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The sum of five integers is 999, while the sum of their squares is X.
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01 Feb 2018, 12:22
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The sum of five integers is 999, while the sum of their squares is X. Which of the following statements is true. A. X is never greater than 1,001,001 B. X is never less than 299794 C. X is never less than 199,601 D. X can never be a perfect square. E. None of the above.
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Re: The sum of five integers is 999, while the sum of their squares is X.
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01 Feb 2018, 14:41
prince00113 wrote: the sum of five integers is 999, while the sum of their squares is X. Which of the following statements is true.
A. X is never greater than 1,001,001 B. X is never less than 299794 C. X is never less than 199,601 D. X can never be a perfect square. E. None of the above.] 999/5=199.8 arithmetic mean let the five integers=200+200+200+200+199=999 X=199,601 X can never be less than this C



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Re: The sum of five integers is 999, while the sum of their squares is X.
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01 Feb 2018, 19:49
Can anyone please explain why option A is incorrect?



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Re: The sum of five integers is 999, while the sum of their squares is X.
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01 Feb 2018, 20:04
csaluja wrote: Can anyone please explain why option A is incorrect? If the 5 integers are 1499,200,100,100,100(the sum is 999) But the sum of the squares of the numbers is definitely greater than 1001001 That is the reason why A is incorrect as X is greater than 1001001 Hope that clears your confusion!
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The sum of five integers is 999, while the sum of their squares is X.
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01 Feb 2018, 22:50
prince00113 wrote: The sum of five integers is 999, while the sum of their squares is X. Which of the following statements is true.
A. X is never greater than 1,001,001 B. X is never less than 299794 C. X is never less than 199,601 D. X can never be a perfect square. E. None of the above. The question points towards looking for ranges.. Few points therefore.. 1) B can be thrown immediately, as B constitutes the range of C.. 2) Max value : Nothing has been said about integers being POSITIVE or NEGATIVE. So the highest value of X can be INFINITY upwards. Say integers are, 1000000.....n times., 10000..n times, 999, 0, 0 Here sum will be 0, but sum of squares can be anything.. Eliminate A 3) Min value : Min value will be when all numbers are smallest possible. And this will happen when all are close by.. here all will be ~ 200... So Sum <5*(200)^2......<5*40000....<200000.. Here C fits in..
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Re: The sum of five integers is 999, while the sum of their squares is X.
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01 Feb 2018, 22:58
prince00113 wrote: The sum of five integers is 999, while the sum of their squares is X. Which of the following statements is true.
A. X is never greater than 1,001,001 B. X is never less than 299794 C. X is never less than 199,601 D. X can never be a perfect square. E. None of the above. This can be best solved by taking all the numbers distributed equally. \(a= b= c = d = e = 200\) \(a^2 + b^2 + c^2 + d^2 + e^2 > 200,000\) As it asks for minimum value \(X > 199, 601\) (Please note that I took the value of e = 200 just to simplify calculation, however it should be 199).
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Re: The sum of five integers is 999, while the sum of their squares is X.
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