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Mathematics

Description: Class VI section test of playing with numbers. Gives you a satisfaction that you have completely understood the concepts behind the chapter.
Number of Questions: 19
Created by:
Tags: Pradeep Kumar Tiwary Understanding Factors and Multiples Arithmetic Ability Prime Factorization and Factor Tree Prime Numbers and Composite Numbers Finding Common Factors Divisibility by 3, 6 and 9 Finding Common Multiples
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HCF (a, b) = 21 and LCM (a, b) = 56. If a = 3, then b = ?

  1. 294

  2. 26

  3. 74

  4. 392

  5. None of these

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Correct Option: D
Explanation:

HCF x LCM = ab 56 x 21 = 3b Or, b = 392

Which of the following is divisible by 9?

  1. 32541679

  2. 32564872

  3. 32587416

  4. 32546874

  5. None of these

Show answer
Correct Option: C
Explanation:

Sum of digits of 32541679 = 37, which is not divisible by 9. Hence, the number is also not divisible by 9. Sum of digits of 32564872 = 37, which is not divisible by 9. Hence, the number is also not divisible by 9. Sum of digits of 32587416 = 36, which is divisible by 9. If the sum of the digits is divisible by 9, then the number itself is divisible by 9. Hence, 32587416 is divisible by 9. Sum of digits of 32546874 = 39, which is not divisible by 9. Hence, the number is also not divisible by 9.  

If the product of two numbers is 'k' and their HCF is 'a', then their LCM is

  1. k/a

  2. a/k

  3. ka

  4. k + a

  5. None of these

Show answer
Correct Option: A
Explanation:

LCM x HCF = Product of the numbers Or, LCM x a = k ----------- (Given) Or, LCM = k/a

The sum of all prime numbers between 80 and 100 is

  1. 259

  2. 269

  3. 267

  4. 257

  5. None of these

Show answer
Correct Option: B
Explanation:

Prime numbers between 80 and 100 are 83, 89 and 97. Therefore, sum = 83 + 89 + 97 = 269

Choose the pair of co-prime numbers among the following.

  1. (14, 15)

  2. (14, 16)

  3. (14, 18)

  4. (14, 20)

  5. None of these

Show answer
Correct Option: A
Explanation:

Out of the given options, only 14 and 15 have 1 as the HCF. Hence, only option 1 is correct.  

The number that will be divisible by both 10 & 18 is

  1. 80

  2. 54

  3. 90

  4. 108

  5. None of these

Show answer
Correct Option: C
Explanation:

Out of the given options, only 90 is divisible by both 10 and 18.

Correct prime factorisation for 76 is

  1. 76 x 1

  2. 19 x 4

  3. 19 x 2 x 2

  4. 13 x 4 x 2

  5. None of these

Show answer
Correct Option: C
Explanation:

Correct; 19 and 2 are prime numbers . 19 x 2 x 2 = 76

Let there be two numbers p and q and let p and q have only two common factors x and y other than 1, such that x > y. Then, the HCF of p and q is

  1. y

  2. x

  3. xy

  4. x/y

  5. None of these

Show answer
Correct Option: B
Explanation:

As x and y are two common factors and x > y, x is the answer.

Which of the following is not a prime number?

  1. 239

  2. 179

  3. 173

  4. 289

  5. 97

Show answer
Correct Option: D
Explanation:

289 = 1 x 17 x 17 x 289. Therefore, it is not a prime number as it has more than two factors.

Which of the following numbers is not co-prime with 14?

  1. 11

  2. 13

  3. 15

  4. 7

  5. None of these

Show answer
Correct Option: B
Explanation:

HCF of 11 and 14 is 1, hence 11 is co-prime with 14. HCF of 13 and 14 is 1, hence 13 is co-prime with 14. HCF of 15 and 14 is 1, hence 15 is co-prime with 14. HCF of 7 and 14 is 7, hence 7 is not co-prime with 14.  

