CAT 2025 Practice Set- Sample Paper, Questions With Solutions | Day 4

CAT Practice Test

Part-A: CAT Quant Questions Topic Wise

Q1. Find the remainder when 6576 is divided by 7.

1. 4

2. 3

3. 2

4. 6

Q2. Find the remainder when 38177 is divided by 17.

1. 12

2. 13

3. 6

4. 4

Q3. My year of birth is 1974. What would the year have been instead of 1974 if base 12 were used (for counting) instead of the decimal system?

1. 1186

2. 1022

3. 2082

4. 1192

Q4. Unit digit of 7243 × 6384 × 7497 × 7676 × 87109 × 8890

1. 2

2. 6

3. 4

4. 8

Q5. The difference of 1035 – 4 and 1034 - x is divisible by 3 for x =?

1. 3

2. 2

3. 4

4. 6

Q6. If 42n + 1 + x and 4n – x is divisible by 5, n being an even integer, find the least value of x.

1. 1

2. 2

3. 3

4. 0

Q7. What is the remainder when 3 + 32 + 33 + ….32n+1 is divided by 6?

1. 1

2. 2

3. 3

4. 4

Q8. The remainder when the number 123456789101112 ……383940 is divided by 16 is:

1. 3

2. 4

3. 5

4. 6

Part-B: LRDI Sets For CAT

Direction (Q1-Q3):

Chart 1: Shows the distribution by the value of a Commodity by top 6 countries in 2000

Chart 2: Shows the distribution by the quantity of top 6 suppliers of a Commodity in 2000

Total value is Rs. 5000 crores

Total quantity is 1000 crore tonnes

Q1. The country which has the highest average price is?

1. USA

2. Sweden

3. INDIA

4. CHINA

Q2. The average price (Rs. per ton) for PNG is roughly?

1. 1.2

2. 0.50

3. 3.75

4. 80

Q3. The country which has the lowest average price is?

1. USA

2. JAPAN

3. INDIA

4. CHINA

Directions for questions 4 to 6: Answer the questions on the basis of the information given below.

P and N are two brands of kitchen Slicers available in the local market. P was introduced in 1990, while N was introduced in 1997. For both these brands, 20% of the slicers bought in a particular year were considered as nonoperative exactly two years later. It is known that 10 P-Slicers were disposed of in 1997. The following figures show the number of P and N Slicers in operation from 1995 to 2000, as of the end of the year.

Q4. How many N Slicers were purchased in 1999?

1. 45

2. 54

3. 50

4. 20

Q5. How many N- Slicers were disposed of by the end of 2000?

1. 20

2. 16

3. 40

4. 30

Q6. How many P-Slicers were disposed of in 2000?

1. 20

2. 16

3. Cannot be determined from data

4. 30

Direction (Q7-9):

Four children, Aman, Sanu, Anil and Rohit become a part of a survey about their weight and heights. Their weights and heights were measured every two years between the ages of 4 years and 16 years. The graph informs us about the ratio of their weights (in kgs) to their heights (in inches).

The following graph informs about the weights (in kgs) with ages at X-axis

Q7. The difference between the heights of Sanu and Rohit at the age of 10 is?

1. 1-inch

2. 1.5 inches

3. 2 inches

4. 2.5 inches

Q8. By how many inches did Anil grow in height from the age of 6 years to 10 years?

1. 7.5 inches

2. 10 inches

3. 12.5 inches

4. 15 inches.

Q9. Who among the four children was the shortest at 8 years of age?

1. Aman

2. Sanu

3. Anil

4. Rohit

Part-C (VARC)

Q1: The management has suggested that he recuse himself from the allegations, whether he is elected or not.

1. have insisted that he recuses himself from the allegations, whether he is elected or not.

2. has insisted that he recuses himself from the allegations, whether or not he is elected.

3. has insisted that he recuses himself from the ongoing allegations, whether he is elected or not.

4. No correction required

Q2. Find out the proper noun in the following sentence:

The beauty of the lake is unparalleled.

1. Beauty

2. Lake

3. Both A & B

4. None of the Above

Q3. Whoever is chosen as the new Vice-Chancellor of University, it is likely to continue some of the policies regarding the dress code.

