CAT Questions

Linear Equations

Consider the system of linear equation

x1 + 2x2 + x3 = 3

2x1 + 3x2 + x3 = 3

3x1 + 5x2 + 2x3 = 1

The system has

  1. Infinite no. of solutions
  2. No solution
  3. Unique solution
  4. Exactly 3 solutions

Linear Equations

The number of solutions of the equation 2x + y = 40 where both x and y are positive integers and x ≤ y is:

  1. 7
  2. 13
  3. 14
  4. 18

Linear Equations

Three times the first of three consecutive odd integers is 3 more than twice the third. What is the third integer?

  1. 5
  2. 9
  3. 11
  4. 15

Linear Equations

Which one of the following conditions must p, q and r satisfy so that the following system of linear simultaneous equations has at least one solution, such that p + q + r ≠ 0?

  • x + 2y - 3z = p
  • 2x + 6y - 11z = q
  • x - 2y + 7z = r
  1. 5p - 2q - r = 0
  2. 5p + 2q + r = 0
  3. 5p + 2q - r = 0
  4. 5p - 2q + r = 0

Linear Equations

If x and y are integers, then the equation 5x + 19y = 64 has

  1. A solution for -59 < y < -56
  2. No solution for x > 250 and y > -100
  3. A solution for 250 < x < 300
  4. No solution for x < 300 and y < 0

Linear Equations

Using only 2, 5, 10, 25, and 50 paisa coins, what will be the minimum number of coins required to pay exactly 78 paise, 69 paise and Rs. 1.01 to three different persons?

  1. 17
  2. 18
  3. 19
  4. 20

Linear Equations

What is the value of k for which the following system of equations has no solution: 2x –- 8y = 3 and kx + 4y = 10.

  1. 2
  2. -2
  3. -1
  4. 1

Linear Equations

Two oranges, three bananas and four apples cost Rs.15. Three oranges, two bananas and one apple cost Rs.10. I bought 3 oranges, 3 bananas and 3 apples. How much did I pay?

  1. Rs 8
  2. Rs 10
  3. Rs 12
  4. Rs 15

Linear Equations

In 2004, Rohini was thrice as old as her brother Arvind. In 2014, Rohini was only six years older than her brother. In which year was Rohini born?

  1. 1984
  2. 1986
  3. 1995
  4. 2000

Linear Equations

A firm is thinking of buying a printer for its office use for the next one year. The criterion for choosing is based on the least per-page printing cost. It can choose between an inkjet printer which costs Rs. 5000 and a laser printer which costs Rs. 8000. The per-page printing cost for an inkjet is Rs. 1.80 and that for a laser printer is Rs. 1.50. The firm should purchase the laser printer, if the minimum number of a pages to be printed in the year exceeds

  1. 5000
  2. 10000
  3. 15000
  4. 18000

Linear Equations

Hari’s family consisted of his younger brother (Chari), younger sister (Gouri), and their father and mother. When Chari was born, the sum of the ages of Hari, his father and mother was 70 years. The sum of the ages of four family members, at the time of Gouri’s birth, was twice the sum of ages of Hari’s father and mother at the time of Hari’s birth. If Chari is 4 years older than Gouri, then find the difference in age between Hari and Chari.

  1. 5 years
  2. 6 years
  3. 7 years
  4. 8 years
  5. 9 years

Averages

A car owner buys petrol at Rs. 7.50, Rs. 8 and Rs. 8.50 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 4000 each year?

  1. Rs. 8.50
  2. Rs. 9
  3. Rs. 8
  4. Rs. 7.98

Averages

A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?

  1. Rs. 4991
  2. Rs. 5991
  3. Rs. 6001
  4. Rs. 6991

Averages

A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is

  1. 250
  2. 276
  3. 280
  4. 285

Averages

A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 50% marks is

  1. 2
  2. 3
  3. 4
  4. 5

Averages

The average marks of a student in 10 papers are 80. If the highest and the lowest scores are not considered, the average is 81. If his highest score is 92, find the lowest.

