CAT Success Blueprint: Trailblazing Practice Set Questions for Top Scores- Day 16

CAT Sample Paper

This CAT Sample paper (CAT solved question papers)consists of three Sections:
This Practice Set consists of three Sections:

• Part- A consists of 8 questions.

• Part- B consists of 7 questions.

• Part- C consists of 9 questions.

Part-A (Quantitative Aptitude - CAT Sample Paper)

CAT Quant solved questions are given below:

Q1. If the roots of equation x² + ax + b = 0 differ by 4, then which of the following is true? (CAT Exam)

(a) a².b² = 4(1 + b)

(b) 4a + b = 1

(c) b² = 4 + a

(d) a² = 4 (b + 4)

Q2. For what value of c does the quadratic equation x² – (c²) x + 3(2c -1) = 0 have the sum of the roots as one-third of their product? (CAT Exam)

(a) 5 (b) 1 (c) 7 (d) 3

Q3. The difference between a fraction and its reciprocal equals 48/7. Find the fraction __________(CAT Exam- TITA]

Q4. For the given pair (x, y) of positive integers, such that 3x- 7y=1 and both x and y < 50, how many integer values of y satisfy the given conditions? (CAT Exam)

(a) 6 (b) 7 (c) 8 (d) 9

Q5. In CAT 2017 there were 62 questions. Each correct answer was rewarded with 3 marks and each wrong answer was penalised by 1 mark. In how many different combinations of the correct and wrong answers is a score of 50 possible? (CAT Exam)

(a) 14 (b) 15 (c) 16 (d) None of these

Q6. ‘Green & Fresh’ purchases y litres of fruit juice from the ‘Juice n Fruits’ for a total price of 6y^2 and sells the entire y litres at a total price of 10 × (7 + 8y/5). Find the minimum value of ‘y’ so that the ‘Green & Fresh’ does not make any loss. (CAT Exam)

(a) 50 (b) 5 (c) 15 (d) 7/3

Q7. If x² – 2x - 3 is a factor of x⁴ – ax² + b = 0 then the values of a and b are (CAT Exam)

(a) –10, –9 (b) 10, 9 (c) –10, 9 (d) 10, –9

Q8. In the land of famous architects, an architect sells his design for Rs 720 at some profit. Had he sold the design at Rs 540, the loss incurred would have been double that of the profit earned. What are the expenses to make a design? (CAT Exam)

(a) Rs 600 (b) Rs 625 (c) Rs 660 (d) None of these

Part-B (LRDI - CAT Sample Paper)

Direction (Q1-Q4): (CAT Exam)
Direction: The following questions are based on the information given below:
A cuboid-shaped wooden block has 10cm length, 8 cm breadth, and 1 cm height.
Two faces measuring 10 cm x 1 cm are coloured in blue.
Two faces measuring 8 cm x 1 cm are coloured in yellow.
Two faces measuring 10 cm x 8 cm are coloured in Pink.
The block is divided into 10 equal cubes of side 1 cm (from 10 cm side), and 8 equal cubes of side 1 cm(from 8 cm side).

Q1. How many cubes will have blue colour on two sides and the rest of the four sides having no colour? (CAT sample Paper)

(a) 24 (b) 48 (c) 8 (d) 32

Q2. How many small cubes will be formed? (CAT sample Paper)

(a) 80 (b) 19 (c) 40 (d) None of these

Q3. How many cubes having blue, yellow, and pink colours on at least one side of the cube will be formed? (CAT sample Paper TITA]

(a) 4 (b) 8 (c) 7 (d) 3

Q4. How many cubes will remain if the cubes having blue and pink coloured are removed? (CAT sample Paper)

(a) 80 (b) 12 (c) 40 (d) None of these

Direction (Q5- Q8)

A family of three generations has eight members A, B, C, D, E, F, G and H of them standing in a playground.
1. D’s daughter stands 6m south of her father.
2. A stands 4m north of his wife.
3. B is the mother of D. 5m towards the northeast of B is D.
4. C is the daughter-in-law of A and the mother of F.
5. D’s nephew stands 12m to the south of D and D’s sister-in-law stands in the middle of both of them.
6. E’s father stands 3m west of D.
7. E is the brother of D. E stands 10m towards the north-east of his father.
8. G stands 6m north of his daughter and 6m south of his brother-in-law.
9. G’s wife stands towards the west of her husband.

