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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.

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

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, 15:03, edited 1 time in total.

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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