  1. 55
  2. 60
  3. 62
  4. 64

Averages

The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is

  1. 3500
  2. 4000
  3. 4050
  4. 5000

Averages Linear Equations

The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

  1. 22 years
  2. 23 years
  3. 24 years
  4. 25 years

Averages

In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?

  1. 6.25
  2. 6.5
  3. 6.75
  4. 7

Averages

Ten years ago, the ages of the members of a joint family of eight people added up to 231 years. Three years later, one member died at the age of 60 years and a child was born during the same year. After another three years, one more member died, again at 60, and a child was born during the same year. The current average age of this eight-member joint family is nearest to

  1. 21 years
  2. 22 years
  3. 23 years
  4. 24 years

Averages

The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs. 20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is

  1. Rs. 19
  2. Rs. 19.50
  3. Rs. 18
  4. Rs. 18.50

Averages

The average weight of 10 apples is 0.4 kg. If the heaviest and lightest apples are taken out, the average is 0.41 kg. If the lightest apple weights 0.2 kg, what is the weight of heaviest apple?

Averages Quant Sets

In a class of 60, along with English as a common subject, students can opt to major in Mathematics, Physics, Biology or a combination of any two. 6 students major in both Mathematics and Physics, 15 major in both Physics and Biology, but no one majors in both Mathematics and Biology. In an English test, the average mark scored by students majoring in Mathematics is 45 and that of students majoring in Biology is 60. However, the combined average mark in English, of students of these two majors, is 50. What is the maximum possible number of students who major ONLY in Physics?

  1. 30
  2. 25
  3. 20
  4. 15
  5. None of the above

Averages

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

  1. 30
  2. 28
  3. 32
  4. 26

Percentages

A report consists of 20 sheets each of 55 lines and each such line consist of 65 characters. This report is retyped into sheets each of 65 lines such that each line consists of 70 characters. The percentage reduction in number of sheets is closest to

  1. 5
  2. 20
  3. 30
  4. 35

Percentages

If a quantity is increased by 20% and then decreased by 10%, then what is the net increase or decrease?

  1. 10% Decrease
  2. 10% Increase
  3. 8% Increase
  4. 8% Decrease

Percentages

In a stockpile of products produced by three machines M1, M2 and M3, 40% and 30% were manufactured by M1 and M2 respectively. 3% of the products of M1 are defective, 1% of products of M2 defective, while 95% of the products of M3 are not defective. What is the percentage of defective in the stockpile?

  1. 5%
  2. 4%
  3. 3%
  4. 2.5%

Percentages

The pre-paid recharge of Airtel gives 21% less talk time than the same price pre-paid recharge of Vodafone. The post-paid talk time of Airtel is 12% more than its pre-paid recharge, having the same price. Further, the post-paid talk time of same price of Vodafone is 15% less than its pre-paid recharge. How much percent less / more talk time can one get from the Airtel post-paid service compared to the post-paid service of Vodafone?

  1. 3.9% more
  2. 4.7% less
  3. 4.7% more
  4. 2.8% less

Percentages

As a strategy towards retention of customers, the service centre of a split AC machine manufacturer offers discount as per the following rule: for the second service in a year, the customer can avail of a 10% discount; for the third and fourth servicing within a year, the customer can avail of 11% and 12% discounts respectively of the previous amount paid, Finally, if a customer gets more than four services within a year, he has to pay just 55% of the original servicing charges. If Rohan has availed 5 services from the same service centre in a given year, the total percentage discount availed by him is approximately

  1. 16.52
  2. 20.88
  3. 22.33
  4. 24.08

Percentages

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

  1. 13600
  2. 13000
  3. 13400
  4. 14000

Percentages

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 

  1. 16
  2. 13
  3. 10
  4. 7

Ratio Proportion

A fraction, which bears the same ratio to 1/27, that 3/11 does to 5/9, is equal to

  1. 1/11
  2. 3/11
  3. 1/55
  4. 55

Ratio Proportion

A, B and C enter into a partnership and their shares are in ratio 1/2 : 1/3 : 1/4, after 2 months, A withdraws half of his capital and after 10 months, a profit of Rs 378 is divided among them. What is B's share?

