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# Number Properties

Author Message
Manager
Joined: 17 Jun 2018
Posts: 52
Schools: IMD '20
GPA: 2.84
WE: Engineering (Real Estate)

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30 Dec 2018, 10:27
00:00

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
Manager
Joined: 01 May 2017
Posts: 82
Location: India

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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
Math Expert
Joined: 02 Sep 2009
Posts: 58435

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31 Dec 2018, 01:44
arpitkansal wrote:
Is $$\sqrt{7x}$$ an integer?

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

(2) $$\sqrt{28x}$$ is an integer

Discussed here: https://gmatclub.com/forum/is-7x-1-2-an ... 45680.html
_________________
Re: Number Properties   [#permalink] 31 Dec 2018, 01:44
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