CAT MCQs on Number System: CAT Questions for Practice with Solutions

The CAT QA section requires speed and accuracy, along with a thorough understanding of the Number System. This article provides a set of MCQs on Number System to help you understand the topic and improve your problem-solving skills with the help of detailed solutions by ensuring conceptual clarity, which will help you in the CAT preparation.

Whether you're revising the basics or testing your knowledge, these MCQs will serve as a valuable practice resource.

The CAT 2025 exam is expected to follow a similar trend to the CAT 2024, with 22 questions from the QA section out of a total of 68 questions.

CAT MCQs on Number System

1. Consider a sequence \( S \) whose \( n \)th term \( T_n \) is defined as \( T_n = 1 + \frac{3}{n} \), where \( n = 1, 2, \ldots \). Find the product of all the consecutive terms of \( S \) starting from the 4th term to the 60th term.

1980.55

1985.55

1990.55

1975.55

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2. Let \( P = \{2, 3, 4, \ldots, 100\} \) and \( Q = \{101, 102, 103, \ldots, 200\} \). How many elements of \( Q \) are there such that they do not have any element of \( P \) as a factor?

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3. Find the remainder when \( 2^{1040} \) is divided by 131.

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4. \( p \) is a prime and \( m \) is a positive integer. How many solutions exist for the equation \[p^5 - p = (m^2 + m + 6)(p - 1)?\]

Infinite

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5. A certain number written in a certain base is 144. Which of the following is always true?

I. Square root of the number written in the same base is 12

II. If base is increased by 2, the number becomes 100

Neither I nor II

Both I and II

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6. When asked for his taxi number, the driver replied, “If you divide the number of my taxi by 2, 3, 4, 5, 6 each time you will find a remainder of one. But if you divide it by 11, the remainder is zero.” What is the taxi number?

121

1001

1881

781

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7. Sujith says: - Multiplying first two digits by 3 gives all ones.
- Multiplying next two digits by 6 gives all twos.
- Multiplying last two digits by 9 gives all threes.
What is the sum of digits in the number?

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Three words “Madhu”, “Sweet”, and “House” blink as follows:
- Each word flashes at regular interval and stays ON for 1 second.
- "Madhu" every 3.5 s, "Sweet" every 5.25 s, "House" every 6.75 s.
All three flash together at 8:00 a.m. Find time until next flash where last two words ("Sweet" and "House") flash together.

45 seconds

22.5 seconds

112 seconds

6.75 seconds

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9. What is the number of positive integers less than or equal to 1000 that are divisible by neither 2 nor 5?

400

300

500

600

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10. The ratio of two numbers is 3:4. If their sum is 70, what is the larger number?

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11. What is the sum of the first 20 terms of the arithmetic sequence 3, 7, 11, …?

800

820

840

860

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12. If \( \sin \theta + \cos \theta = \sqrt{2} \), what is \( \sin \theta \cos \theta \)?

\( \frac{1}{2} \)

\( \frac{1}{4} \)

\( \frac{1}{3} \)

\( \frac{1}{6} \)

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13. A number when divided by 7 leaves a remainder of 4. What is the remainder when the square of the number is divided by 7?

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14. If \( r, s, t \) are consecutive odd integers with r

A
\( r + t = 2s \)

B
\( r + t = 2s + 2 \)

C
\( r + s = t - 2 \)

D
\( r + t = 2s + 5 \)

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15. \( P, Q, R \) are three consecutive odd numbers in ascending order. If the value of three times \( P \) is three less than two times \( R \), find the value of \( R \).

A
5

B
7

C
9

D
11

View Solution

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CAT MCQs on Number System: CAT Questions for Practice with Solutions

CAT MCQs on Number System

3.
A price is increased by 15 to Rs. 230. What was the original price?

4.
The price of a Maruti car rises by 30% while the sales of the car come down by 20%. What is the percentage change in the total revenue?

