CAT 2023QASlot 1 · Morning

CAT 2023 Slot 1 QA Question Paper with Solutions

40 Minutes22 QuestionsNov 26, 20233 marks correct · −1 wrong

Questions

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Q1CAT 2023 Slot 1 QA

\sqrt{5x+9}+\sqrt{5x-9}=3(2+\sqrt{2})

, then

\sqrt{10x+9}

is equal to

Q2CAT 2023 Slot 1 QA

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If x and y are positive real numbers such that

\log_x (x^2+12)=4

and

3 \log_y x = 1

, then

x + y

equals

Q3CAT 2023 Slot 1 QA

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Let n be the least positive integer such that 168 is a factor of

1134^n

. If m is the least positive integer such that

1134^n

is a factor of

168^m

, then

m+n

equals

Q4CAT 2023 Slot 1 QA

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If x and y are real numbers such that

x^2 + (x-2y-1)^2 = -4y(x+y)

, then the value of

x - 2y

Q5CAT 2023 Slot 1 QA

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The number of integer solutions of the equation

2 \left|x\right|(x^2+1)=5x^2

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Q6CAT 2023 Slot 1 QA

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Let α and β be the two distinct roots of the equation

2x^2 - 6x + k = 0

, such that

(\alpha + \beta)

and

\alpha \beta

are distinct roots of the equation

x^2 + px + p = 0

. Then, the value of

8(k-p)

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Q7CAT 2023 Slot 1 QA

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he equation

x^3 + (2r+1)x^2 + (4r-1)x + 2 = 0

has -2 as one of the roots. If the other two roots are real, then the minimum possible non-negative integer value of r is

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Q8CAT 2023 Slot 1 QA

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Brishti went on an 8-hour trip in a car. Before the trip, the car had travelled a total of x km till then, where x is a whole number and is palindromic, i.e., x remains unchanged when its digits are reversed. At the end of the trip, the car had travelled a total of 26862 km till then, this number again being palindromic. If Brishti never drove at more than 110 km/h, then the greatest possible average speed at which she drove during the trip, in km/h, was

Q9CAT 2023 Slot 1 QA

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In an examination, the average marks of 4 girls and 6 boys is 24. Each of the girls has the same marks while each of the boys has the same marks. If the marks of any girl is at most double the marks of any boy, but not less than the marks of any boy, then the number of possible distinct integer values of the total marks of 2 girls and 6 boys is

Q10CAT 2023 Slot 1 QA

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Gita sells two objects A and B at the same price such that she makes a profit of 20% on object A and a loss of 10% on object B. If she increases the selling price such that objects A and B are still sold at an equal price and a profit of 10% is made on object B, then the profit made on object A will be nearest to

Q11CAT 2023 Slot 1 QA

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A mixture P is formed by removing a certain amount of coffee from a coffee jar and replacing the same amount with cocoa powder. The same amount is again removed from mixture P and replaced with the same amount of cocoa powder to form a new mixture Q. If the ratio of coffee and cocoa in mixture Q is 16 : 9, then the ratio of cocoa in mixture P to that in mixture Q is

Q12CAT 2023 Slot 1 QA

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The minor angle between the hour hand and minute hand of a clock was observed at 8:48 am. The minimum duration, in minutes, after 8:48 am when this angle increases by 50% is

Q13CAT 2023 Slot 1 QA

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The salaries of three friends Sita, Gita and Mita are initially in the ratio 5 : 6 : 7, respectively. In the first year, they get salary hikes of 20%, 25% and 20%, respectively. In the second year, Sita and Mita get salary hikes of 40% and 25%, respectively, and the salary of Gita becomes equal to the mean salary of the three friends. The salary hike of Gita in the second year is

Q14CAT 2023 Slot 1 QA

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Arvind travels from town A to town B, and Surbhi from town B to town A, both starting at the same time along the same route. After meeting each other, Arvind takes 6 hours to reach town B while Surbhi takes 24 hours to reach town A. If Arvind travelled at a speed of 54 km/h, then the distance, in km, between town A and town B is

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Q15CAT 2023 Slot 1 QA

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Anil invests Rs. 22000 for 6 years in a certain scheme with 4% interest per annum, compounded half-yearly. Sunil invests in the same scheme for 5 years, and then reinvests the entire amount received at the end of 5 years for one year at 10% simple interest. If the amounts received by both at the end of 6 years are same, then the initial investment made by Sunil, in rupees, is

