100+ Arithmetic CAT Questions and Answers PDF Download

Overview: Regular practice of Arithmetic CAT questions 2026 is very important if you want to score well in the final exam. To help you out, we have provided the important formulas and key CAT arithmetic questions that will boost your preparation and give you an extra edge in the CAT 2026 exam

• This section forms a major part of the Quantitative Aptitude portion and checks your understanding of basic maths concepts like percentages, profit and loss, simple and compound interest, time and work, and ratio and proportion. 

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• These topics may seem simple, but they often appear in tricky ways in the exam. Practising them regularly helps you get faster, more accurate, and also makes it easier to identify and improve your weak areas.

This article offers an in-depth analysis of Arithmetic CAT questions, covering the CAT syllabus, weightage, strategies, and tips for mastering this crucial segment.

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Basics for Understanding Arithmetic CAT Questions 2026

Arithmetic forms a crucial part of the Quantitative Ability section in the CAT exam. Mastering arithmetic concepts is essential as CAT arithmetic questions often test your problem-solving speed and accuracy on topics like percentages, ratios, time, work, and more.

1) Number Systems

Number systems form the backbone of arithmetic. It includes the study of various types of numbers and their properties.

• Natural Numbers (N): Positive integers starting from 1 (1, 2, 3, ...).
• Whole Numbers (W): Natural numbers including zero (0, 1, 2, 3, ...).
• Integers (Z): All positive and negative whole numbers, including zero (..., -2, -1, 0, 1, 2, ...).
• Rational Numbers (Q): Numbers that can be expressed as a fraction of two integers where the denominator is not zero (e.g., 1/2, -3/4).
• Irrational Numbers: Numbers that cannot be expressed as a simple fraction (e.g., √2, π).
• Real Numbers (R): All rational and irrational numbers.
• Prime Numbers: Natural numbers greater than 1 with no positive divisors other than 1 and itself (e.g., 2, 3, 5, 7).
• Composite Numbers: Natural numbers greater than 1 that are not prime (e.g., 4, 6, 8, 9).

Check: Important Formulas for the CAT exam

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Important List of Arithmetic CAT Questions for 2026

Here is the list of important easy-level arithmetic questions for CAT 2026:

Q1. A shopkeeper gives a discount of 10% on a shirt marked at Rs. 500. What is the selling price?

1. Rs. 450
2. Rs. 460
3. Rs. 470
4. Rs. 480

Answer: A. Rs. 450

Q2. A person covers a distance of 120 km in 3 hours. What is the speed?

1. 30 km/hr
2. 40 km/hr
3. 50 km/hr
4. 60 km/hr

Answer: B. 40 km/hr

Q3. Find the average of the first 5 odd numbers.

1. 4
2. 5
3. 6
4. 7

Answer: B. 5

Q4. A man spends 80% of his income. If his income is Rs. 40,000, what is his savings?

1. Rs. 6,000
2. Rs. 7,000
3. Rs. 8,000
4. Rs. 9,000

Answer: C. Rs. 8,000

Q5. A train travels 60 km in 1.5 hours. What is the speed in km/hr?

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

Answer: C. 40

Q6. A number is first increased by 20% and then decreased by 20%. What is the net change in the number?

1. No change
2. Decreased by 4%
3. Increased by 4%
4. Decreased by 2%

Answer: B. Decreased by 4%

Q7. A student scored 72 marks in English and 86 marks in Maths out of 100 each. What percent of total marks did the student score?

1. 70%
2. 72%
3. 79%
4. 81%

Answer: C. 79%

Q8. What is the simple interest on Rs. 4,000 at 8% per annum for 2.5 years?

1. Rs. 700
2. Rs. 800
3. Rs. 900
4. Rs. 1,000

Answer: B. Rs. 800

Q9. At what rate of simple interest does a sum double itself in 12 years?

6. 6.67%
7. 8%
8. 8.33%
9. 10%

Answer: C. 8.33%

Q10. If A:B = 2:3 and B:C = 4:5, what is A:B:C?

1. 8:12:15
2. 2:3:5
3. 4:6:10
4. 6:9:15

Answer: A. 8:12:15

Q11. Divide Rs. 1,260 among A, B and C in the ratio 1:2:3. How much does B get?

