Number System Questions for the CAT exam are part of the Quantitative Aptitude section in the CAT exam. Through number system questions, aspirants are tested on concepts related to Factors, Factorials, HCF and LCM, base system & remainders. The difficulty level of the number system questions can be easy to moderate.

**Number System Practice Questions for CAT exams**

**Q1.** Jay has 3 types of boxes: Large, medium and small. He first puts 10 large boxes on a table. He leaves some of these boxes empty and in all the other boxes puts 7 empty medium-sized boxes. He then leaves some of the medium-sized boxes empty and places 7 empty small boxes in the other medium-sized boxes. If 82 boxes on the table were empty, then what is the total number of boxes he used? (All large boxes are of the same size, all medium boxes are of the same size and all small boxes are of the same size)

A. 88

B. 90

C. 94

D. 98

**Answer:** Option C

**Q2.** The sum of all two-digit numbers that give a remainder of A when they are divided by 7 is 654. What is the value of A?

**Answer:**2

**Q3.** 207 people who attend "Bold Gym" in Kondapur take four types of juices Apple, Orange, Pomegranate and Mango. There are a few people who do not take any of the juices. It is known that for every person in the Gym who takes atleast 'N' types of juices there are 2 persons who take atleast 'N-1' juices for N = 2, 3 and 4. If the number of people who take all four types of juices is equal to the number of people who do not take any juice at all, what is the number of people who take exactly 2 types of juices?

A. 23

B. 46

C. 69

D. 92

**Answer:** Option C

**Q4. **Aron bought some pencils and sharpeners. Spending the same amount of money as Aron, Aditya bought twice as many pencils and 10 less sharpeners. If the cost of one sharpener is â‚¹ 2 more than the cost of a pencil, then the minimum possible number of pencils bought by Aron and Aditya together is

A. 33

B. 27

C. 30

D. 36

**Answer: **Option** ** A

**Q5. **Students in a college have to choose at least two subjects from chemistry, mathematics and physics. The number of students choosing all three subjects is 18, choosing mathematics as one of their subjects is 23 and choosing physics as one of their subjects is 25. The smallest possible number of students who could choose chemistry as one of their subjects is

A. 22

B. 21

C. 20

D. 19

**Answer:** Option C

**What are the must-do number system questions for the CAT exam?**

**Q6.** The mean of all 4-digit even natural numbers of the form 'aabb', where a > 0, is

A. 4466

B. 5050

C. 4864

D. 5544

**Answer:** Option D

**Q7. **Among 100 students, have birthdays in January, have birthdays in February, and so on. If , then the smallest possible value of is

A. 8

B. 9

C. 10

D. 12

**Answer:** Option B

**Q8.** How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7?

**Answer: **21

**Q9. **A gentleman decided to treat a few children in the following manner. He gives half of his total stock of toffees and one extra to the first child, and then the half of the remaining stock along with one extra to the second and continues giving away in this fashion. His total stock exhausts after he takes care of 5 children. How many toffees were there in his stock initially?

**Answer: **62

**Q10. **In a school, every student likes one of the three sports - Cricket, Football, Rugby. 65% of the students like Cricket, 86% like Football and 57% of the students like Rugby. What is the maximum percentage of students who like exactly two sports?

A. 92%

B. 80%

C. 54%

D. 46%

**Answer:** Option A

**Which are the most expected number system questions for the CAT 2024?**

**Q 11**. 9 × 25, where 9 and 25 are co-primes.

Clearly, a number is divisible by 225 if it is divisible by both 9 and 25.

Now, a number is divisible by 9 if the sum of its digits is divisible by 9 and a number is divisible by 25 if the number formed by the last two digits is divisible by 25.

The smallest number which is made up of digits 1 and 0 and divisible by 225 = 11111111100.

Hence, number of digits = 11. -7m -[3n -{8m -(4n - 10m)}]

A. 11m - 5n

B. 11m - 7n

C. 11n - 7m

D. 13n - 11m

**Answer**: Option B

**Q 12.** What is the number of zeros at the end of the product 55 × 1010 × 1515 × ........ × 125125?

**Solution**. Clearly, the highest power of 2 is less than that of 5 in N.

So, the highest power of 2 in N shall give us the number of zeros at the end of N.

Highest power of 2

= Number of multiples of 2 + Number of multiples of 4 (i.e. 22) + Number of multiples of 8 (i.e. 23) + Number of multiples of 16 (i.e. 24)

= [(10 + 20 + 30 +....... + 120) + (20 + 40 + 60 +........ + 120) + (40 + 80 + 120) + 80] = (780 + 420 + 240 + 80)

= 1520. Hence, required number of zeros = 1520

**Q 13.** A number when divided by 114, leaves remainder 21. If the same number is divided by 19, find the remainder.

**Solution**. On dividing the given number by 114, let k be the quotient and 21 the remainder.

Then, number = 114 k + 21 = 19 × 6k + 19 + 2 = 19 (6k + 1) + 2.

