Directions : Each question below is followed by two statements A and B...
Let greater and smaller digits of the number be x and y
respectively. Then,
From statement A, xy = 0
From statement B, x – y = 7
x –y = 7
x = 7, y = 0
Two digit number is 70.
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Directions : Each question below is followed by two statements A and B...
Understanding the Problem
To determine the two-digit number based on the provided statements, we need to analyze each statement carefully.
Statement A: The product of the two digits of the number is 0.
- This indicates that at least one of the digits in the two-digit number is 0.
- The only possible two-digit number with a 0 in any digit is 10 (where the digits are 1 and 0).
- However, this alone does not provide sufficient information to conclude the specific number, as we cannot ascertain the complete range of two-digit numbers based solely on this statement.
Statement B: The difference between the two digits of the number is 7.
- This indicates that if we denote the two digits as 'x' and 'y', then |x - y| = 7.
- The possible pairs of digits that satisfy this condition could be (7, 0) or (8, 1) or (9, 2).
- This statement alone also does not yield a specific two-digit number, as multiple combinations could satisfy this condition.
Combining Statements A and B
- When we consider both statements together, we know that one digit must be 0 (from Statement A) and the other digit must differ from it by 7 (from Statement B).
- The only viable combination from both statements is the digit pairs (7, 0) leading to the number 70.
Conclusion
- While each statement provides some information, neither alone is sufficient to determine the two-digit number.
- Only when combined do they lead us to a single solution (the number 70).
- Therefore, the correct answer is option 'C': both statements together are needed to answer the question.