1. Rs. 210
2. Rs. 420
3. Rs. 630
4. Rs. 315

Answer: B. Rs. 420

Q12. If 15 men can do a work in 12 days, how many men are needed to do the same work in 9 days?

1. 16
2. 18
3. 20
4. 24

Answer: C. 20

Q13. The average of 5 consecutive numbers is 25. What is the largest number?

1. 27
2. 28
3. 29
4. 30

Answer: A. 27

Q14. A batsman's average in 15 innings is 36. In his 16th innings he scores 80. What is his new average?

1. 38
2. 38.75
3. 39
4. 40

Answer: B. 38.75

Q15. The average of 10 numbers is 40. One number 35 is replaced by 55. What is the new average?

1. 41
2. 42
3. 43
4. 44

Answer: B. 42

Q16. The LCM of two numbers is 84 and their HCF is 7. If one of the numbers is 28, what is the other?

1. 14
2. 21
3. 42
4. 63

Answer: B. 21

Q17. Find the sum of first 20 terms of the AP: 5, 8, 11, 14 ...

1. 640
2. 670
3. 710
4. 750

Answer: B. 670

Q18. The area of a circle is 154 sq. cm. What is its circumference? (use π = 22/7)

1. 40 cm
2. 44 cm
3. 48 cm
4. 52 cm

Answer: B. 44 cm

Q19. The perimeter of a square is 40 cm. What is its area?

1. 90 sq. cm
2. 95 sq. cm
3. 100 sq. cm
4. 110 sq. cm

Answer: C. 100 sq. cm

Q20. The diagonal of a square is 10√2 cm. What is the area of the square?

1. 100 sq. cm
2. 150 sq. cm
3. 200 sq. cm
4. 120 sq. cm

Answer: A. 100 sq. cm

Q21. The radius of a sphere is doubled. By what factor does its volume increase?

1. 2
2. 4
3. 6
4. 8

Answer: D. 8

Q22. The sum of three consecutive even numbers is 78. What is the largest number?

1. 24
2. 26
3. 28
4. 30

Answer: C. 28

Q23. A number when divided by 6 gives quotient 5 and remainder 4. What is the number?

1. 30
2. 34
3. 36
4. 40

Answer: B. 34

Q24. The digit in the unit's place of the product 459 × 46 × 28 × 125 is:

1. 0
2. 2
3. 4
4. 6

Answer: A. 0

Q25. Two cyclists start from the same point and cycle in opposite directions at 20 km/hr and 30 km/hr respectively. After how many hours will they be 250 km apart?

1. 4 hrs
2. 5 hrs
3. 6 hrs
4. 7 hrs

Answer: B. 5 hrs

Q26. A box contains 4 red, 5 blue, and 6 green balls. If one ball is picked at random, what is the probability it is NOT red?

1. 4/15
2. 11/15
3. 7/15
4. 8/15

Answer: B. 11/15

Q27. The marked price of a jacket is Rs. 2,000. The shopkeeper first gives a 10% discount and then a further 5% discount. What is the final price?

1. Rs. 1,650
2. Rs. 1,700
3. Rs. 1,710
4. Rs. 1,750

Answer: C. Rs. 1,710

Q28. The income of X is 4/3 times the income of Y. What percentage of Y's income is X's income?

1. 120%
2. 125%
3. 133.33%
4. 150%

Answer: C. 133.33%

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Medium Level Arithmetic CAT Questions for 2026

Q29. The ratio of two numbers is 4:5. If their sum is 180, find the numbers.

1. 80 and 100
2. 70 and 110
3. 60 and 120
4. 90 and 90

Answer: A. 80 and 100

Q30. A train is moving at 60 km/hr. How much time will it take to cover 450 metres?

1. 27 sec
2. 30 sec
3. 25 sec
4. 20 sec

Answer: A. 27 sec

Q31. If the cost price of an item is Rs. 250 and the profit is 20%, find the selling price.

1. Rs. 280
2. Rs. 300
3. Rs. 320
4. Rs. 350

Answer: B. Rs. 300

Q32. A and B together can do a work in 20 days. B alone can do it in 30 days. In how many days can A alone do the work?