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Q16CAT 2023 Slot 1 QA

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The amount of job that Amal, Sunil and Kamal can individually do in a day are in harmonic progression. Kamal takes twice as much time as Amal to do the same amount of job. If Amal and Sunil work for 4 days and 9 days, respectively, Kamal needs to work for 16 days to finish the remaining job. Then the number of days Sunil will take to finish the job working alone is

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Q17CAT 2023 Slot 1 QA

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A quadrilateral ABCD is inscribed in a circle such that

AB:CD = 2:1

and

BC:AD = 5:4

. If AC and BD intersect at the point E, then

AE:CE

equals

Q18CAT 2023 Slot 1 QA

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Let C be the circle

x^2 + y^2 + 4x - 6y - 3 = 0

and L be the locus of the point of intersection of a pair of tangents to C with the angle between the two tangents equal to

60^\circ

. Then, the point at which L touches the line

x = 6

Q19CAT 2023 Slot 1 QA

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In a right-angled triangle ∆ABC, the altitude AB is 5 cm, and the base BC is 12 cm. P and Q are two points on BC such that the areas of ∆ABP, ∆ABQ and ∆ABC are in arithmetic progression. If the area of ∆ABC is 1.5 times the area of ∆ABP, the length of PQ, in cm, is

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Q20CAT 2023 Slot 1 QA

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The number of all natural numbers up to 1000 with non-repeating digits is

Q21CAT 2023 Slot 1 QA

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For some positive and distinct real numbers x, y and z, if

\dfrac{1}{\sqrt{y}+\sqrt{z}}

is the arithmetic mean of

\dfrac{1}{\sqrt{x}+\sqrt{z}}

and

\dfrac{1}{\sqrt{x}+\sqrt{y}}

, then the relationship which will always hold true is

Q22CAT 2023 Slot 1 QA

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A lab experiment measures the number of organisms at 8 am every day. Starting with 2 organisms on the first day, the number of organisms on any day is equal to 3 more than twice the number on the previous day. If the number of organisms on the

n^{\text{th}}

day exceeds one million, then the lowest possible value of n is

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About CAT 2023 Slot 1 QA

The QA section of CAT 2023 Slot 1 was conducted on November 30, 2023, the last Sunday of November — consistent with IIM's scheduling across all recent years. The section contains 24 questions to be answered in 40 minutes, carrying 72 marks in total. There is no sectional time limit within the overall exam, but students choosing to switch sections mid-paper lose the ability to return — making pacing within QA critical.

Passage Topics in CAT 2023 Slot 1 QA

CAT 2023 Slot 1 QA featured four reading comprehension passages and a standalone Verbal Ability block. The RC passages spanned complexity theory and global systems, the aesthetics of electronic music, the economics of income inequality, and the legal history of criminal responsibility — a typical CAT spread across the sciences, humanities, and social sciences. The VA section included Para Jumbles, Para Summary, and Odd Sentence Out questions, consistent with the pattern since CAT 2019.

CAT 2023 QA Marking Scheme

Correct answer (MCQ): +3 marks
Wrong answer (MCQ): −1 mark
Unattempted (MCQ): 0 marks
TITA questions (if any): +3 correct, no negative marking

How to Use This Question Paper

Click any answer option to immediately check your answer. The correct option is highlighted in green; if you selected the wrong option, it is shown in red and the correct answer is revealed. A detailed explanation appears below each question after you answer it, along with statistics showing what percentage of students answered correctly in the actual exam.

The question navigator at the top of the page updates in real time — green bubbles indicate correct answers and red indicate wrong. Use this to spot weak areas at a glance. To practice under timed conditions, use the Take Full Mock button to attempt the complete CAT 2023 Slot 1 paper with a live timer and percentile benchmarking.

Tips for CAT QA Preparation

Reading Comprehension accounts for roughly two-thirds of the QA section. The passages in CAT are dense and argumentative — they reward close reading of the author's position rather than skimming for facts. Practising on past papers is the most reliable way to calibrate your reading speed, improve inference accuracy, and recognise the types of questions IIM setters favour. Use the answer statistics on this page to benchmark yourself; questions where more than 50% of test-takers answered correctly are ones you should aim to get right every time.