3 Mark Question

Question 13 Marks

A trader has three bundles of string 392 m, 308 m and 490 m long. What is the greatest length of string that the bundles can be cut up into without any left over string ?

Answer

The required greatest length of the string is the highest common factor (HCF) of 392, 308 and 490.
∴ 392 = 2 x 2 x 2 x 7 x 7
308 = 2 x 2 x 7 x 11
490 = 2 x 7 x 7 x 5
∴ HCF of 392, 308 and 490 = 2 x 7 = 14
∴ The required greatest length of the string is 14 m.

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Question 23 Marks

Find the smallest number which when divided by 8,9,10,15,20 gives a remainder of 5 every time.

Answer

Here, the smallest number for division is LCM of 8, 9, 10,15 and 20.
8 = 2 x 2 x 2
9 = 3 x 3
10 = 2 x 5
15 = 3 x 5
20 = 2 x 2 x 5
LCM of given numbers = 2 x 2 x 2 x 3 x 3 x 5 = 360
∴ Required, smallest number = LCM + Remainder
= 360 + 5
= 365
∴ The required smallest number is 365.

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Question 33 Marks

Find the HCF and LCM of the numbers given below. Verify that their product is equal to the product of the given numbers : 46, 51

Answer

46 = 2 x 23 x 1
51 = 3 x 17 x 1
∴ HCF of 46 and 51 = 1
LCM of 46 and 51 = 2 x 23 x 3 x 17
= 2346
HCF x LCM = 1 x 2346
= 2346
Product of the given numbers = 46 x 51
= 2346
∴ HCF x LCM = Product of the given numbers.

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Question 43 Marks

Find the HCF by the division method and reduce to the simplest form:

$\frac{161}{69}$

Answer

$\frac{161}{69}$

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Question 53 Marks

Find the HCF by the division method and reduce to the simplest form:

$\frac{76}{133}$

Answer

$\frac{76}{133}$

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Question 63 Marks

Find the HCF by the division method and reduce to the simplest form:
$\frac{275}{525}$

Answer

$\frac{275}{525}$

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Question 73 Marks

Answer the following questions.
i. Which is the smallest prime number ?
ii. List the prime numbers from 1 to 50. How many are they ?
iii. Identify the prime numbers in the list below.
17, 15 ,4, 3, 1, 2, 12, 23, 27, 35, 41, 43, 58, 51, 72, 79, 91, 97.

Answer

i. 2 is the smallest prime number.
ii. There are 15 prime numbers from 1 to 50.
They are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.
iii. [17], 15 ,4, [3], 1, [2], 12, [23], 27, 35, [41], [43], 58, 51, 72, [79], 91, [97]

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Maths 3 Mark Question

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