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

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Manager
Joined: 17 Dec 2005
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If x is a multiple of 8 and x>37, which of the following [#permalink]  11 Jun 2006, 19:56
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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.
VP
Joined: 14 May 2006
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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?
Manager
Joined: 29 Apr 2006
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Re: PS Number Properties [#permalink]  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
GMAT Club Legend
Joined: 07 Jul 2004
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Location: Singapore
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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
SVP
Joined: 30 Mar 2006
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I did it by using the folowng equation

12*12 = 3*8*X and checking which number is divisible.
VP
Joined: 02 Jun 2006
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Kudos [?]: 48 [0], given: 0

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.
VP
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Re: PS Number Properties [#permalink]  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.
Manager
Joined: 10 May 2006
Posts: 186
Location: USA
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Kudos [?]: 3 [0], given: 0

Re: PS Number Properties [#permalink]  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.
CEO
Joined: 20 Nov 2005
Posts: 2910
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
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Kudos [?]: 132 [0], given: 0

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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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Manager
Joined: 17 Dec 2005
Posts: 162
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Kudos [?]: 12 [0], given: 0

Re: PS Number Properties [#permalink]  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.

mc
Senior Manager
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Solution [#permalink]  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

SVP
Joined: 03 Jan 2005
Posts: 2246
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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.
_________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

Manager
Joined: 23 Jan 2006
Posts: 192
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Kudos [?]: 12 [0], given: 0

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
SVP
Joined: 03 Jan 2005
Posts: 2246
Followers: 13

Kudos [?]: 226 [0], given: 0

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.
_________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

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