Number Systems for Competitive Exam Success

Number Systems

Base Systems Digital Sum Divisibility Rules Factors & Multiples HCF & LCM Modular Arithmetic Remainders

Q. If the LCM of three numbers is 120 and their HCF is 2, what is the maximum possible product of the three numbers? (2023)

A. 240
B. 480
C. 600
D. 720

Solution

The maximum product occurs when the numbers are 2, 10, and 6, giving a product of 120.

Correct Answer: C — 600

Learn More →

Q. If the LCM of three numbers is 180 and their HCF is 3, what is the maximum possible product of the three numbers? (2023)

A. 540
B. 1800
C. 5400
D. 18000

Solution

The maximum product of the three numbers can be calculated as (LCM * HCF^2) = 180 * 3^2 = 5400.

Correct Answer: C — 5400

Learn More →

Q. If the LCM of three numbers is 180 and their HCF is 3, what is the product of the three numbers? (2023)

A. 540
B. 1800
C. 5400
D. 18000

Solution

The product of the three numbers is equal to LCM * HCF^2. Therefore, 180 * 3^2 = 180 * 9 = 1620.

Correct Answer: C — 5400

Learn More →

Q. If the LCM of two numbers is 120 and their HCF is 10, what is the product of the two numbers? (2023)

A. 1200
B. 1000
C. 2400
D. 600

Solution

The product of two numbers is equal to the product of their LCM and HCF. Therefore, 120 * 10 = 1200.

Correct Answer: A — 1200

Learn More →

Q. If the LCM of two numbers is 120 and their HCF is 5, what is the product of the two numbers? (2023)

A. 600
B. 1200
C. 240
D. 300

Solution

The product of two numbers is equal to the product of their LCM and HCF. Therefore, 120 * 5 = 600.

Correct Answer: A — 600

Learn More →

Q. If the LCM of two numbers is 180 and their HCF is 15, what is the sum of the two numbers? (2023)

A. 75
B. 90
C. 105
D. 120

Solution

Let the two numbers be 15a and 15b. Then, LCM = 15ab = 180, so ab = 12. The pairs (3, 4) give the numbers 45 and 60, summing to 105.

Correct Answer: C — 105

Learn More →

Q. If the LCM of two numbers is 60 and one of the numbers is 15, what is the other number?

A. 30
B. 45
C. 20
D. 12

Solution

Using the relation LCM(a, b) = (a * b) / HCF(a, b), we can find the other number. Here, 60 = (15 * x) / HCF(15, x). The other number is 60 / 15 = 4.

Correct Answer: A — 30

Learn More →

Q. If the LCM of two numbers is 60 and their HCF is 4, what is the product of the two numbers? (2023)

A. 240
B. 120
C. 300
D. 180

Solution

The product of two numbers is equal to the product of their LCM and HCF. Therefore, 60 * 4 = 240.

Correct Answer: A — 240

Learn More →

Q. If the LCM of two numbers is 60 and their HCF is 5, what is the sum of the two numbers if they are both less than 30? (2023)

A. 25
B. 35
C. 40
D. 30

Solution

Let the two numbers be 5a and 5b. Then, LCM(5a, 5b) = 5 * LCM(a, b) = 60, which gives LCM(a, b) = 12. The pairs (3, 4) work, giving numbers 15 and 20, which sum to 35.

Correct Answer: D — 30

Learn More →

Q. If the LCM of two numbers is 72 and one of the numbers is 24, what is the other number? (2023)

A. 18
B. 36
C. 48
D. 12

Solution

Using the relationship between LCM and the numbers: (24 * x) / HCF = 72. The other number is 36.

Correct Answer: B — 36

Learn More →

Q. If the LCM of two numbers is 84 and their HCF is 7, what is the sum of the two numbers if one of them is 21? (2023)

A. 42
B. 63
C. 84
D. 105

Solution

Let the other number be x. Then, 84 = (21 * x) / 7. Solving gives x = 28. The sum is 21 + 28 = 49.

Correct Answer: B — 63

Learn More →

Q. If the least common multiple (LCM) of two numbers is 36 and their greatest common divisor (GCD) is 6, what can be inferred about the product of the two numbers?

A. It is 216.
B. It is 72.
C. It is 36.
D. It is 6.

Solution

The product of two numbers is equal to the product of their LCM and GCD: 36 * 6 = 216.

Correct Answer: A — It is 216.

Learn More →

Q. If the least common multiple (LCM) of two numbers is 60 and one of the numbers is 15, what could be the other number?

A. 20
B. 30
C. 45
D. 60

Solution

The LCM of 15 and 20 is 60, making 20 a valid option. 30 and 60 would not work as they would exceed the LCM.

Correct Answer: B — 30

Learn More →

Q. If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 12, what is the product of the two numbers?

A. 720
B. 180
C. 120
D. 60

Solution

The product of two numbers is equal to the product of their LCM and GCD. Therefore, 60 * 12 = 720.

Correct Answer: A — 720

Learn More →

Q. If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 5, which of the following pairs could represent these two numbers?

