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CAT Type-In-The-Answer (TITA) Questions (Zero Negative Marking)

490+ Official non-MCQ numerical entry questions across QA, DILR & VARC with zero penalty for wrong attempts. Official questions curated from CAT 2017–2025 with detailed explanations.

496 Total Questions
TITA: 496 (0 Negative Penalty)
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Official Exam Questions & Explanations (25 of 496)

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Question 1 of 496
CAT 2025 Slot 2QAGeometryCirclesHard
Two tangents drawn from a point PP touch a circle with center OO at points QQ and RR. Points AA and BB lie on PQPQ and PRPR, respectively, such that ABAB is also a tangent to the same circle. If AOB=50\angle AOB = 50^\circ, then APB\angle APB, in degrees, equals
TITA Answer:
Question 2 of 496
CAT 2025 Slot 2QANumber SystemsIntegral SolutionsHard
Suppose a,b,ca,b,c are three distinct natural numbers, such that 3ac=8(a+b)3ac = 8(a+b). Then, the smallest possible value of 3a+2b+c3a+2b+c is
TITA Answer:
Question 3 of 496
CAT 2025 Slot 2QAArithmeticMean, Median & ModeModerate
The average number of copies of a book sold per day by a shopkeeper is 60 in the initial seven days and 63 in the initial eight days, after the book launch. On the ninth day, she sells 11 copies less than the eighth day, and the average number of copies sold per day from second day to ninth day becomes 66. The number of copies sold on the first day of the book launch is
TITA Answer:
Question 4 of 496
CAT 2025 Slot 2QANumber SystemsIntegral SolutionsHard
If mm and nn are integers such that (m+2n)(2m+n)=27(m+2n)(2m+n) = 27, then the maximum possible value of 2m3n2m-3n is
TITA Answer:
Question 5 of 496
CAT 2025 Slot 2QAArithmeticTime, Speed & DistanceModerate
Rita and Sneha can row a boat at 5 km/h and 6 km/h in still water, respectively. In a river flowing with a constant velocity, Sneha takes 48 minutes more to row 14 km upstream than to row the same distance downstream. If Rita starts from a certain location in the river, and returns downstream to the same location, taking a total of 100 minutes, then the total distance, in km, Rita will cover is
TITA Answer:
Question 6 of 496
CAT 2025 Slot 2QANumber SystemsMiscellaneousModerate
The sum of digits of the number (625)65×(128)36(625)^{65} \times (128)^{36}, is
TITA Answer:
Question 7 of 496
CAT 2025 Slot 2QAArithmeticTime & WorkModerate
Ankita is twice as efficient as Bipin, while Bipin is twice as efficient as Chandan. All three of them start together on a job, and Bipin leaves the job after 20 days. If the job got completed in 60 days, the number of days needed by Chandan to complete the job alone, is
TITA Answer:
Question 8 of 496
CAT 2025 Slot 2QAAlgebraMinima & MaximaModerate
If a,b,ca,b,c and dd are integers such that their sum is 46, then the minimum possible value of (ab)2+(ac)2+(ad)2(a-b)^2 + (a-c)^2 + (a-d)^2 is
TITA Answer:
Question 9 of 496
CAT 2025 Slot 1QANumber SystemsIntegral SolutionsModerate
The number of distinct pairs of integers (x,y)(x, y) satisfying the inequalities x>y3x > y \geq 3 and x+y<14x + y < 14 is
TITA Answer:
Question 10 of 496
CAT 2025 Slot 1QAAlgebraPolynomialsEasy
The number of non-negative integer values of kk for which the quadratic equation x25x+k=0x^2 - 5x + k = 0 has only integer roots, is
TITA Answer:
Question 11 of 496
CAT 2025 Slot 1QANumber SystemsFactorisationModerate
In a 3-digit number N, the digits are non-zero and distinct such that none of the digits is a perfect square, and only one of the digits is a prime number. Then, the number of factors of the minimum possible value of N is
TITA Answer:
Question 12 of 496
CAT 2025 Slot 1QAGeometryQuadrilateralsModerate
If the length of a side of a rhombus is 36 cm and the area of the rhombus is 396 sq. cm, then the absolute value of the difference between the lengths, in cm, of the diagonals of the rhombus is
TITA Answer:
Question 13 of 496
CAT 2025 Slot 1QAArithmeticPercentagesModerate
In a class, there were more than 10 boys and a certain number of girls. After 40% of the girls and 60% of the boys left the class, the remaining number of girls was 8 more than the remaining number of boys. Then, the minimum possible number of students initially in the class was
TITA Answer:
Question 14 of 496
CAT 2025 Slot 1QAArithmeticPercentagesModerate
Kamala divided her investment of Rs 100000 between stocks, bonds, and gold. Her investment in bonds was 25% of her investment in gold. With annual returns of 10%, 6%, 8% on stocks, bonds, and gold, respectively, she gained a total amount of Rs 8200 in one year. The amount, in rupees, that she gained from the bonds, was
TITA Answer:
Question 15 of 496
CAT 2025 Slot 1QAAlgebraLinear EquationEasy
Stocks A, B and C are priced at rupees 120, 90 and 150 per share, respectively. A trader holds a portfolio consisting of 10 shares of stock A, and 20 shares of stocks B and C put together. If the total value of her portfolio is rupees 3300, then the number of shares of stock B that she holds, is
