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Ajay took a 4-digit number in base 5 notation. He subtracted the sum of the digits of the numbers from the number. From the result, he struck off one of the digits. The remaining 3 digits were 1, 0 and 2. Then the digit struck off by Ajay was:
- a)2
- b)1
- c)4
- d)Cannot be determined
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Ajay took a 4-digit number in base 5 notation. He subtracted the sum o...
a + b + c = 2003 It is possible only if all the three a, b and c are odd, or two of the three are even and one is odd.
Hence, E can have only two values.
Hence, E can have only two values.
Most Upvoted Answer
Ajay took a 4-digit number in base 5 notation. He subtracted the sum o...
Explanation:
Given information:
Ajay took a 4-digit number in base 5 notation. He subtracted the sum of the digits of the numbers from the number. From the result, he struck off one of the digits. The remaining 3 digits were 1, 0, and 2.
Approach:
To find the digit struck off by Ajay, we need to analyze the possible scenarios based on the given information.
Possible Scenarios:
1. Let the 4-digit number in base 5 notation be ABCD.
2. After subtracting the sum of the digits from the number, the result can be expressed as ABCD - (A + B + C + D) = XYZ, where XYZ is the resulting 3-digit number.
3. Given that the remaining 3 digits are 1, 0, and 2, we can assume that one of these digits was struck off.
Analysis:
1. If the digit struck off is 1:
- Let's assume that 1 was the digit struck off. The resulting 3-digit number would be 102.
- In base 5 notation, 102 is equivalent to 5^2 + 0*5^1 + 2*5^0 = 25 + 0 + 2 = 27.
- The sum of the digits of 27 is 2 + 7 = 9.
- 27 - 9 = 18, which is not possible with the remaining digits 1, 0, and 2.
2. If the digit struck off is 0:
- Let's assume that 0 was the digit struck off. The resulting 3-digit number would be 120.
- In base 5 notation, 120 is equivalent to 5^2 + 2*5^1 + 0*5^0 = 25 + 10 + 0 = 35.
- The sum of the digits of 35 is 3 + 5 = 8.
- 35 - 8 = 27, which contradicts the given information that the resulting number cannot be 27.
3. If the digit struck off is 2:
- Let's assume that 2 was the digit struck off. The resulting 3-digit number would be 102.
- In base 5 notation, 102 is equivalent to 5^2 + 0*5^1 + 2*5^0 = 25 + 0 + 2 = 27.
- The sum of the digits of 27 is 2 + 7 = 9.
- 27 - 9 = 18, which satisfies the condition with the remaining digits 1, 0, and 2.
Conclusion:
Based on the analysis, it can be concluded that the digit struck off by Ajay was 2. Therefore, the correct answer is option (d) Cannot be determined.
Given information:
Ajay took a 4-digit number in base 5 notation. He subtracted the sum of the digits of the numbers from the number. From the result, he struck off one of the digits. The remaining 3 digits were 1, 0, and 2.
Approach:
To find the digit struck off by Ajay, we need to analyze the possible scenarios based on the given information.
Possible Scenarios:
1. Let the 4-digit number in base 5 notation be ABCD.
2. After subtracting the sum of the digits from the number, the result can be expressed as ABCD - (A + B + C + D) = XYZ, where XYZ is the resulting 3-digit number.
3. Given that the remaining 3 digits are 1, 0, and 2, we can assume that one of these digits was struck off.
Analysis:
1. If the digit struck off is 1:
- Let's assume that 1 was the digit struck off. The resulting 3-digit number would be 102.
- In base 5 notation, 102 is equivalent to 5^2 + 0*5^1 + 2*5^0 = 25 + 0 + 2 = 27.
- The sum of the digits of 27 is 2 + 7 = 9.
- 27 - 9 = 18, which is not possible with the remaining digits 1, 0, and 2.
2. If the digit struck off is 0:
- Let's assume that 0 was the digit struck off. The resulting 3-digit number would be 120.
- In base 5 notation, 120 is equivalent to 5^2 + 2*5^1 + 0*5^0 = 25 + 10 + 0 = 35.
- The sum of the digits of 35 is 3 + 5 = 8.
- 35 - 8 = 27, which contradicts the given information that the resulting number cannot be 27.
3. If the digit struck off is 2:
- Let's assume that 2 was the digit struck off. The resulting 3-digit number would be 102.
- In base 5 notation, 102 is equivalent to 5^2 + 0*5^1 + 2*5^0 = 25 + 0 + 2 = 27.
- The sum of the digits of 27 is 2 + 7 = 9.
- 27 - 9 = 18, which satisfies the condition with the remaining digits 1, 0, and 2.
Conclusion:
Based on the analysis, it can be concluded that the digit struck off by Ajay was 2. Therefore, the correct answer is option (d) Cannot be determined.
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Ajay took a 4-digit number in base 5 notation. He subtracted the sum of the digits of the numbers from the number. From the result, he struck off one of the digits. The remaining 3 digits were 1, 0 and 2. Then the digit struck off by Ajay was:a)2b)1c)4d)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer?
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