A. (5, 12)
B. (10, 30)
C. (15, 20)
D. (5, 15)

Solution

The product of the two numbers is equal to the LCM multiplied by the GCD. Thus, 60 * 5 = 300. The pair (15, 20) satisfies this condition since 15 * 20 = 300.

Correct Answer: C — (15, 20)

Learn More →

Q. If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 5, what is the product of the two numbers?

A. 300
B. 60
C. 12
D. 15

Solution

The product of two numbers is equal to the product of their LCM and GCD. Therefore, 60 * 5 = 300.

Correct Answer: A — 300

Learn More →

Q. If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 12, what can be inferred about the product of the two numbers?

A. It is 720.
B. It is 60.
C. It is 12.
D. It is 5.

Solution

The product of two numbers is equal to the product of their LCM and GCD. Therefore, 60 * 12 = 720.

Correct Answer: A — It is 720.

Learn More →

Q. If the number 'A' in a base-6 system is equal to 30 in decimal, what is the value of 'A'?

A. 50
B. 42
C. 34
D. 30

Solution

In base-6, 'A' = 3*6^1 + 0*6^0 = 18 + 0 = 18. Therefore, 'A' is 42 in decimal.

Correct Answer: B — 42

Learn More →

Q. If the number 'XYZ' in base-5 equals 100 in decimal, what is the value of 'X'?

A. 2
B. 3
C. 4
D. 1

Solution

In base-5, 'XYZ' = X*5^2 + Y*5^1 + Z*5^0 = 100. Solving gives X = 3.

Correct Answer: B — 3

Learn More →

Q. If the number 1011 in binary is converted to decimal, what is its value?

A. 11
B. 10
C. 12
D. 13

Solution

The binary number 1011 converts to decimal as follows: 1*2^3 + 0*2^2 + 1*2^1 + 1*2^0 = 8 + 0 + 2 + 1 = 11.

Correct Answer: A — 11

Learn More →

Q. If the number 1011 in binary is converted to decimal, what is the result?

A. 11
B. 10
C. 12
D. 13

Solution

To convert from binary to decimal, calculate: 1*2^3 + 0*2^2 + 1*2^1 + 1*2^0 = 8 + 0 + 2 + 1 = 11.

Correct Answer: A — 11

Learn More →

Q. If the number 1A in hexadecimal is converted to decimal, what is the result?

A. 26
B. 27
C. 28
D. 29

Solution

In hexadecimal, A represents 10. Therefore, 1A = 1*16^1 + 10*16^0 = 16 + 10 = 26.

Correct Answer: A — 26

Learn More →

Q. If the number 36 is expressed in terms of its prime factors, which of the following is correct?

A. 2^2 * 3^2
B. 2^3 * 3^1
C. 3^2 * 4^1
D. 6^2

Solution

The prime factorization of 36 is 2^2 * 3^2, as 36 = 2 * 2 * 3 * 3.

Correct Answer: A — 2^2 * 3^2

Learn More →

Q. If the product of two consecutive integers is 72, which of the following pairs could represent these integers?

A. 8 and 9
B. 6 and 7
C. 5 and 6
D. 9 and 10

Solution

6 and 7 are consecutive integers whose product is 42, not 72.

Correct Answer: B — 6 and 7

Learn More →

Q. If the product of two consecutive integers is 72, which of the following pairs could represent those integers?

A. 8 and 9
B. 6 and 7
C. 5 and 6
D. 4 and 5

Solution

The product of 6 and 7 is 42, while 8 and 9 gives 72. Therefore, the correct pair is 8 and 9.

Correct Answer: B — 6 and 7

Learn More →

Q. If the product of two numbers is 144 and one of the numbers is 12, what is the other number? (2023)

A. 12
B. 10
C. 8
D. 6

Solution

The other number can be found by dividing the product by the known number: 144 / 12 = 12.

Correct Answer: D — 6

Learn More →

Q. If the product of two numbers is 48 and one of the numbers is 6, what can be inferred about the other number?

A. It is 8.
B. It is 12.
C. It is 6.
D. It is 4.

Solution

If the product is 48 and one number is 6, then the other number must be 48 ÷ 6 = 8.

Correct Answer: A — It is 8.

Learn More →

Q. If the product of two numbers is 48, which of the following pairs could represent these numbers?

A. (2, 24)
B. (3, 16)
C. (4, 12)
D. (All of the above)

Solution

All pairs listed multiply to 48, hence they are valid pairs.

Correct Answer: D — (All of the above)

Learn More →

Q. If the product of two numbers is 72 and one of the numbers is 8, what is the other number?

A. 6
B. 9
C. 10
D. 12

Solution

The other number is 72 divided by 8, which equals 9.

Correct Answer: A — 6

Learn More →

Q. If the product of two numbers is a multiple of 15, which of the following must be true?

A. At least one of the numbers is a multiple of 3.
B. At least one of the numbers is a multiple of 5.
C. Both numbers are even.
D. Both numbers are odd.

Solution

For the product to be a multiple of 15, at least one of the numbers must be a multiple of 5.

Correct Answer: B — At least one of the numbers is a multiple of 5.

Learn More →

Showing 211 to 240 of 618 (21 Pages)

Number Systems

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?