1. 60 days
2. 50 days
3. 40 days
4. 30 days

Answer: A. 60 days

Q33. A man spends 30% on rent, 20% on food, and saves Rs. 20,000 which is 25% of his income. What is his total income?

1. Rs. 80,000
2. Rs. 70,000
3. Rs. 60,000
4. Rs. 90,000

Answer: A. Rs. 80,000

Q34. If the marked price of a product is Rs. 1,000 and two successive discounts of 20% and 10% are given, find the selling price.

1. Rs. 700
2. Rs. 800
3. Rs. 720
4. Rs. 750

Answer: C. Rs. 720

Q35. A car travels from A to B at 60 km/hr and returns at 40 km/hr. What is the average speed?

1. 48 km/hr
2. 50 km/hr
3. 52 km/hr
4. 54 km/hr

Answer: A. 48 km/hr

Q36. A sum of Rs. 10,000 is invested at 10% per annum for 2 years compounded annually. Find the amount.

1. Rs. 12,100
2. Rs. 11,500
3. Rs. 12,000
4. Rs. 11,800

Answer: A. Rs. 12,100

Q37. If x% of y is equal to y% of x, what is the relation between x and y?

1. x = y
2. x > y
3. x < y
4. Cannot be determined

Answer: A. x = y (Always true for any values)

Q38. A man walks at 5 km/hr. How long will he take to cover 1.25 km?

1. 10 min
2. 12 min
3. 15 min
4. 18 min

Answer: C. 15 min

Q39. If the price of sugar is increased by 25%, by what percentage should a family reduce its consumption so that the expenditure on sugar remains the same?

1. 20%
2. 25%
3. 15%
4. 10%

Answer: A. 20%

Q40. In an election between two candidates, the winner got 55% of the total valid votes. If 20% of votes were invalid and the total votes were 7,500, by what margin did the winner win?

1. 750
2. 600
3. 900
4. 1200

Answer: A. 750

Q41. The population of a town is 8,000. It decreases by 10% in the first year and increases by 5% in the second year. What is the population after 2 years?

1. 7,560
2. 7,200
3. 7,800
4. 7,640

Answer: A. 7,560

Q42. A trader buys goods at 20% discount on marked price. If he sells at a 10% discount on marked price, what is his profit percentage?

1. 12%
2. 12.5%
3. 10%
4. 15%

Answer: B. 12.5%

Q43. By selling an article for Rs. 900, a person gains 20%. At what price should it be sold to gain 35%?

1. Rs. 1,000
2. Rs. 1,012.50
3. Rs. 950
4. Rs. 1,050

Answer: B. Rs. 1,012.50

Q44. A man sells two items for Rs. 9,900 each. On one he gains 10% and on the other he loses 10%. His overall profit or loss is:

1. No profit no loss
2. Loss of Rs. 200
3. Profit of Rs. 200
4. Loss of Rs. 100

Answer: B. Loss of Rs. 200

Q45. If cost price is 90% of selling price, what is the profit percentage?

1. 10%
2. 11.11%
3. 12.5%
4. 9.09%

Answer: B. 11.11%

Q46. A shopkeeper buys 100 oranges for Rs. 200 and sells 80 oranges for Rs. 200. What is his profit or loss percentage?

1. Profit 25%
2. Loss 20%
3. Profit 20%
4. Loss 25%

Answer: A. Profit 25%

Q47. The difference between compound interest and simple interest on a sum for 2 years at 10% per annum is Rs. 50. What is the principal?

1. Rs. 4,000
2. Rs. 5,000
3. Rs. 6,000
4. Rs. 7,000

Answer: B. Rs. 5,000

Q48. Rs. 12,000 is invested at 10% compounded half-yearly. What is the amount after 1 year?

1. Rs. 13,200
2. Rs. 13,230
3. Rs. 13,120
4. Rs. 13,250

Answer: B. Rs. 13,230

Q49. The ratio of milk to water in a mixture is 3:1. If 4 litres of water is added, the ratio becomes 3:2. Find the initial quantity of milk.

1. 12 litres
2. 16 litres
3. 18 litres
4. 24 litres

Answer: A. 12 litres

Q50. The ages of two persons are in the ratio 5:7. After 4 years the ratio will be 3:4. What is the sum of their present ages?

