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If x and y are positive integers and x^2 + y^2 = 100 [#permalink]

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18 Aug 2012, 15:22

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

50% (01:30) correct
50% (00:59) wrong based on 16 sessions

HideShow timer Statistics

If x and y are positive integers and \(x^2 + y^2 = 100\), then the greatest possible value of x is between (A) 4 and 5 (B) 6 and 7 (C) 7 and 8 (D) 9 and 10 (E) 10 and 11

I don't agree with the OA. According to the question, x is an integer, therefore the greatest value of x could be 8 (Choice C). However, the OE is this: To maximize x, minimize y. Since both variables are positive integers, the smallest y could be is 1. Thus: \(x^2 + y^2 = 100\) \(x^2 + 1^2 = 100\) \(x^2 = 99\) Since 100 is \(10^2\), 99 must be the square of a little less than 10. The correct choice is (D).

Re: If x and y are positive integers and x^2 + y^2 = 100 [#permalink]

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18 Aug 2012, 15:37

metallicafan wrote:

If x and y are positive integers and \(x^2 + y^2 = 100\), then the greatest possible value of x is between (A) 4 and 5 (B) 6 and 7 (C) 7 and 8 (D) 9 and 10 (E) 10 and 11

I don't agree with the OA. According to the question, x is an integer, therefore the greatest value of x could be 8 (Choice C). However, the OE is this: To maximize x, minimize y. Since both variables are positive integers, the smallest y could be is 1. Thus: \(x^2 + y^2 = 100\) \(x^2 + 1^2 = 100\) \(x^2 = 99\) Since 100 is \(10^2\), 99 must be the square of a little less than 10. The correct choice is (D).

Both x and y can take integer values between 1 and 9, so not really sure as to the phrasing of the question, especially the word between.
_________________

If x is an integer, then without even reading the rest of the question none of the answer choices could possibly be right ('between' means 'strictly between' unless you add the word 'inclusive').

I don't know if there's a typo in the original question - I guess so, considering how the OE reads - but the question makes no sense as written. I suppose it makes sense if you take out the word 'integers' and just require x and y to be positive.

edit: or perhaps the question means to say "If \(x^2\) and \(y^2\) are positive integers..." Then the solution is right.
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Re: If x and y are positive integers and x^2 + y^2 = 100
[#permalink]
19 Aug 2012, 01:54

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