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Let a, b, and c be three integers, and let a be a perfect square. If a
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21 May 2017, 05:20
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Let a, b, and c be three integers, and let a be a perfect square. If a/b = b/c, then which one of the following statements must be true? (A) c must be an even number (B) c must be an odd number (C) c must be a perfect square (D) c must not be a perfect square (E) c must be a prime number Source: Nova GMAT
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Re: Let a, b, and c be three integers, and let a be a perfect square. If a
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21 May 2017, 19:02
Given: \(\frac{a}{b}\)=\(\frac{b}{c}\) Thus, \(b^2\)= ac It is given that a is a perfect square From the above equation, It is concluded that b is also a perfect square Therefore, C must be a perfect square \(Answer: C.\) Kudos please if you like my explanation!
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Re: Let a, b, and c be three integers, and let a be a perfect square. If a
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10 Sep 2018, 00:29
varun4s wrote: Given: \(\frac{a}{b}\)=\(\frac{b}{c}\) Thus, \(b^2\)= ac It is given that a is a perfect square From the above equation, It is concluded that b is also a perfect square Therefore, C must be a perfect square
\(Answer: C.\)
Kudos please if you like my explanation! Hi! I don't quite get how C is obviously a perfect square too, could someone elaborate on that? Thank you!



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Re: Let a, b, and c be three integers, and let a be a perfect square. If a
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10 Sep 2018, 01:01
SajjadAhmad wrote: Let a, b, and c be three integers, and let a be a perfect square. If a/b = b/c, then which one of the following statements must be true?
(A) c must be an even number (B) c must be an odd number (C) c must be a perfect square (D) c must not be a perfect square (E) c must be a prime number
Source: Nova GMAT a, b and c are integers. \(a/b = b/c\) \(a*c = b^2\) The right hand side is a perfect square (since it is the square of an integer, say b = 6 so b^2 = 6^2 = 36 = 2^2 * 3^2). All prime factors of a perfect square are in pairs. Then the left hand side must be a perfect square too i.e. have all prime factors in pairs. Now we are given that a is a perfect square. This implies all prime factors in a are in pairs. (Say a = 4 = 2^2) Then all leftover prime factors must be in pairs too (i.e. 3^2). So c must be a perfect square too. Answer (C)
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Re: Let a, b, and c be three integers, and let a be a perfect square. If a
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10 Sep 2018, 07:39
SajjadAhmad wrote: Let a, b, and c be three integers, and let a be a perfect square. If a/b = b/c, then which one of the following statements must be true?
(A) c must be an even number (B) c must be an odd number (C) c must be a perfect square (D) c must not be a perfect square (E) c must be a prime number
Source: Nova GMAT \(a = k^2\) So, \(\frac{a}{b} = \frac{b}{c}\) Or, \(a = \frac{b^2}{c}\) Hence, \(k^2 = \frac{b^2}{c}\) Or, \(c = \frac{b^2}{k^2}\) Or, \(c = (\frac{b}{k})^2\), Answer must be (C) c must be a perfect square
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