1. 48 years
2. 56 years
3. 60 years
4. 72 years

Answer: A. 48 years

Q51. Two trains of length 150 m and 200 m run on parallel tracks. When running in opposite directions they cross each other in 10 seconds. What is the sum of their speeds?

1. 120 km/hr
2. 126 km/hr
3. 105 km/hr
4. 140 km/hr

Answer: B. 126 km/hr

Q52. A car covers the first half of the journey at 60 km/hr and the second half at 40 km/hr. What is the average speed?

1. 50 km/hr
2. 48 km/hr
3. 45 km/hr
4. 52 km/hr

Answer: B. 48 km/hr

Q53. A thief steals a car and drives away at 60 km/hr. The owner notices after 30 minutes and follows at 75 km/hr. How long will it take the owner to catch the thief?

1. 1.5 hours
2. 2 hours
3. 2.5 hours
4. 3 hours

Answer: B. 2 hours

Q54. A man can row at 6 km/hr in still water. The river flows at 2 km/hr. How long will it take him to row 32 km upstream?

1. 6 hrs
2. 7 hrs
3. 8 hrs
4. 9 hrs

Answer: C. 8 hrs

Q55. The average marks scored by 40 students is 72. If the top 5 scored an average of 90, what is the average of the remaining 35 students?

66. 66.43
67. 68
68. 69.43
69. 70

Answer: C. 69.43

Q56. The average weight of 20 students in a class is 50 kg. When 5 new students join, the average becomes 52 kg. What is the average weight of the 5 new students?

1. 56 kg
2. 58 kg
3. 60 kg
4. 62 kg

Answer: C. 60 kg

Q57. In what ratio must rice at Rs. 50/kg be mixed with rice at Rs. 80/kg to get a mixture worth Rs. 65/kg?

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

Answer: C. 1:1

Q58.In what ratio should water be mixed with alcohol worth Rs. 25 per litre to get a profit of 25% by selling the mixture at Rs. 25 per litre?

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

Answer: A. 1:4

Q59. Pipe A can fill a tank in 30 minutes and pipe B can empty it in 45 minutes. If both pipes are opened simultaneously, how long will it take to fill the tank?

1. 90 min
2. 60 min
3. 75 min
4. 100 min

Answer: A. 90 min

Q60. Three pipes A, B, C can fill a tank in 12, 15, and 20 hours respectively. How long will it take to fill the tank if all three are opened together?

1. 4 hrs
2. 5 hrs
3. 5.5 hrs
4. 6 hrs

Answer: B. 5 hrs

Q61. The sum of ages of father and son is 50. Five years ago, the father's age was 5 times his son's age. Find the present ages.

1. 35 and 15
2. 40 and 10
3. 38 and 12
4. 32 and 18

Answer: A. 35 and 15

Q62. Ravi is 3 times as old as his daughter. 5 years later, he will be 2.5 times as old. What is Ravi's present age?

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

Answer: D. 45 years

Q63. If the present age of A is three times that of B and after 10 years A will be twice as old as B, then the present age of A is:

1. 20 years
2. 30 years
3. 40 years
4. 50 years

Answer: B. 30 years

Q64. What is the largest 4-digit number divisible by 12, 15, and 18?

1. 9900
2. 9720
3. 9980
4. 9840

Answer: B. 9720

Q65. The product of two numbers is 120 and their sum is 26. What is the sum of their reciprocals?

1. 13/60
2. 26/120
3. 11/60
4. 7/30

Answer: A. 13/60

Q66. How many 3-digit numbers are divisible by both 5 and 7?

1. 12
2. 13
3. 14
4. 15

Answer: B. 13

Q67. Find the sum of all natural numbers from 1 to 100 that are divisible by 3 or 5.

1. 2318
2. 2310
3. 2403
4. 2418

Answer: C. 2403

Q68. The 10th term of an AP is 20 and the 20th term is 10. What is the 30th term?

1. -10
2. 0
3. 10
4. -5

Answer: B. 0

Q69. How many terms of the AP 3, 7, 11, ... are needed for the sum to be at least 500?

1. 14
2. 15
3. 16
4. 17

Answer: C. 16

Q70. A rectangle's length is twice its breadth. If the perimeter is 84 cm, find the area.

