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

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If x is a multiple of 8 and x>37, which of the following [#permalink] New post 11 Jun 2006, 19:56
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B
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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

I got the answer by backsolving which took almost 3 mins. I was wondering if there was a shorter way/the correct way to solve. Thanks.
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 [#permalink] New post 11 Jun 2006, 20:20
I squared each of the answer choices (getting rid of sqrt) to see which ones are divisible by 3

A 100
B 144/3
C 196
D 225/3, but in no way is a multiple of 8
E 256

so b is the answer, correct?
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Re: PS Number Properties [#permalink] New post 11 Jun 2006, 20:25
mrmikec 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

I got the answer by backsolving which took almost 3 mins. I was wondering if there was a shorter way/the correct way to solve. Thanks.


B: 12

Find a multiple of 8 greater than 37. In this case it would be 40 or 48.
Using 40 , 3x =120 but sqrt(120) = 2sqrt(30) which is not one of the answers.
Using 48, 3x = 144 sqrt(144) = 12
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 [#permalink] New post 11 Jun 2006, 20:48
x = 8n and n >= 5.

sqrt(3x) = m
3x = m^2
24n = m^2

(2^3)(3)n = m^2
So n must be (2)(3) minimun.

m^2 = 144
m = sqrt(3x) = 12

Ans B
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 [#permalink] New post 12 Jun 2006, 01:41
I did it by using the folowng equation

12*12 = 3*8*X and checking which number is divisible.
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 [#permalink] New post 12 Jun 2006, 09:50
For this the easiest way is to look at the solutions given and square them and check for divisibilty by 3 & then by 8

a. 10 => 100/3 = ??? Not divisible
b. 12 => 144/4 = 48/8 = 6 Answer.

B.
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Re: PS Number Properties [#permalink] New post 12 Jun 2006, 10:24
mrmikec 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

B.
x = 8k where k is an integer..
sqrt (3x) = p, where p is an integer.
sqrt (3 * 8k) = p
sqrt (24k) = p
squaring both sides

24k = p^2
k = (p^2)/24

only the square value of 12 is divisible 24. So it is B.
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Re: PS Number Properties [#permalink] New post 12 Jun 2006, 13:19
mrmikec 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




sqrt (3x) = sqrt (3*8*k) ...then I broke the equation down to primes = sqrt(3*2*2*2*k).

Taking a look at the answers, we know that ths is a perfect square. Therefore, K MUST have a 2 and a 3 in it. If that's the case (assuming K = 2*3) then sqrt (3*2*2*2*2*3) = 3*2*2 = 12.....B.

Last edited by tl372 on 12 Jun 2006, 14:03, edited 1 time in total.
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 [#permalink] New post 12 Jun 2006, 13:30
SQRT(3x) = SQRT(3*8*a) where a is +ve integer

Now check for which a this number is a perfect square and a = 6
So ans = 12.
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Re: PS Number Properties [#permalink] New post 12 Jun 2006, 18:44
MA wrote:
mrmikec 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

B.
x = 8k where k is an integer..
sqrt (3x) = p, where p is an integer.
sqrt (3 * 8k) = p
sqrt (24k) = p
squaring both sides

24k = p^2
k = (p^2)/24

only the square value of 12 is divisible 24. So it is B.


Great. I think this is the best most succinct way to do this problem. Would probably only have taken less than a min to do it this way. thanks.

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Solution [#permalink] New post 12 Jun 2006, 19:23
Let the x= 8n
n > 5 for x > 37
p = sqrt(3x) = sqrt (3.8.n) = sqrt (3.2.4.n) = 2.sqrt(6.n)

putting n = 6 (so that n > 5)

Therefore p = 2.6 = 12

Right answer is B
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 [#permalink] New post 14 Jun 2006, 06:30
If 3x or 3*2^3m is a perfect square then 3 and 2 must be able to be square rooted out. So the square root has to be a multiple of 6.
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 [#permalink] New post 14 Jun 2006, 16:48
How about this:
the smallest factorization of a number that is a multiple of both 3 and 8, that is a perfect square would be:
2*2*2*2*3*3 = 144

sqrt of 144 = 12
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 [#permalink] New post 14 Jun 2006, 17:25
The thing with guessing is, if the correct option is something other than 12, say if it's 24 or 30, etc, then it will take you sometime to make the number. Whereas knowing that the number should be multiple of six, then it takes you about the same amount of time to spot the right answer.
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  [#permalink] 14 Jun 2006, 17:25
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