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Number Properties

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Manager
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Joined: 17 Jun 2018
Posts: 52
Location: Canada
Schools: IMD '20
GPA: 2.84
WE: Engineering (Real Estate)
Number Properties  [#permalink]

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New post 30 Dec 2018, 10:27
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

36% (00:57) correct 64% (01:11) wrong based on 11 sessions

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Is \(\sqrt{7x}\) an integer?

(1) \(\sqrt{x/7}\) is an integer.

(2) \(\sqrt{28x}\) is an integer
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Number Properties  [#permalink]

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New post 30 Dec 2018, 11:27
Is √7x an integer?

(1) \(\sqrt{(x/7)}\) is an integer.
since \(\sqrt{(x/7)}\)is integer it means x = 7p (p some constant)
\(\sqrt{p}\)= integer
So \(\sqrt{7x}\) = \(\sqrt{(7*7*p)}\) = \(7*\sqrt{p}\) = integer
\(\sqrt{x/7}\) = \(\sqrt{(7*p)/7}\)
= \(\sqrt{p}\)
= integer (given)
Sufficient

(2) √28x is an integer
28 = 2*2*7
\(\sqrt{28x}\) = \(2*\sqrt{7x}\)
Given \(\sqrt{28x}\) an integer so, \(\sqrt{7x}\) is also an integer

But, if x = 1/28 implies \(\sqrt{28*x}\) = \(\sqrt{1}\)
resulting in integer but, \(\sqrt{7*x}\) != integer
Insufficient

Option A is correct
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Re: Number Properties  [#permalink]

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New post 31 Dec 2018, 01:44
GMAT Club Bot
Re: Number Properties   [#permalink] 31 Dec 2018, 01:44
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Number Properties

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