1. 288 sq. cm
2. 392 sq. cm
3. 196 sq. cm
4. 256 sq. cm

Answer: A. 288 sq. cm

Q71. If (x + 1/x) = 5, what is (x^2 + 1/x^2)?

1. 23
2. 25
3. 27
4. 29

Answer: A. 23

Q72. A fraction becomes 1/2 when 1 is added to both numerator and denominator, and becomes 1/3 when 1 is subtracted from both. Find the fraction.

1. 3/7
2. 2/5
3. 3/8
4. 1/4

Answer: A. 3/7

Q73. A starts a business with Rs. 20,000. After 4 months, B joins with Rs. 30,000. At the end of a year, they earn a profit of Rs. 63,000. What is A's share?

1. Rs. 36,000
2. Rs. 32,000
3. Rs. 28,000
4. Rs. 24,000

Answer: A. Rs. 36,000

Q74. A, B and C enter a partnership. A's capital is Rs. 5,000 for 6 months, B's is Rs. 4,000 for 8 months, C's is Rs. 6,000 for 5 months. Who gets the largest share of profit?

1. A
2. B
3. C
4. All equal

Answer: B. B

Q75. What is the compound interest on Rs. 15,000 for 2 years at 8% per annum, compounded annually?

1. Rs. 2,400
2. Rs. 2,496
3. Rs. 2,592
4. Rs. 2,700

Answer: C. Rs. 2,592

Q76. The salary of A is 30% more than B and the salary of B is 20% more than C. By what percentage is A's salary more than C's salary?

1. 50%
2. 54%
3. 56%
4. 60%

Answer: C. 56%

Q77. A person saves Rs. 6,000 at the end of each year. If the annual rate of simple interest is 10%, what is the total interest earned at the end of 4 years?

1. Rs. 3,600
2. Rs. 4,000
3. Rs. 4,200
4. Rs. 3,000

Answer: A. Rs. 3,600

Q78. A sum of money doubles itself in 8 years at compound interest. In how many years will it become 4 times?

1. 12 years
2. 16 years
3. 20 years
4. 24 years

Answer: B. 16 years

Q79. Two numbers are in the ratio 7:9. If 12 is subtracted from each, the ratio becomes 3:5. What are the numbers?

1. 21 and 27
2. 28 and 36
3. 35 and 45
4. 42 and 54

Answer: B. 28 and 36

Q80. A train 240 m long passes a 360 m long bridge in 60 seconds. What is the speed of the train?

1. 30 km/hr
2. 32 km/hr
3. 36 km/hr
4. 40 km/hr

Answer: C. 36 km/hr

Q81. A boat goes 30 km upstream in 6 hours and comes back in 3 hours. What is the speed of the stream?

2. 2.5 km/hr
3. 3.5 km/hr
4. 5 km/hr
5. 7.5 km/hr

Answer: A. 2.5 km/hr

Q82. In a class of 50 students, 60% are girls. If 10 more boys join the class, what percentage of the class are girls now?

1. 45%
2. 50%
3. 54.55%
4. 55%

Answer: B. 50%

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Difficult Level Arithmetic CAT Questions for 2026

Q83. A shopkeeper marks an item 50% above cost and gives a 20% discount. What is the profit percentage?

1. 10%
2. 15%
3. 20%
4. 25%

Answer: C. 20%

Q84. A person can row downstream at 12 km/hr and upstream at 8 km/hr. What is the speed of the current?

1. 2 km/hr
2. 4 km/hr
3. 6 km/hr
4. 3 km/hr

Answer: A. 2 km/hr

Q85. A, B and C can do a work in 10, 20, and 30 days respectively. If they all work together, how long will they take?

5. 5.45 days
6. 6 days
7. 7.5 days
8. 4.5 days

Answer: A. 5.45 days

Q86. A invests Rs. 5,000 at 10% CI, B invests Rs. 5,000 at 12% SI. After 2 years, who has more money and by how much?

1. B has Rs. 150 more
2. A has Rs. 150 more
3. Equal
4. B has Rs. 100 more

Answer: B. A has Rs. 150 more

Q87. A reduction of 20% in price enables a person to buy 25% more quantity. What is the ratio of old price to new price?