TITA Answer:
Question 16 of 496
CAT 2025 Slot 1QAArithmeticProfit & LossModerate
A shopkeeper offers a discount of 22% on the marked price of each chair, and gives 13 chairs to a customer for the discounted price of 12 chairs to earn a profit of 26% on the transaction. If the cost price of each chair is Rs 100, then the marked price, in rupees, of each chair is
TITA Answer:
Question 17 of 496
CAT 2025 Slot 2DILRLogical ReasoningMath PuzzlesHard
Caselet / Problem Set Context~148 words
The two most populous cities and the non-urban region (NUR) of each of three states, Whimshire, Fogglia, and Humbleset, are assigned Pollution Measures (PMs). These nine PMs are all distinct multiples of 10, ranging from 10 to 90. The six cities in increasing order of their PMs are: Blusterburg, Noodleton, Splutterville, Quackford, Mumpypore, Zingaloo. The Pollution Index (PI) of a state is a weighted average of the PMs of its NUR and cities, with a weight of 50% for the NUR, and 25% each for its two cities. There is only one pair of an NUR and a city (considering all cities and all NURs) where the PM of the NUR is greater than that of the city. That NUR and the city both belong to Humbleset. The PIs of all three states are distinct integers, with Humbleset and Fogglia having the highest and the lowest PI respectively.
What is the PI of Whimshire?
TITA Answer:
Question 18 of 496
CAT 2025 Slot 2DILRLogical ReasoningMath PuzzlesHard
Caselet / Problem Set Context~148 words
The two most populous cities and the non-urban region (NUR) of each of three states, Whimshire, Fogglia, and Humbleset, are assigned Pollution Measures (PMs). These nine PMs are all distinct multiples of 10, ranging from 10 to 90. The six cities in increasing order of their PMs are: Blusterburg, Noodleton, Splutterville, Quackford, Mumpypore, Zingaloo. The Pollution Index (PI) of a state is a weighted average of the PMs of its NUR and cities, with a weight of 50% for the NUR, and 25% each for its two cities. There is only one pair of an NUR and a city (considering all cities and all NURs) where the PM of the NUR is greater than that of the city. That NUR and the city both belong to Humbleset. The PIs of all three states are distinct integers, with Humbleset and Fogglia having the highest and the lowest PI respectively.
What is the PI of Fogglia?
TITA Answer:
Question 19 of 496
CAT 2025 Slot 2DILRLogical ReasoningMath PuzzlesHard
Caselet / Problem Set Context~148 words
The two most populous cities and the non-urban region (NUR) of each of three states, Whimshire, Fogglia, and Humbleset, are assigned Pollution Measures (PMs). These nine PMs are all distinct multiples of 10, ranging from 10 to 90. The six cities in increasing order of their PMs are: Blusterburg, Noodleton, Splutterville, Quackford, Mumpypore, Zingaloo. The Pollution Index (PI) of a state is a weighted average of the PMs of its NUR and cities, with a weight of 50% for the NUR, and 25% each for its two cities. There is only one pair of an NUR and a city (considering all cities and all NURs) where the PM of the NUR is greater than that of the city. That NUR and the city both belong to Humbleset. The PIs of all three states are distinct integers, with Humbleset and Fogglia having the highest and the lowest PI respectively.
What is the PI of Humbleset?
TITA Answer:
Question 20 of 496
CAT 2025 Slot 2DILRLogical ReasoningMath PuzzlesHard
Caselet / Problem Set Context~148 words
The two most populous cities and the non-urban region (NUR) of each of three states, Whimshire, Fogglia, and Humbleset, are assigned Pollution Measures (PMs). These nine PMs are all distinct multiples of 10, ranging from 10 to 90. The six cities in increasing order of their PMs are: Blusterburg, Noodleton, Splutterville, Quackford, Mumpypore, Zingaloo. The Pollution Index (PI) of a state is a weighted average of the PMs of its NUR and cities, with a weight of 50% for the NUR, and 25% each for its two cities. There is only one pair of an NUR and a city (considering all cities and all NURs) where the PM of the NUR is greater than that of the city. That NUR and the city both belong to Humbleset. The PIs of all three states are distinct integers, with Humbleset and Fogglia having the highest and the lowest PI respectively.
For how many of the cities and NURs is it possible to identify their PM and the state they belong to?
TITA Answer:
Question 21 of 496
CAT 2025 Slot 2DILRLogical ReasoningGridsModerate
Caselet / Problem Set Context~137 words
There are six spherical balls, B1, B2, B3, B4, B5, and B6, and four circular hoops H1, H2, H3, and H4. Each ball was tested on each hoop once, by attempting to pass the ball through the hoop. If the diameter of a ball is not larger than the diameter of the hoop, the ball passes through the hoop and makes a "ping". Any ball having a diameter larger than that of the hoop gets stuck on that hoop and does not make a ping. The following additional information is known:
1
B1 and B6 each made a ping on H4, but B5 did not.
2
B4 made a ping on H3, but B1 did not.
3
All balls, except B3, made pings on H1.