Q5: How is B related to F? (CAT sample Paper)

1. B is the grandmother of F

2. F is the nephew of B

3. B is the mother of F

4. Relation cannot be determined.

Q6. Which of the following about C is not true? (CAT sample Paper)

1. C is 6 m north of F

2. C is the daughter of B

3. C is the mother of F

4. E is the husband of C

Q7. Which of the following is not true? (CAT sample Paper)

1. C and H are on the same line

2. H is the cousin of F

3. The distance between E and C is 12 m.

4. E is the husband of C

Q8. If a male member from the 1st generation is the head of the family, then who is the head of the family? (CAT sample Paper)

(a) E (b) G (c) A (d) F

Part-C (VARC - CAT Sample Paper)

In the questions below, find the phrase with an error.

Q1: If I was the chief minister of the country, I will make primary education and poverty my top priorities. (CAT sample Paper)

1. If I was the chief minister of the country, I would

2. If I were the chief minister of the country, I would

3. If I were the chief minister of the country, I will

4. No correction required

Q2. One of the problems of the diamond industry are the increasing incidences of child exploitation. (CAT sample Paper)

1. Industry is the increasing incidence

2. Industry are the increasing incidence

3. Industry is the increasing incidences

4. No correction required

Q3. The large number of people have all but blocked all the highways in the city. (CAT sample Paper)

1. The sheer number of people have all

2. The large number of people has all

3. The greater number of people have all

4. No correction Required

Q4. Being a teacher, I was hoping if there were some tips you can give me on how to handle a class. (CAT sample Paper)

1. Being a teacher, I was hoping that you could give me some tips.

2. As you are a teacher, I was hoping if you could give me some tips

3. Being that you are a teacher, I was hoping if you could give me some tips

4. As you are a teacher, I was hoping that you could give me some tips.

Q5. As a child (1)/ I always want to (2)/ have a bicycle of my choice. (3)/ No error (4)

(a) 1 (b) 2 (c) 3 (d) 4

Q6. Without appointment, (1)/ your desire to meet(2)/ the prime minister cannot fulfill.(3)/ No error(4)

(a) 1 (b) 2 (c) 3 (d) 4

Q7. The professor is (1)/ delivering the lecture(2)/ for the last three hours.(3)/ No error(4)

(a) 1 (b) 2 (c) 3 (d) 4

Q8. The skilled labors (1)/ had always contributed (2)/ in the economy.(3)/ No error (4)

(a) 1 (b) 2 (c) 3 (d) 4

Q9. My wife paints (1)/ furniture whenever (2)/ she had time. (3)/ No error(4)

(a) 1 (b) 2 (c) 3 (d) 4

CAT Sample Papers: CAT questions with answers and Solutions

Part-A (Quantitative Aptitude - CAT Sample Paper Solution)

Ans 1: (d)

Let roots be α and β;

Sum of roots; α + β = -a

Product of roots; αβ = b

Also, α – β = 4

(α + β)² = (α – β)² + 4αβ

So, (-a)² = 4² + 4b

⇒ a² = 4² + 4b

⇒ a² = 4(4 + b)

Ans 2: (b)

Sum of roots = c² (Using sum of roots = -b/a)

Product of roots = 3(2c - 1)

According to question

c² = 1/3 (3(2c - 1)) = 2c - 1

⇒ c² - 2c + 1 = 0

⇒ (c -1)² = 0

⇒ c = 1

Ans 3: 7

Let the fraction be ‘x’

It's reciprocal will be 1/x

So, x – 1/x = 48/7

⇒ x² – 1 = 48x/7

⇒ 7x² – 48x – 7 = 0

⇒ 7x² – 49x + x – 7 = 0

⇒ 7x (x – 7) + (x – 7) = 0

⇒ (x – 7) (7x + 1) = 0

⇒ x = 7 or x = -1/7

So, x = 7 will be the answer.