1. 4:3
2. 5:4
3. 3:2
4. 6:5

Answer: B. 5:4

Q88. A train crosses a pole in 15 seconds and a platform of 150 m in 25 seconds. Find the length of the train.

1. 225 m
2. 250 m
3. 275 m
4. 200 m

Answer: A. 225 m

Q89. If 3 men or 5 women can do a job in 12 days, in how many days can 6 men and 5 women do it?

1. 4 days
2. 5 days
3. 6 days
4. 3 days

Answer: A. 4 days

Q90. A sum triples in 8 years at simple interest. In how many years will it become 5 times?

1. 16 years
2. 18 years
3. 20 years
4. 14 years

Answer: A. 16 years

Q91. Two pipes fill a tank in 20 and 30 mins respectively. A third pipe empties the tank in 15 mins. In how much time will all 3 working together fill the tank?

1. 60 mins
2. 40 mins
3. 30 mins
4. 50 mins

Answer: A. 60 mins

Q92. A man travels 1/3 of the distance at 10 km/hr, next 1/3 at 20 km/hr, and last 1/3 at 30 km/hr. What is the average speed?

16. 16.36 km/hr
17. 20 km/hr
18. 22 km/hr
19. 18.5 km/hr

Answer: A. 16.36 km/hr

Q93. A sum of Rs. 8,000 becomes Rs. 9,261 in 3 years at compound interest. What is the rate of interest?

1. 5%
2. 5.5%
3. 6%
4. 7%

Answer: A. 5%

Q94. Rahul starts from A to B at 9 am at 40 km/hr. Priya starts from B to A at 11 am at 60 km/hr. If distance AB = 400 km, at what time do they meet?

1. 1:00 PM
2. 12:30 PM
3. 2:00 PM
4. 1:30 PM

Answer: A. 1:00 PM

Q95. A can do a work in 12 days and B in 18 days. They start working together but B leaves 4 days before completion. How many total days does the work take?

1. 8 days
2. 9 days
3. 10 days
4. 11 days

Answer: C. 10 days

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Q96. 20 workers can complete a project in 30 days. After 10 days, 5 workers leave. How many more days will it take to finish the remaining work?

1. 24 days
2. 26.67 days
3. 30 days
4. 25 days

Answer: B. 26.67 days

Q97. P is twice as efficient as Q and Q is thrice as efficient as R. If P, Q and R together can complete a work in 10 days, in how many days can Q alone complete it?

1. 55 days
2. 60 days
3. 50 days
4. 45 days

Answer: A. 55 days

Q98. A can complete a work in 15 days and B in 20 days. They work together for 4 days, then C joins and finishes the remaining work in 2 days. How long would C take to do the whole work alone?

1. 40 days
2. 45 days
3. 50 days
4. 60 days

Answer: C. 50 days

Q99. A and B together can complete a work in 8 days. B and C together can complete it in 12 days. A and C together can complete it in 16 days. How long would A alone take?

1. 24 days
2. 48/5 days
3. 192/13 days
4. 30 days

Answer: C. 192/13 days

Q100. A vessel contains 50 litres of milk. 5 litres are taken out and replaced with water. This process is repeated twice more. What fraction of the mixture is milk?

1. 729/1000
2. 729/1100
3. 81/100
4. 7/10

Answer: A. 729/1000

Q101. Two solutions of acid and water contain acid in the ratio 2:5 and 1:3. In what ratio should they be mixed to get a solution with acid and water in ratio 5:13?

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

Answer: A. 2:3

Q102. A tank is 3/5 full. Pipe A can fill it in 20 minutes and pipe B empties it in 12 minutes. If both are opened, when will the tank be empty?

1. 9 min
2. 10 min
3. 12 min
4. 15 min

Answer: A. 9 min

Q103. What is the remainder when 2^(100) is divided by 7?

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

Answer: B. 2

Q104. A man buys a TV for Rs. 15,000 and sells it at a loss of 12%. From that money he buys another article and sells it at 10% profit. What is his overall gain or loss?