1. Whoever is chosen as the new chief, they are

2. Whomever is chosen as the new chief, he is

3. Whoever is chosen as the new chief is

4. No correction required

Q4. The Footballer, whose record is exemplary, bagged a seven-year endorsement contract with a sports equipment manufacturer.

1. who’s record is exemplary, bagged eight years’ endorsement contract

2. who’s record is exemplary, bagged eight year’s endorsement contract

3. whose record is exemplary, bagged an eight-years endorsement contract

4. No correction required

Q5. One of the problems that occur as a result of increasing population is the decrease in the opportunities of Job.

1. that occurs as a result of increasing population are the

2. that occurs as a result of increasing population is the

3. that occur as a result of increasing population are the

4. that occur as a result of increasing population is the

Q6. The sheer number of trucks on the Express way have all but paralyzed the traffic system.

1. The sheer number of trucks on the Express way has

2. The shear number of trucks on the Express way have

3. The shear number of trucks on the Express way has

4. No correction required

Q7. ‘To be, or not to be, that is the question.’

Identify the verb in the sentence

1. Is

2. To be

3. Or

4. That

Q8. The striking panorama of elegantly spread flowers in the state of Uttarakhand provides evidence of why Uttarakhand, a state, is called “Valley of Flower”.

1. provide evidence of why Uttarakhand, a state, is called “Valley of Flower”.

2. provide evidence of why Uttarakhand, a state, are called “Valley of Flower”.

3. provides evidence of why Uttarakhand, a state, is called “Valley of Flower”.

4. provides evidence of why Uttarakhand, a state, are called “Valley of Flower”.

CAT Practice Papers: Answers And Solutions

Part A (Quantitative Aptitude)

Ans 1: C

Rem (65/7) ? 2

276 ? (23)25x2

Rem ((23)/7) ?1

Rem (125/7) ? 1

Rem [(2x (23)25)/7] ? 2x1 =2; where Rem (x/y) represents the value of remainder when x is divided by y.

Ans 2: (c)

Rem (381/17) ? 7

777 ? (72)38x7

Rem ((72)/17) ?-2

Rem ((-2)38/17) ? Rem [((-2)4x9x(-2)2)/17] ? Rem [(4x169)/17]

When 16 is divided by 17, remainder is -1 and (-1)^9 is -1.

Therefore, when (4x169) is divided by 17, remainder is 4x(-1) = -4.

So, the remainder when (72)38 is divided by 17 = (17-4) = 13.

So, when 777 is divided by 17 remainders = Rem (7x13/17)= 6

where Rem (x/y) represents the value of remainder when x is divided by y.

Ans 3: A

For that, divide 1974 by 12 as shown

Write the remainders from bottom to top

So, in base 12 years of birth is (1186)

Ans 4: (b)

Cyclicity of 2 is 4 i.e. unit digit is repeated after every 4th power of 2

So, Unit digit of 7243 is same as unit digit of 23 which is equal to 8.

The cyclicity of 3 is 4 i.e. unit digit is repeated after every 4th power of 3

So, the unit digit of 6384 is the same as the unit digit of 34 which is equal to 1.

The unit digit of 4^odd is always 4.

The unit digit to any power of 6 is 6.

Cyclicity of 7 is 4 i.e. unit digit is repeated after every 4th power of 7

So, the Unit digit of 87109 is the same as the unit digit of 71 which is equal to 7.

Cyclicity of 8 is 4 i.e. unit digit is repeated after every 4th power of 8.

So, the unit digit of 8890 is the same as the unit digit of 82 which is equal to 4.

Therefore, the Unit digit of 7243 × 6384 × 7497 × 7676 × 87109 × 8890 will be equal to the unit digit of 8x1x4x6x7x4 i.e. equal to 6.

Ans 5: (c)

Difference = (1035 – 4) – (1034 - x) = (1035 – 1034 + x- 4) = 1034(10 – 1) + (x-4) = 9x1034 + (x-4)

9x1034 is divisible by 3 since it is multiple of 3.

(x-4) is divisible by 3 if x is 4 in the given options.

Ans 6: (a)

Since n is even, unit digit of 42n + 1 = 4 (Since 4^odd is always gives 4 as unit digit)

and unit digit of 4n = 6 (Since 4^odd is always gives 6 as unit digit)

Therefore, 42n + 1 + x is divisible by 5 if x is 1, 6, 11, 16, …….

and 4n – x is divisible by 5 if x is 1, 6, 11, 16, …….