Ans 4: (a)

3x = 1+ 7y

For integral solutions, (1 +7y) should be a multiple of 3.

y= 2, x = 5

y = 5, x = 12

y = 11, x = 26

y = 14, x = 33

y = 17, x = 40

y = 20, x = 47

y = 23, x = 54, where x is greater than 50. So the total solutions are 6.

Ans 5: (d)

Let correct questions be x, wrong questions are y and non-attempted are z.

So, x + y + z = 62

and 3x -y + 0 = 50 (according to question)

The minimum value of x for which 3x – y = 50 is 17.

The maximum value of x is when z = 0.

If z = 0, x + y = 62 or y = 62 – x

So, 3x – (62 – x) = 50

So, x = 28.

Therefore, No. of valid values for x will be from 17 to 28 = 12.

Ans 6: (b)

Profit = 10(7 +8y/5) – 6y2

To find the minimum profit

10(7 +8y/5) – 6y2 ≥ 0

Or, 70 + 16y – 6y2 ≥ 0

Or, 6y2 – 16y -70 ≤ 0

On solving, we get

Or, y ≥ 5 or y ≤ -7/3

So, the minimum value of y is 5.

Ans 7: (b)

Factor of x² – 2x + 3 are (x-3) and (x + 1)

So, x =3 and x = -1 will also satisfy x⁴ – ax² + b = 0

At x = 3, 34 – a x 32 + b = 0 ⇒ 81 - 9a + b = 0

At x = -1, (-1) 4-a (-1) 2+b = 0 ⇒ 1 – a + b = 0

On solving the above equations, a = 10, b = 9.

Ans 8: (c)

Profit = 720 – CP

Loss = CP – 540

According to the conditions;

Loss = 2 x Profit

CP – 540 = 2 (720 – CP)

So, CP = Rs 660.

Part-B (LRDI - CAT Sample Paper Solution)

Ans 1: (b)

Except for boundary cubes, all other cubes will satisfy this condition.
Total cubes will be 80 and boundary cubes will be 32 so the rest cubes will be 80 – 32 = 48.

Ans 2: (a)

Since the block is divided into 10 equal cubes of side 1 cm (from 10 cm side), and 8 equal cubes of side 1 cm(from 8 cm side). So, the total number of small cubes = 10 × 8 = 80.

Ans 3: (a)

only corner cubes will have three surface paints and this cuboid has only four corner faces. so, the answer will be 4.

Ans 4: (b)

Only a single side-colored yellow cube will be left out. So, the answer will be
6 + 6 = 12 cubes.

Ans 5: (a)

B is the grandmother of F

Ans 6: (b)

C is the daughter of B. All are true except (2).

Ans 7: (c)

The distance between E and C is 12 m.
The distance between E and C cannot be determined since we don’t know the distance between C and H.

Ans 8: (c)

From the given information, draw a family tree and distance diagram as shown:

Part-C (VARC - CAT Sample Paper Solution)

Ans 1: (b)

‘Was’ is associated with the past tense. In discussing hypothetical situations, the subjunctive mood is used.
The correct usage is ‘If I were…I would….’

Ans 2: (c)

One of the problems is singular, as it refers to one of many problems. So, the right verb to be used with this subject is ‘is’, not ‘are’. The correct usage is “One of the problems……..is…

Ans 3: (b)

The expression ‘the number’ indicates a single arithmetical value. So, it is followed by a singular verb. On the other hand, the expression ‘a number’ serves as an indefinite pronoun meaning many. So, it is followed by a plural verb.

Ans 4: (d)

The first error is corrected by either saying ‘as you are a teacher’, or ‘being that you are a teacher’. The second error is in the use of ‘if’ after ‘hoping’. ‘Hoping’ is normally followed by a noun clause beginning with ‘that’(either explicitly stated or implied), or it is followed by ‘for’, or ‘to’.

Ans 5: (b)

use the 2nd form of the verb. Wanted in place of want.

Ans 6: (c)

Be fulfilled in place of fulfil

Ans 7: (a)

replace is with has been

Ans 8: (b)

have in place of “had”.

Ans 9: (c)

replace had with has

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