul join the business?

The time in the wall clock is 3.25; the acute angle between the hours hand and the minutes hand is