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If x is a multiple of 8 and x > 37, which of the following could be

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Bunuel
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If x is a multiple of 8 and x > 37, which of the following could be [#permalink] New post   26 Sep 2022, 11:43
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A
B
C
D
E

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Question Stats:

90% (01:39) correct 10% (02:00) wrong based on 69 sessions
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If x is a multiple of 8 and x > 37, which of the following could be the value of \(\sqrt{3x}\)?

A. 10
B. 12
C. 14
D. 15
E. 16
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B
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B
darunp
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Re: If x is a multiple of 8 and x > 37, which of the following could be [#permalink] New post   26 Sep 2022, 23:28
since x is a multiple of 8, \(x = 8*A = 2^3*A\), where A is an integer

since x > 37, A > 4

\(3x = 2^3*3*A\)

since we want \(\sqrt{3x}\), 3x must have even powers, so A must have odd powers of 2 & 3, so A must be multiple of 6.

test it out:
if A = 6,
\(3x = 2^3*3*6 = 2^3*3*2*3 = 2^4*3^2\)
\(\sqrt{3x}=\sqrt{2^4*3^2}=2^2*3 = 4*3=12\)

hence B
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SaquibHGMATWhiz
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Re: If x is a multiple of 8 and x > 37, which of the following could be [#permalink] New post   27 Sep 2022, 03:55
Expert Reply
Bunuel wrote:
If x is a multiple of 8 and x > 37, which of the following could be the value of \(\sqrt{3x}\)?

A. 10
B. 12
C. 14
D. 15
E. 16

Solution:

  • Since x is a multiple of 8 greater than 37, let us assume \(x=8n\) where n is an integer and n ≥ 5
  • We need a possible value of \(\sqrt{3x}=\sqrt{3\times 8n}=\sqrt{3\times 2^3\times n}=2\sqrt{6n}\)
  • The minimum integral value of \(2\sqrt{6n}\) is when n = 6
  • \(2\sqrt{6n}=2\sqrt{6\times 6}=2\times 6=12\)

Hence the right answer is Option B
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hassi01
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If x is a multiple of 8 and x > 37, which of the following could be [#permalink] New post   27 Sep 2022, 04:26
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Given: x > 37
and
x is a multiple of 8

Go through the answers,

A. 10 = \(\sqrt{3x}\)

square both sides

100 = 3x, we're not getting a multiple of 8, rather x is not even an integer, so this is out.

B. 12 = \(\sqrt{3x}\)

square both sides

144 = 3x

48 = x, welp lucky me. 48 is a multiple of 8 and greater than 37, what we were looking for.

In case the option B was also not the answer, from what we did in option A and option B we can see that the other options when squared should be:
1. A multiple of 3
2. after divided by 3 the result should be a multiple of 8

I hope this helps, and kindly let me know in case I messed something up :blushing:
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gmatclubot
If x is a multiple of 8 and x > 37, which of the following could be [#permalink]
27 Sep 2022, 04:26
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