The given number when divided by 19 gives remainder = 2.

**Q 14.** What is the place value of 5 in 3254710?

(a) 5

(b) 10000

(c) 50000

(d) 54710

**Answer.** Option (C)

**Find some previous year number system questions from the CAT 2023**

**Q 15.** The face value of 8 in the number 458926 is

(a) 8

(b) 1000

(c) 8000

(d) 8926

**Answer.** Option (A)

**Q 16.** The sum of the place values of 3 in the number 503535 is

(a) 6

(b) 60

(c) 3030

(d) 3300

**Answer.** Option (C)

**Q 17.** What is the sum of all natural numbers from 1 to 100?

(a) 5050

(b) 6000

(c) 5000

(d) 5052

**Answer.** Option (A)

**Q 18.** If the sum of two numbers is 14 and their difference is 10, find the product of these two numbers.

(a) 18

(b) 20

(c) 24

(d) 22

**Answer.** Option (C)

**Q 19.** If the sum of two numbers is 14 and their difference is 10. Find the product of these two numbers.

(a) 24

(b) 22

(c) 20

(d) 18

**Answer.** Option (B)

**What are the most important number system questions for the CAT 2024?**

**Q 20.** Two consecutive even positive integers, sum of the squares of which is 1060, are

(a) 12 and 14

(b) 20 and 22

(c) 22 and 24

(d) 15 and 18

**Answer.** Option (C)

**Q 21.** The number of three digit numbers which are multiples of 9 are

(a) 100

(b) 99

(c) 98

(d) 101

**Answer.** Option (A)

**Q 22. **The least number of five-digit is exactly divisible by 88 is

(a) 10032

(b) 10132

(c) 10088

(d) 10023

**Answer.** Option (A)

**Q 23. **What minimum value should be assigned to *, so that 2361*48 is exactly divisible by 9? (a) 2

(b) 3

(c) 9

(d) 4

**Answer.** Option (B)

**Q 24.** Every rational number is also

(a) an integer

(b) a real number

(c) a natural number

(d) a whole number

**Answer.** Option (B)

**Which are the most repeating number system questions in the CAT Exam?**

**Q 25.** The difference between the place values of 7 and 3 in the number 527435 is

(a) 4

(b) 5

(c) 45

(d) 6970

**Answer.** Option (D)

**Q 26.** What are the five rational numbers between 1 and 2?

**Solution:** We need to find 5 rational numbers between 1 and 2

Divide and multiply both the numbers by (5+1)

Hence,

6/6 and 12/6 are rational numbers now.

Therefore, the required rational numbers between 1 and 2 are:

6/6, 7/6, 8/6, 9/6, 10/6, 11/6, 12/6

**Q 27**. Show that 0.3333…, can be expressed in the form of a rational number, i.e. p/q.

Solution: Let x = 0.33333

10 x = 10 × (0.333…) = 3.333…

We can write,

3.3333… = 3 + 0.3333… = 3 + x

Thus,

10 x = 3 + x

9x = 3

x=â…“

**Q 28**. The difference between the greatest and the least four-digit numbers that begin with 3 and ends with 5 is

(a) 900

(b) 909

(c) 999

(d) 990

**Answer.** Option (D)

**Q 29.** Consider the following statements for the sequence of numbers given below: 11, 111, 1111, 11111, …. 1. Each number can be expressed in the form (4m + 3), where m is a natural number. 2. Some numbers are squares. Which of the above statements is/are correct?

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) neither 1 nor 2

**Answer.** Option (A)

**Which are the most difficult number system questions for the CAT exam?**

**Q 30.** The number of three-digit numbers which are multiples of 9 are

(a) 100

(b) 99

(c) 98

(d) 101

**Answer**. Option (B)

**Q 31.** The least number of five-digit is exactly divisible by 88 is

(a) 10032

(b) 10132

(c) 10088

(d) 10023

**Answer.** Option (A)

**Q 32.** When a number is divided by 13, the remainder is 11. When the same number is divided by 17, the remainder is 9. What is the number?remainder 1. What will be the remainder when the number is divided by 6?

(a) 2

(b) 3

(c) 4

(d) 5

**Answer.** Option (B)

**Q 33.** If the sum of two numbers is 14 and their difference is 10. Find the product of these two numbers.

(a) 24

(b) 22

(c) 20

(d) 18

**Answer.** Option (A)

**Q 34. **The sum of the perfect squares between 120 and 300 is

(a) 1204

(b) 1024

(c) 1296

(d) 1400

**Answer.** Option (D)

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