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Real Numbers - 1

Description: Real Number Class X
Number of Questions: 15
Created by:
Tags: Real Number Writing Chemical Reactions Real Numbers
Attempted 0/15 Correct 0 Score 0

If A = 2n + 13 and B = n + 7, where n is a natural number, then HCF of A and B is

  1. 2

  2. 3

  3. 1

  4. 4

  5. 5


Correct Option: C
Explanation:

A and B are co-prime.

The LCM of 5, 8, 12 and 20 will not be a multiple of

  1. 5

  2. 3

  3. 9

  4. 20

  5. 8


Correct Option: C
Explanation:

5 = 58 = 2 x 312 = 2 x 2 x 320 = 2 x 2 x 5 LCM = 2 x 3 x 3 x 5 (Take highest power of common factor 2, 5 and remaining left out factor 3) = 120 By definition of LCM, 5, 8, 12 and 20 have to be multiples of 120, so the left out number 9 will not be a multiple of LCM.

Three runners running around a circular track can complete one revolution in 2, 3 and 4 hrs, respectively. They will meet again at the starting point after

  1. 8 hrs

  2. 6 hrs

  3. 12 hrs

  4. 18 hrs

  5. 24 hrs


Correct Option: C
Explanation:

LCM shall give the time at which they will meet.

The pairs of natural numbers having least common multiple 78 and greatest common divisor 13 are

  1. 58 and 13 or 16 and 39

  2. 68 and 23 or 36 and 49

  3. 18 and 73 or 56 and 93

  4. 78 and 13 or 26 and 39

  5. 88 and 13 or 26 and 39


Correct Option: D
Explanation:

As GCD or HCF is 13, so the pair must be divisible by 13.

Two natural numbers have their sum as 85 and LCM as 102. Which of the following are the two numbers?

  1. 30 and 55

  2. 17 and 68

  3. 35 and 55

  4. 51 and 34

  5. 55 and 30


Correct Option: D
Explanation:

The given LCM of 102 should be divisible by both the numbers.

Four bells toll together at 9.00 am. They toll after 7, 8, 11 and 12 seconds, respectively. How many times will they toll together again in the next 3 hours?

  1. 3

  2. 4

  3. 5

  4. 9

  5. 7


Correct Option: C
Explanation:

The LCM of 7, 8, 11 and 12 is 1848. So, the bells will toll together after every 1848 seconds. In 1848 seconds, all four bells toll 1 time. In 3 hrs (3 x 60 x 60), i.e. 10800 seconds, they will toll 3 x 60 x 60/1848 times = 5.84 times. As it has to be an integral part, so the answer is 5.

Two natural numbers with difference 66 and LCM 360 are

  1. 120 and 54

  2. 90 and 24

  3. 180 and 114

  4. 130 and 64

  5. 136 and 70


Correct Option: B
Explanation:

LCM 360 should be divisible by each number of the pair.

The LCM of 2.5, 0.5 and 0.175 is

  1. 2.5

  2. 5

  3. 7.5

  4. 17.5

  5. 1.75


Correct Option: D
Explanation:

This option is correct.

What is the smallest number which when increased by 6 becomes divisible by 36, 63 and 108?

  1. 750

  2. 752

  3. 754

  4. 756

  5. 758


Correct Option: A
Explanation:

The required number + 6 = LCM of the 3 numbers LCM = 756 The required number is 750.

The HCF and LCM of two numbers are 33 and 264, respectively. When the first number is completely divided by 2, the quotient is 33. The other number is

  1. 66

  2. 130

  3. 132

  4. 196

  5. 135


Correct Option: C
Explanation:

This option is correct.

Two alarm clocks beep at regular intervals of 50 seconds and 48 seconds. If they first beep together at 12.00 pm noon, at what time will they beep again?

  1. 12:20 pm

  2. 12:12 pm

  3. 12:11 pm

  4. 12:15 pm

  5. None of these


Correct Option: A
Explanation:

LCM of 50 and 48 is 1200 seconds. 1200 seconds = 20 minutes So, they will beep again at 12:20 p.m.

Two friends were discussing their marks in an examination. While doing so, they realised that both the numbers had the same prime factors, although one got a score which had two more factors than the other. If their marks are represented by one of the option as given below, which option is correct?

  1. 30, 60

  2. 20, 80

  3. 40, 80

  4. 20, 60

  5. 10, 20


Correct Option: B
Explanation:

Prime factors forĀ 20 = 5 x 2 x 2 80 = 5 x 2 x 2 x 2 x 2 As the number 80 has two other prime factors 2, 2 other than common prime factors 5, 2, 2.

Two equilateral triangles have sides of lengths 34 cm and 85 cm. The greatest length of tape that can measure the sides of both of them exactly is

  1. 34 cm

  2. 17 cm

  3. 51 cm

  4. 68 cm

  5. None of these


Correct Option: B
Explanation:

HCF of 34 and 85: 34 = 17 x 2 85 = 17 x 5 HCF is 17. Hence, the length of the tape is 17 cm.

The HCF of 2472, 1284 and a third number N is 12. If their LCM is 23 x 32 x 5 x 103 x 107, then the number N is

  1. 22 x 32 x 7

  2. 22 x 33 x 103

  3. 22 x 32 x 5

  4. 24 x 32 x 11

  5. 21 x 33 x 15


Correct Option: C
Explanation:

2472 = 2 x 2 x 2 x 3 x 103 1284 = 2 x 2 x 3 x 107 N = 2 x 2 x 3 x y (2, 2, 3 are common values and should product with y) HCF = 2 x 2 x 3 = 12 LCM = 2 x 2 x 3 x y x 2 x 103 x 107 We know the LCM and solve to find y. We get 15 Now, N = 180 = 22 x 32 x 15

There are three pieces of timber of lengths 42 m, 49 m and 63 m. These have to be divided into planks of the same length. The least possible number of planks is

  1. 5

  2. 11

  3. 13

  4. 8

  5. None of these


Correct Option: E
Explanation:

LCM of 42, 49 and 63: 42 = 7 x 3 x 2 49 = 72 63 = 7 x 32 LCM = 72 x 32 x 2 = 882

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