So, the least value of x is 1.

Ans 7: (c)

When 3 is divided by 6, the remainder is 3.

When 32 is divided by 6, the remainder is 3.

When 33 is divided by 6, the remainder is 3.

When 34 is divided by 6, the remainder is 3 and so on.

So, the remainder is 3 + 3 + 3 + ……up to 2n+1 terms.

If 3 is added to an odd number of terms, after dividing by 6 it will give a remainder of 3.

Ans 8: (b)

Divide the last 4 digits of the number to find the remainder when the number is divided by 16 (according to the divisibility rule of 16)

So, Rem (3940/16) = 4

Part B (LRDI Practice Sets)

Ans 1: B

Average Price will be calculated by Average Price = Total value/ Total quantity

As seen from charts Sweden will have highest ratio = 20/11

So, Sweden will have the highest average Price.

Ans 2: C

Average Price will be calculated by Average Price = Total value/ Total quantity

For PNG = Price/ Quantity = (12% of 5000)/(16% of 1000) = Rs 3.75 per ton.

Ans 3: C

The country which will have the least ratio of ‘share in total value’ to ‘share in total quantity’ will have the least average value.

Average Price will be calculated by Average Price = Total value/ Total quantity

As seen from the table, PNG will have the lowest average Price.

Ans 4: C

Total N-slicers in 1999 = 124

Initially slicers in 1997 the slicers were 30 and in 1998, 50 slicers were bought

In 1999, 20% of slicers from 1997 must be disposed of (20% of 30= 6) which means 24 remains in operative condition.

So, N-Slicers bought in 1998 must be 80 – 30 = 50

So, N-Slicers bought in 1999 must be 124 – 50 - 24 = 50

Ans 5: B

Number of slicers disposed of in 1999 is 20% of 30 (bought in 1997) = 6

Number of slicers disposed of in 2000 is 20% of 50 (Which were bought in 1998) = 10

So total by end of 2000 is = 10 + 6= 16

Ans 6: C

Since P-slicers were introduced in 1990, we don't have data from 1990 to 1995. Therefore, we cannot find this answer.

Ans 7: C

we know that R = and we also know the weights from the second graph.

Thus, the heights can be found as Height = .

Height of Sanu when he was 10 years old = 42/0.8 = 52.5 inches.

Height of Rohit when he was 10 years old = 60/1.1 = 54.54 inches.

Thus, the required difference = 54.54 – 52.5 = 2.04 inches

Ans 8: D

Anil's height when he was 6 years old = 40/1.3 = 30.76

Anil's height when he was 10 years old = 46/1 = 46

Thus, Height increases by 15.24 inches.

Ans 9: A

The heights of Aman, Sanu, Anil and Rohit when 8 years old are 48/1.3, 46/1, 38/1, 54/1.2 i.e. 36.9, 46, 38, 45 respectively. Thus the shortest among them is Aman.

Part C (VARC)

Ans 1: D

A verb associated with suggestion is used with a noun clause beginning with ‘that’, the clause (whether the clause is singular or plural) uses the base verb. So, in the given sentence, ‘recuse’ is correct.

So, no correction is required.

Ans 2: B

Lake is proper noun

Beauty is an abstract noun.

Ans 3: C

In the underlined portion, “Whoever is chosen as the new Vice-Chancellor of University” is followed by ‘it’ which is incorrect because ‘Whoever’ cannot be followed by ‘it’ pronoun.

‘Whoever’ is a singular pronoun. So, ‘they’ cannot be used for ‘whoever’ (option A is incorrect)

‘Whomever’ is the wrong word in this context. (Option B is incorrect)

Option C contains no error.

Ans 4: D

The underlined part is grammatically correct.

Ans 5: D

Two Verbs are used:

1. occur ? it is referred to ‘problems’, so it is correctly used.

2. is ? referred to ‘one of the problems’ which is singular. So, it is also correctly used.

Ans 6: A

the subject of the sentence is ‘the sheer number’ which is singular, since the noun (‘number’) is singular. The verb ‘have’ relates to this, and not ‘trucks’.

Therefore ‘have’ should be replaced by ‘has’.

Answer 7: A

‘Is’ acting as the main verb in the sentence

Ans 8: C

‘Panorama’ is singular. So, the verb associated with this is ‘provides’, not ‘provide

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