4
None of the balls, except B2, made a ping on H2.
What was the total number of pings made by B1, B2, and B3?
TITA Answer:
Question 22 of 496
CAT 2025 Slot 2DILRLogical ReasoningArrangementsHard
Caselet / Problem Set Context~213 words
Ananya Raga, Bhaskar Tala, Charu Veena, and Devendra Sur are four musicians. Each of them started and completed their training as students under each of three Gurus - Pandit Meghnath, Ustad Samiran, and Acharya Raghunath between 2013 and 2024, including both the years. Each Guru trains any student for consecutive years only, for a span of 2, 3, or 4 years, with each Guru having a different span. During some of these years, a student may not have trained under these Gurus; however, they never trained under multiple Gurus in the same year. In none of these years, any of these Gurus trained more than two of these students at the same time. When two students train under the same Guru at the same time, they are referred to as Gurubhai, irrespective of their gender. The following additional facts are known.
1
Ustad Samiran never trained more than one of these students in the same year.
2
Acharya Raghunath did not train any of these students during 2015-2018, as well as during 2021-24.
3
Ananya and Devendra were never Gurubhai; neither were Bhaskar and Charu. All other pairs of musicians were Gurubhai for exactly 2 years.
4
In 2013, Ananya and Bhaskar started their trainings under Pandit Meghnath and under Ustad Samiran, respectively.
In how many of the years between 2013-24, were only two of these four musicians training under these three Gurus?
TITA Answer:
Question 23 of 496
CAT 2025 Slot 2DILRData InterpretationBar GraphsModerate
Caselet / Problem Set Context~109 words
The following charts depict details of research papers written by four authors, Arman, Brajen, Chintan, and Devon. The papers were of four types, single-author, two-author, three-author, and four-author, that is, written by one, two, three, or all four of these authors, respectively. No other authors were involved in writing these papers.
The following additional facts are known.
1
Each of the authors wrote at least one of each of the four types of papers.
2
The four authors wrote different numbers of single-author papers.
3
Both Chintan and Devon wrote more three-author papers than Brajen.
4
The number of single-author and two-author papers written by Brajen were the same.
What was the total number of two-author and three-author papers written by Brajen?
TITA Answer:
Question 24 of 496
CAT 2025 Slot 2DILRData InterpretationBar GraphsModerate
Caselet / Problem Set Context~109 words
The following charts depict details of research papers written by four authors, Arman, Brajen, Chintan, and Devon. The papers were of four types, single-author, two-author, three-author, and four-author, that is, written by one, two, three, or all four of these authors, respectively. No other authors were involved in writing these papers.
The following additional facts are known.
1
Each of the authors wrote at least one of each of the four types of papers.
2
The four authors wrote different numbers of single-author papers.
3
Both Chintan and Devon wrote more three-author papers than Brajen.
4
The number of single-author and two-author papers written by Brajen were the same.
If Devon wrote more than one two-author papers, then how many two-author papers did Chintan write?
TITA Answer:
Question 25 of 496
CAT 2025 Slot 2DILRData InterpretationScatter PlotHard
Caselet / Problem Set Context~176 words
The Sustainability Index (SI) of a country at a point in time is an integer between 1 and 100. This question is related to SI of six countries - A, B, C, D, E, and F - at three different points in time - 2016, 2020, and 2024. The plot represents the exact changes in their SI, with X-coordinate representing % increase in 2020 from 2016, i.e., (SI in 2020 minus SI in 2016) / (SI in 2016), and Y-coordinate representing % increase in 2024 from 2020. At any point in time, the country with highest SI is ranked 1, while the country with the lowest SI is ranked 6. The following additional facts are known.
1
In 2016, B, C, E, and A had ranks 1, 2, 3, and 4 respectively.
2
F had lower SI than any other country in 2016, 2020, and 2024.
3
In 2024, E was the only country with SI of 90.
4
The range of SI of the six countries was 60 in 2016 as well as in 2024.
What was the SI of E in 2016?
TITA Answer:

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Frequently Asked Questions about CAT Type-In-The-Answer (TITA) Questions (Zero Negative Marking)

Why are TITA questions crucial for scoring 99+ percentile in CAT?

CAT convenors place heavy emphasis on testing core intuition in TITA problems. Mastering standard patterns allows candidates to secure +3 marks with high accuracy and minimal time.

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Yes, 100% of the questions in this module are official previous year questions administered in CAT 2017 through CAT 2025.

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