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The following question has three statements. Study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. What is the sum of two numbers? I. HCF of two numbers is 17 II. Both the numbers are of 3 digits III. LCM of two numbers is 714

The following question has three statements. Study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. What is the sum of two numbers? I. HCF of two numbers is 17 II. Both the numbers are of 3 digits III. LCM of two numbers is 714 Correct Answer All the statements

Since HCF and LCM are 17 and 714 (Statement I and III)

Let two numbers be 17x and 17y respectively, as 17 is the HCF of these numbers

Now, LCM of 17x and 17y is 17xy

According to the question LCM of these two numbers = 714

⇒ 17xy = 714

⇒ xy = 714/17

⇒ xy = 42 = 7 × 6

Now as numbers are of 3 digits (Statement II)

In this scenario, where x = 7 and y = 6,

Numbers will be,

17x = 17 × 7 = 119

17y = 17 × 6 = 102

Required sum would be,

⇒ 102 + 119

⇒ 221

Hence All the statements are necessary to answer the question

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