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

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Manager
Joined: 10 Feb 2011
Posts: 114
Followers: 1

Kudos [?]: 178 [0], given: 10

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

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17 Feb 2011, 15:06
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35% (medium)

Question Stats:

64% (02:58) correct 36% (00:28) wrong based on 11 sessions

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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
Math Expert
Joined: 02 Sep 2009
Posts: 33089
Followers: 5778

Kudos [?]: 70925 [0], given: 9857

Re: 186. For positive integer x, if x2 has 4 digits, which of th [#permalink]

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17 Feb 2011, 16:15
Expert's post
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).

_________________
Re: 186. For positive integer x, if x2 has 4 digits, which of th   [#permalink] 17 Feb 2011, 16:15
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# For positive integer x, if x^2 has 4 digits, which of the

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