CSAT › Quantitative Aptitude – UPSC Prelims PYQs

In a tournament 14 teams play league matches. If each team plays against every other team once only then how many matches are played?

Two trains leave New Delhi at the same time. One travels north at 60 kmph and the other travels south at 40 kmph. After how many hours will the trains be 150 km apart?

A question paper had ten questions. Each question could only be answered as True (T) or False (F). Each candidate answered all the questions. Yet, no two candidates wrote the answers in an identical sequence. How many different sequences of answers are possible?

Running at a speed of 60 km per hour, a train passed through a 1.5 km long tunnel in two minutes. What is the length of the train?

A person X has four notes of Rupee 1, 2, 5 and 10 denomination. The number of different sums of money she can form from them is

Two numbers X and Y are respectively 20% and 28% less than a third number Z. By what percentage is the number Y less than the number X?

A person travelled a distance of 50 km in 8 hours. He covered a part of the distance on foot at the rate of 4 km per hour and a part on a bicycle at the rate of 10 km per hour. How much distance did he travel on foot ?

How many numbers from 0 to 999 are NOT divisible by either 5 or 7?

Each person's performance compared with all other persons is to be done to rank them subjectively. How many comparisons are needed in total, if there are 11 persons?

Three men start together to travel the same way around a circular track of 11 km. Their speeds are 4, 5.5 and 8 kmph respectively. When will they meet at the starting point for the first time?

A man fills a basket with eggs in such a way that the number of eggs added on each successive day is the same as the number already present in the basket. This way the basket gets completely filled in 24 days. After how many days was the basket 1⁄4th full?

The diameters of two circular coins are in the ratio of 1 : 3. The smaller coin is made to roll around the bigger coin till it returns to the position from where the process of rolling started. How many times did the smaller coin roll around the bigger coin?

The difference between the simple interest received from two banks on Rs. 500 for two years is Rs. 2·50. What is the difference between their rates?

When ten persons shake hands with one another, in how many ways is it possible?

A candidate attempted 12 questions and secured full marks in all of them. If he obtained 60% marks in the test and all questions carried equal marks, then what is the total number of questions in the test?

In how many ways can four children be made to stand in a line such that two of them, A and B, are always together?

A person has 4 coins each of different denomination. What is the number of different sums of money the person can form (using one or more coins at a time)?

How many numbers lie between 300 and 500 in which 4 comes only one time?

How many three-digit numbers can be generated from 1, 2, 3, 4, 5, 6, 7, 8, 9 such that the digits are in ascending order?

There are four persons A, B, C, D; and A has some coins. A gave half of the coins to B and 4 more besides. B gave half of the coins to C and 4 more besides. C gave half of the coins to D and 4 more besides. Both B and D end up with same number of coins. How many coins did A have originally?

While adding the first few continuous natural numbers, a candidate missed one of the numbers and wrote the answer as 177. What was the number missed?

Four metal rods of lengths 78 cm, 104 cm, 117 cm and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut?

In an examination, there are three subjects A, B and C. A student has to pass in each subject. 20% students failed in A, 22% students failed in B and 16% failed in C. The total number of students passing the whole examination lies between

How many times are an hour hand and a minute hand of a clock at right angles during their motion from 1.00 p.m. to 10.00 p.m.?

There are 240 balls and n number of boxes B1, B2, B3, … , Bn. The balls are to be placed in the boxes such that B1 should contain 4 balls more than B2, B2 should contain 4 balls more than B3, and so on.

Which one of the following cannot be the possible value of n?

In a carrom board game competition, m boys and n girls (m > n > 1) of a school participate in which every student has to play exactly one game with every other student. Out of the total games played, it was found that in 221 games one player was a boy and the other player was a girl. Consider the following statements :

1. The total number of students that participated in the competition is 30.
2. The number of games in which both players were girls is 78.

Which of the statements given above is/are correct ?

What is the number of terms in the series 117, 120, 123, 126, ..., 333?

In how many different ways can four books A, B, C and D be arranged one above another in a vertical order such that the books A and B are never in continuous position?

Carpenter A can make a chair in 6 hours, carpenter B in 7 hours and carpenter C in 8 hours. If each carpenter works for 8 hours per day, how many chairs will be made in 21 days?

A person purchases 100 pens at a discount of 10%. The net amount of money spent by the person to purchase the pens is Rs 600. The selling expenses incurred by the person are 15% on the net cost price. What should be the selling price for 100 pens in order to earn a profit of 25%?

A schoolteacher has to select the maximum possible number of different groups of 3 students out of a total of 6 students. In how many groups any particular student will be included?

In an examination, 70% of the students passed in the Paper I, and 60% of the students passed in the Paper II. 15% of the students failed in both the papers while 270 students passed in both the papers. What is the total number of students?

March 1, 2008 was Saturday. Which day was it on March 1, 2002?

Which one of the following is the correct sequence in respect of the Roman numerals—C, D, L and M?

In how many different ways can all of 5 identical balls be placed in the cells shown above such that each row contains at least 1 ball?

There are 6 different letters and 6 correspondingly addressed envelopes. If the letters are randomly put in the envelopes, what is the probability that exactly 5 letters go into the correctly addressed envelopes?

There are two identical red, two identical black and two identical white balls. In how many different ways can the balls be placed in the cells (each cell to contain one ball) shown above such that balls of the same colour do not occupy any two consecutive cells?

(Each small circle represents a different station) Refer to the figure showing a network between station A and station B. What is the maximum number of different paths that exist between station A and station B?

In how many maximum different ways can 3 identical balls be placed in 12 squares (each ball is placed in the exact centre of a square) shown in the figure above such that they do not lie along the same straight line? The original figure is not available for this question.

In the figure shown above, what is the maximum number of different ways in which 8 identical balls can be placed in small triangles 1, 2, 3 and 4 such that each triangle contains at least one ball?

Amit has five friends: 3 girls and 2 boys. Amit’s wife also has five friends: 3 boys and 2 girls. In how many maximum different ways can they invite 2 boys and 2 girls such that two of them are Amit’s friends and two are his wife’s friends?

Five balls of different colours are to be placed in three different boxes such that any box contains at least one ball. What is the maximum number of different ways in which this can be done?

All six letters of the name SACHIN are arranged to form different words without repeating any letter in any one word. The words so formed are then arranged as a dictionary. What will be the position of the word SACHIN in that sequence?

Three dice (each having six faces with each face showing one number from 1 to 6) are rolled. What is the number of possible outcomes such that at least one die shows the number 2?

Groups, each containing 3 boys, are to be formed out of 5 boys – A, B, C, D and E – such that no one group contains both C and D together. What is the maximum number of different groups?

Each of the 3 persons is to be given some identical items such that the product of the numbers of items received by each of the three persons is equal to 30. In how many maximum different ways can this distribution be done?

Six equidistant vertical lines are drawn on a board. Six equidistant horizontal lines are also drawn on the board cutting the six vertical lines and the distance between any two consecutive horizontal lines is equal to that between any two consecutive vertical lines. What is the maximum number of squares thus formed?

A person has to completely put each of three liquids – 403 litres of petrol, 465 litres of diesel and 496 litres of mobile oil – in bottles of equal size without mixing any of the three types of liquids such that each bottle is completely filled. What is the least possible number of bottles required?

A and B can complete work together in 5 days. If A works at twice his speed and B at half of his speed, this work can be finished in 4 days. How many days would it take for A alone to complete the job?

If all the numbers from 501 to 700 are written, what is the total number of times the digit 6 appears?