For positive integer x, if x^2 has 4 digits, which of the : GMAT Data Sufficiency (DS)
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For positive integer x, if x^2 has 4 digits, which of the

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For positive integer x, if x^2 has 4 digits, which of the [#permalink]

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New post 17 Feb 2011, 14:06
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186. For positive integer x, if x^2 has 4 digits, which of the following must be true?
I. x must be a 2-digit integer
II. 2x must be a 3-digit integer
III. 3x must be a 3-digit integer
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
[Reveal] Spoiler: OA
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Re: 186. For positive integer x, if x2 has 4 digits, which of th [#permalink]

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New post 17 Feb 2011, 15:15
banksy wrote:
186. For positive integer x, if x^2 has 4 digits, which of the following must be true?
I. x must be a 2-digit integer
II. 2x must be a 3-digit integer
III. 3x must be a 3-digit integer
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only


As \(x\) is an integer and \(x^2\) is a 4-digit perfect square then \(32\leq{x}\leq{99}\) (32^2=1024 is the first 4-digit perfect square and 100^2=10,000 is already a 5-digit perfect square).

Hence only I must be true (if \(x=32\) then \(2x=64\) and \(3x=96\) so not the 3-digit integers).

Answer: A.
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Re: 186. For positive integer x, if x2 has 4 digits, which of th   [#permalink] 17 Feb 2011, 15:15
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