Let the 107th multiple of 15 be 'x' and the 115th multiple be 'y'. Then, the value of (x + y)/10 to the nearest tens is

  1. 33330

  2. 3330

  3. 333

  4. 330

  5. None of these

Show answer
Correct Option: D
Explanation:

Given,x = 107 x 15 = 1605 Also, y = 115 x 15 = 1725 Therefore, x + y = 1725 + 1605 = 3330. Therefore, (x + y)/10 = 333 Rounded off to the nearest tens, it becomes 330.

If the 7th positive multiple of 48 is 'x' and the 8th positive multiple is 'y', then the value of xy to the nearest thousand is

  1. 129024

  2. 129000

  3. 129030

  4. 93000

  5. None of these

Show answer
Correct Option: B
Explanation:

Given, x = 48 x 7 = 336 Also, y = 48 x 8 = 384 Then, xy = 129024. Written to the nearest thousand, it becomes 129000.  

In prime factorisation of a number, the number is expressed as _______ factors of the number.

  1. even

  2. odd

  3. composite

  4. prime

  5. None of these

Show answer
Correct Option: D
Explanation:

In prime factorisation, the numbers are expressed as prime factors.

The sum of the prime factors of 1358 to the nearest tens is

  1. 106

  2. 110

  3. 100

  4. 105

  5. None of these

Show answer
Correct Option: B
Explanation:

Prime factors of 1358 are 2, 7, 97 Therefore, sum = 2 + 7 + 97 = 106. 106 when written to the nearest tens becomes 110.

Let a, b and c be three numbers such that a : b : c = 1 : 2 : 3. Also, the sum of the three numbers is 66. Then, the value of (a + b)(a + c) will be

  1. 1452

  2. 1815

  3. 1089

  4. 432

  5. None of these

Show answer
Correct Option: A
Explanation:

Let a = k, b = 2k and c = 3k Then, k + 2k + 3k = 66 Also, 6k = 66 Or k = 11 Therefore, a = 11, b = 22, c = 33 Also, (a + b)(a + c) = (11 + 22)(11 + 33) = 33 x 44 = 1452

If HCF (x, y) = 15 and LCM (x, y) = 200, then the value of xy/30 is

  1. 3000

  2. 300

  3. 1000

  4. 100

  5. None of these

Show answer
Correct Option: D
Explanation:

xy = product of x and y    = HCF x LCM    = 15 x 200    = 3000 xy/30 = 100

In the number 324_586, fill in the blanks with such a digit so that it will make the number exactly divisible by 2.

  1. 2

  2. 3

  3. 4

  4. All of the above

  5. None of these

Show answer
Correct Option: D
Explanation:

All of the above will divide 2 because the units digit is even.

In the number 1635_ , fill in the blank with a suitable number so that new number so obtained becomes divisible by 3.

  1. 2

  2. 4

  3. 0

  4. 5

  5. None of these

Show answer
Correct Option: C
Explanation:

The first choice is 2. The number so obtained is 16352. Now, the sum of the digits = 1 + 6 + 3 + 5 + 2 = 17 As 17 is not divisible by 3, so the number so formed will not be divisible by 3. The second choice is 4. The number so obtained is 16354. Now, the sum of the digits = 1+ 6 + 3 + 5 + 4 = 19 As 19 is not divisible by 3, so the number so formed will not be divisible by 3. The third choice is 0. The number so obtained is 16350. Sum of digits = 1 + 6 + 3 + 5 + 0 = 15. Now 15 is divisible by 3, therefore the number will also be divisible by 3. The fourth choice is 5. The number so obtained is 16355. Now, the sum of the digits = 1 + 6 + 3 + 5 + 5 = 20 As 20 is not divisible by 3, so the number so formed will not be divisible by 3.  

Let 'x' & 'y' be two numbers such that x and y are relatively co-prime, then the LCM of x and y will be

  1. addition of x & y

  2. multiplication of x & y

  3. division of x & y

  4. subtraction of x & y

  5. None of these

Show answer
Correct Option: B
Explanation:

Multiplication of x & y will give the LCM of x & y because they are co-prime.

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