  1. Rs 124
  2. Rs 144
  3. Rs 156
  4. Rs 165

Ratio Proportion

From each of the two given numbers, half the smaller number is subtracted. Of the resulting numbers the larger one is three times as large as the smaller. What is the ratio of the two numbers?

  1. 2 : 3
  2. 3 : 2
  3. 3 : 1
  4. 2 : 1

Ratio Proportion

In a certain examination, the number of students who passed, was three times the number of those who were rejected. If there had been 16 fewer candidates and if six more had been rejected, the number of those who passed and of those who were rejected would have been in the ratio 2 : 1. Find the number of candidates?

  1. 120
  2. 130
  3. 136
  4. 156

Ratio Proportion

The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8, then the second number is

  1. 20
  2. 30
  3. 48
  4. 58

Ratio Proportion

A milkman mixes 20 litres of water with 80 litres of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he had sold. What is the current proportion of water to milk?

  1. 3 : 4
  2. 2 : 3
  3. 1 : 3
  4. 1 : 2

Ratio Proportion

A milkman mixes 20 L of water with 80 L of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he has sold. What is the current proportion of water to milk?

  1. 2 : 3
  2. 1 : 2
  3. 1 : 3
  4. 2 : 1

Ratio Proportion

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)?

  1. 201
  2. 205
  3. 207
  4. 210

Time Distance

A train 280 m long is moving at a speed of 60 kmph. What is the time taken by the train to cross a platform 220 m long?

  1. 45 s
  2. 40 s
  3. 35 s
  4. 30 s

Time Distance

A and B walk from X to Y, a distance of 27 km at 5 kmph and 7 kmph respectively. B reaches Y and immediately turns back meeting A at Z. What is the distance from X to Z?

  1. 24 km
  2. 25 km
  3. 20 km
  4. 22.5 km

Time Distance

A man can walk up a moving 'up' escalator in 30 s. The same man can walk down this moving 'up' escalator in 90 s. Assume that his walking speed is same upwards and downwards. How much time will he take to walk up the escalator, when it is not moving?

  1. 30 s
  2. 45 s
  3. 60 s
  4. 90 s

Time Distance

A man travels from A to B at a speed x km/hr. He then rests at B for x hours. He then travels from B to C at a speed 2x km/hr and rests for 2x hours. He moves further to D at a speed twice as that between B and C. He thus reaches D in 16 hr. If distances A-B, B-C and C-D are all equal to 12 km, the time for which he rested at B could be

  1. 2 hr
  2. 3 hr
  3. 4 hr
  4. 6 hr

Time Distance

A train can travel 50% faster than a car. Both start from point A at the same time and reach point B, 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:

  1. 100 kmph
  2. 110 kmph
  3. 120 kmph
  4. 130 kmph

Time Distance

In a watch, the minute hand crosses the hour hand for the third time exactly after every 3 hr 18 min and 15 s of watch time. What is the time gained or lost by this watch in one day?

  1. 13 min 50 s lost
  2. 14 min 40 s gained
  3. 14 min 10 s lost
  4. 13 min 20 s gained

Time Distance

Two boats, traveling at 5 and 10 kms per hour, head directly towards each other. They begin at a distance of 20 kms from each other. How far apart are they (in kms) one minute before they collide?

  1. 1/6
  2. 1/4
  3. 1/3
  4. 1/12

Time Distance

If a man cycles at 10 km/hr, then he arrives at a certain place at 1 PM. If he cycles at 15 km/hr, he will arrive at the same place at 11 AM. At what speed must he cycle to get there at noon?

  1. 11 km/hr
  2. 12 km/hr
  3. 13 km/hr
  4. 14 km/hr

Time Distance

In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is:

  1. 1 hour
  2. 2 hours
  3. 3 hours
  4. 4 hours

Time Distance

It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:

  1. 2 : 3
  2. 3 : 4
  3. 4 : 3
  4. 3 : 2

Time Distance

It takes the pendulum of a clock 7 seconds to strike 4 o'clock. How much time will it take to strike 11 o'clock?

  1. 18 seconds
  2. 19.25 seconds
  3. 20 seconds
  4. 23.33 seconds