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

Question

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

darunp · Answer

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

SaquibHGMATWhiz · Answer

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	imes 8n}=\sqrt{3	imes 2^3	imes n}=2\sqrt{6n}  
 The minimum integral value of  2\sqrt{6n}  is when  n = 6  
  2\sqrt{6n}=2\sqrt{6	imes 6}=2	imes 6=12

Hence the right answer is    Option B

hassi01 · Answer

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

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

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