5.
40% of the employees of an organization are men. Of these 75% earn more than Rs. 25,000 per year. If 45% of the total employees of the company earn more than Rs. 25,000 per year, then what fraction of the women earn more than Rs. 25,000 per year?

6.
I bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was half more what I had paid. What per cent of the total amount paid by me was paid for the pens?

9.
In the final examination, Bishnu scored 52% and Asha scored 64%. The marks obtained by Bishnu is 23 less, and that by Asha is 34 more than the marks obtained by Ramesh. The marks obtained by Geeta, who scored 84%, is

10.
A number is increased by 25 and then decreased by 25. What is the net percentage change?

11.
Out of two-thirds of the total number of basketball matches, a team has won 17 matches and lost 3 of them. What is the maximum number of matches that the team can lose and still win more than three fourths of the total number of matches, if it is true that no match can end in a tie?

12.
After two successive increments, Gopal's salary became 187.5% of his initial salary. If the percentage of salary increase in the second increment was twice of that in the first increment, then the percentage of salary increase in the first increment was

13.
Seventy percent of the employees in a multinational corporation have VCD players, 75% have microwave ovens, 80% have ACS and 85% have washing machines. At least what percentage of employees has all four gadgets?

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CAT MCQs on Number System

3.A price is increased by 15 to Rs. 230. What was the original price?

4.The price of a Maruti car rises by 30% while the sales of the car come down by 20%. What is the percentage change in the total revenue?

5.40% of the employees of an organization are men. Of these 75% earn more than Rs. 25,000 per year. If 45% of the total employees of the company earn more than Rs. 25,000 per year, then what fraction of the women earn more than Rs. 25,000 per year?

6.I bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was half more what I had paid. What per cent of the total amount paid by me was paid for the pens?

9.In the final examination, Bishnu scored 52% and Asha scored 64%. The marks obtained by Bishnu is 23 less, and that by Asha is 34 more than the marks obtained by Ramesh. The marks obtained by Geeta, who scored 84%, is

10.A number is increased by 25 and then decreased by 25. What is the net percentage change?

11.Out of two-thirds of the total number of basketball matches, a team has won 17 matches and lost 3 of them. What is the maximum number of matches that the team can lose and still win more than three fourths of the total number of matches, if it is true that no match can end in a tie?

12.After two successive increments, Gopal's salary became 187.5% of his initial salary. If the percentage of salary increase in the second increment was twice of that in the first increment, then the percentage of salary increase in the first increment was

13.Seventy percent of the employees in a multinational corporation have VCD players, 75% have microwave ovens, 80% have ACS and 85% have washing machines. At least what percentage of employees has all four gadgets?

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3.
A price is increased by 15 to Rs. 230. What was the original price?

4.
The price of a Maruti car rises by 30% while the sales of the car come down by 20%. What is the percentage change in the total revenue?

5.
40% of the employees of an organization are men. Of these 75% earn more than Rs. 25,000 per year. If 45% of the total employees of the company earn more than Rs. 25,000 per year, then what fraction of the women earn more than Rs. 25,000 per year?

6.
I bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was half more what I had paid. What per cent of the total amount paid by me was paid for the pens?

9.
In the final examination, Bishnu scored 52% and Asha scored 64%. The marks obtained by Bishnu is 23 less, and that by Asha is 34 more than the marks obtained by Ramesh. The marks obtained by Geeta, who scored 84%, is

10.
A number is increased by 25 and then decreased by 25. What is the net percentage change?

11.
Out of two-thirds of the total number of basketball matches, a team has won 17 matches and lost 3 of them. What is the maximum number of matches that the team can lose and still win more than three fourths of the total number of matches, if it is true that no match can end in a tie?

12.
After two successive increments, Gopal's salary became 187.5% of his initial salary. If the percentage of salary increase in the second increment was twice of that in the first increment, then the percentage of salary increase in the first increment was

13.
Seventy percent of the employees in a multinational corporation have VCD players, 75% have microwave ovens, 80% have ACS and 85% have washing machines. At least what percentage of employees has all four gadgets?