1. Loss of Rs. 348
2. Loss of Rs. 280
3. Gain of Rs. 280
4. Loss of Rs. 480

Answer: A. Loss of Rs. 348

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Must Solve Arithmetic CAT Questions for 2026

Question 105: If y is a negative number such that 2y2log35 = 5log23, then y equals:

1. Log2 (1/5)
2. Log2 (1/3)
3. log2 (1/3)
4. log2 (1/5)

Correct Answer: log2 (1/3)

Question 106: The number of real-valued solutions of the equation 2x+2−x=2−(x−2)22^x + 2^{-x} = 2 - (x - 2)^22x+2−x=2−(x−2)2

1. 0
2. 1
3. Infinite
4. 2

Correct Answer: 1

Question 107:  A train traveled at one-third of its usual speed, and hence reached 30 minutes late. On the return journey, the train initially traveled at its usual speed for 5 minutes but then stopped for 4 minutes for an emergency. The percentage by which the train must now increase its usual speed so as to reach the destination at the scheduled time is nearest to:

1. 58
2. 67
3. 50
4. 61

Correct Answer: 50

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Question 108: The mean of all 4-digit even natural numbers of the form ‘aabb’, where a>0a > 0a>0, is:

1. 5050
2. 4864
3. 5544
4. 4466

Correct Answer: 5544

Question 109: An alloy is prepared by mixing metals A, B, and C in the proportion 3:4:7 by volume. Weights of the same volume of metals A, B, and C are in the ratio 5:2:6. In 130 kg of the alloy, the weight of metal C is:

1. 84
2. 96
3. 70
4. 48

Correct Answer: 70

Question 110: If f (5 + x) = f (5 - x) for every real x, and f (x) = 0 has four distinct real roots, then the sum of these roots is

1. 20
2. 40
3. 0
4. 10

Correct Answer: 20

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Important Arithmetic Formulas for CAT 2026

Topic	Concept	Formula / Explanation
Number Systems	Prime Numbers	A number > 1 with no divisors other than 1 and itself
	LCM (Least Common Multiple)	Smallest positive integer divisible by both a and b
	HCF (Highest Common Factor)	Largest positive integer that divides both a and b without remainder
Percentages	Percentage Formula	Percentage = (Part / Whole) * 100
	Percentage Increase/Decrease	[(New - Original) / Original] * 100
Profit and Loss	Profit	Profit = SP - CP
	Loss	Loss = CP - SP
	Profit Percentage	Profit % = (Profit / CP) * 100
	Loss Percentage	Loss % = (Loss / CP) * 100
Simple and Compound Interest	Simple Interest (SI)	SI = (P * R * T) / 100
	Compound Interest (CI)	CI = P * (1 + R / 100)^T - P
Ratio and Proportion	Ratio	a : b = a / b
	Proportion	If a / b = c / d, then ad = bc
Time, Speed, and Distance	Speed	Speed = Distance / Time
	Distance	Distance = Speed * Time
	Time	Time = Distance / Speed
Time and Work	Work	Work = Days * Work Rate
	Work Rate	Work Rate = Work / Days
Mixtures and Alligations	Weighted Average	(Σ Weight × Value) / (Σ Weights)
	Alligation Rule	(Cheaper / Dearer) = (Dearer - Mean) / (Mean - Cheaper)
Pipes and Cisterns	Filling Time	Part filled in 1 hour = 1 / x
	Emptying Time	Part emptied in 1 hour = 1 / y
Arithmetic Progression	Nth Term of AP	aₙ = a + (n - 1)d
	Sum of First n Terms	Sₙ = n / 2 [2a + (n - 1)d]

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Importance of Arithmetic CAT Questions 2026

CAT Arithmetic Questions is a core part of the CAT Quant section and comes from topics we’ve been studying since school days. Concepts like percentages, profit & loss, and ratios are easy to grasp and CAT previous year papers will help you understand how these concepts are applied in the actual exam.. That’s why it's often seen as low-hanging fruit in the exam.

These Arithmetic CAT questions are mostly formula-based and don’t need heavy calculations. If you’ve practised enough, you can solve them in a jiffy. It’s all about speed and smart thinking under pressure.

Conclusion

Practising a variety of Arithmetic CAT questions 2026 regularly can help to develop problem-solving skills. It will also improve your speed and accuracy. Try to solve as many as CAT arithmetic questions you can.

Get a comprehensive overview of the CAT 2026 syllabus to guide your preparation for all sections of the exam.