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Sachin Tendulkar has a certain batting average N (a whole number) in his career of 86 innings. In the 87th inning, he gets out after scoring 270 runs which increases his batting average by a whole number. The batting average is calculated by dividing the total number of runs scored by the total number of innings played by the player. How many values of his new average is/are possible?
- a)0
- b)1
- c)2
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Sachin Tendulkar has a certain batting average N (a whole number) in h...
Total number of runs scored till 86th inning = 86 N Now, 86 N + 270 = 87 (N + S), where S is the increase in batting average.
Different values of S possible now S = 0, 1, 2 and 3.
Different values of S possible now S = 0, 1, 2 and 3.
Most Upvoted Answer
Sachin Tendulkar has a certain batting average N (a whole number) in h...
Solution:
Let's assume the previous average to be A.
Total runs before the 87th inning = A*86
Total runs after the 87th inning = A*86 + 270
Total innings after the 87th inning = 87
New average = (A*86 + 270)/(87)
To get a whole number as the new average, (A*86 + 270) should be a multiple of 87.
Let's consider the following cases:
Case 1: When 87 is a factor of A
If 87 is a factor of A, then (A*86 + 270) will also be a multiple of 87. In this case, the new average will be a whole number.
Example: If A = 87, then (A*86 + 270) = 7656, which is a multiple of 87.
Case 2: When (A*86 + 270) is a multiple of 87
If (A*86 + 270) is a multiple of 87, then the new average will be a whole number.
Example: If A = 50, then (A*86 + 270) = 4440, which is a multiple of 87.
Case 3: When neither 87 is a factor of A nor (A*86 + 270) is a multiple of 87
In this case, the new average will not be a whole number.
Example: If A = 30, then (A*86 + 270) = 2700 + 270 = 2970, which is not a multiple of 87.
Therefore, there can be 0, 1, or 2 possible values of the new average.
Hence, the correct answer is option D.
Let's assume the previous average to be A.
Total runs before the 87th inning = A*86
Total runs after the 87th inning = A*86 + 270
Total innings after the 87th inning = 87
New average = (A*86 + 270)/(87)
To get a whole number as the new average, (A*86 + 270) should be a multiple of 87.
Let's consider the following cases:
Case 1: When 87 is a factor of A
If 87 is a factor of A, then (A*86 + 270) will also be a multiple of 87. In this case, the new average will be a whole number.
Example: If A = 87, then (A*86 + 270) = 7656, which is a multiple of 87.
Case 2: When (A*86 + 270) is a multiple of 87
If (A*86 + 270) is a multiple of 87, then the new average will be a whole number.
Example: If A = 50, then (A*86 + 270) = 4440, which is a multiple of 87.
Case 3: When neither 87 is a factor of A nor (A*86 + 270) is a multiple of 87
In this case, the new average will not be a whole number.
Example: If A = 30, then (A*86 + 270) = 2700 + 270 = 2970, which is not a multiple of 87.
Therefore, there can be 0, 1, or 2 possible values of the new average.
Hence, the correct answer is option D.
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Sachin Tendulkar has a certain batting average N (a whole number) in his career of 86 innings. In the 87th inning, he gets out after scoring 270 runs which increases his batting average by a whole number. The batting average is calculated by dividing the total number of runs scored by the total number of innings played by the player. How many values of his new average is/are possible?a)0b)1c)2d)None of theseCorrect answer is option 'D'. Can you explain this answer?
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Sachin Tendulkar has a certain batting average N (a whole number) in his career of 86 innings. In the 87th inning, he gets out after scoring 270 runs which increases his batting average by a whole number. The batting average is calculated by dividing the total number of runs scored by the total number of innings played by the player. How many values of his new average is/are possible?a)0b)1c)2d)None of theseCorrect answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Sachin Tendulkar has a certain batting average N (a whole number) in his career of 86 innings. In the 87th inning, he gets out after scoring 270 runs which increases his batting average by a whole number. The batting average is calculated by dividing the total number of runs scored by the total number of innings played by the player. How many values of his new average is/are possible?a)0b)1c)2d)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sachin Tendulkar has a certain batting average N (a whole number) in his career of 86 innings. In the 87th inning, he gets out after scoring 270 runs which increases his batting average by a whole number. The batting average is calculated by dividing the total number of runs scored by the total number of innings played by the player. How many values of his new average is/are possible?a)0b)1c)2d)None of theseCorrect answer is option 'D'. Can you explain this answer?.
Sachin Tendulkar has a certain batting average N (a whole number) in his career of 86 innings. In the 87th inning, he gets out after scoring 270 runs which increases his batting average by a whole number. The batting average is calculated by dividing the total number of runs scored by the total number of innings played by the player. How many values of his new average is/are possible?a)0b)1c)2d)None of theseCorrect answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Sachin Tendulkar has a certain batting average N (a whole number) in his career of 86 innings. In the 87th inning, he gets out after scoring 270 runs which increases his batting average by a whole number. The batting average is calculated by dividing the total number of runs scored by the total number of innings played by the player. How many values of his new average is/are possible?a)0b)1c)2d)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sachin Tendulkar has a certain batting average N (a whole number) in his career of 86 innings. In the 87th inning, he gets out after scoring 270 runs which increases his batting average by a whole number. The batting average is calculated by dividing the total number of runs scored by the total number of innings played by the player. How many values of his new average is/are possible?a)0b)1c)2d)None of theseCorrect answer is option 'D'. Can you explain this answer?.
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