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Let a,b,c,d be the four integers such that a+b+c+d = 4m+1, where m is a positive integer. Given m, which one of the following is true?

A) The maximum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2+2m+1

B)The minimum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 + 2m + 1

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A) The maximum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2+2m+1

B)The minimum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 + 2m + 1

Explain this question please?

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Mahinder Singh
May 22, 2021 |

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Let a,b,c,d be the four integers such that a+b+c+d = 4m+1, where m is a positive integer. Given m, which one of the following is true?A) The maximum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2+2m+1B)The minimum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 + 2m + 1Explain this question please?

For any expression of the form a+b+c+d, the minimum value of a^2 + b^2+c^2+ d^2 will be when a = b = c = d. Or in other words, the four numbers have to be as close to the average as much as is possible. As the sum is in the form of 4m+ 1, we can say that the four numbers would give the minimum value of the above expression if they are m, m, m and m+1.

So, we get the sum of their squares to be:

4m^2 + 2m + 1 and so, option b is correct.

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Let a,b,c,d be the four integers such that a+b+c+d = 4m+1, where m is a positive integer. Given m, which one of the following is true?A) The maximum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2+2m+1B)The minimum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 + 2m + 1Explain this question please? for CAT 2022 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Let a,b,c,d be the four integers such that a+b+c+d = 4m+1, where m is a positive integer. Given m, which one of the following is true?A) The maximum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2+2m+1B)The minimum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 + 2m + 1Explain this question please? covers all topics & solutions for CAT 2022 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let a,b,c,d be the four integers such that a+b+c+d = 4m+1, where m is a positive integer. Given m, which one of the following is true?A) The maximum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2+2m+1B)The minimum possible value of a^2 + b^2 + c^2 + d^2 is 4m^2 + 2m + 1Explain this question please?.

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For any expression of the form a+b+c+d, the minimum value of a^2 + b^2+c^2+ d^2 will be when a = b = c = d. Or in other words, the four numbers have to be as close to the average as much as is possible. As the sum is in the form of 4m+ 1, we can say that the four numbers would give the minimum value of the above expression if they are m, m, m and m+1.So, we get the sum of their squares to be:4m^2 + 2m + 1 and so, option b is correct.