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The following questions are accompanied by three statements (I), (II), and (III). You have to determine which statements(s) is/are sufficient/necessary to answer the questions. Find the two-digit number? I. Difference between the two digits is 5. II. Product of two digits is 36. III. Total sum of two-digit number and twice of two-digit number is 282.

The following questions are accompanied by three statements (I), (II), and (III). You have to determine which statements(s) is/are sufficient/necessary to answer the questions. Find the two-digit number? I. Difference between the two digits is 5. II. Product of two digits is 36. III. Total sum of two-digit number and twice of two-digit number is 282. Correct Answer Only III

Given:

Statement I:  Difference between the two digits is 5.

Statement II: Product of two digits is 36.

Statement III: Total sum of two-digit number and twice of two-digit number is 282.

Calculation:

Let the two-digit number be 10A + B.

Statement I:  Difference between the two digits is 5.

⇒ A – B = 5

But because it is not specified if A is greater or B is greater, we may also get 

⇒ B – A = 5

Statement II: Product of two digits is 36.

⇒ AB = 36

Statement III: Total sum of two-digit number and twice of two-digit number is 282.

⇒ 10A + B + 2(10A + B) = 282

⇒ 10A + B + 20A + 2B = 282

⇒ 10A + B = 94

From the above statements, it is clear that 

We can directly obtain the value of the two digit number from the statement III alone.

∴ Only III is our answer.

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