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# Ive been able to find explanations for some of the questions

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Manager
Joined: 06 Jan 2008
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Ive been able to find explanations for some of the questions [#permalink]  13 Jan 2008, 12:34
Ive been able to find explanations for some of the questions I got wrong, but couldnt find this one..

if x is a positive integer, what is the least common multiple of x, 6, and 9?
1) the least common multiple of x and 6 is 30
2) the least common multiple of x and 9 is 45

I said C, answer is D.
CEO
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Re: GMAT Prep Cat 1 questions [#permalink]  13 Jan 2008, 12:43
Manbehindthecurtain wrote:
Ive been able to find explanations for some of the questions I got wrong, but couldnt find this one..

if x is a positive integer, what is the least common multiple of x, 6, and 9?
1) the least common multiple of x and 6 is 30
2) the least common multiple of x and 9 is 45

I said C, answer is D.

1: for the least common multiple of x and 6 to be 30, x must be 5,15, or 30.
Now least common multiple is calculated by all the terms including those of the greater number.

Ex/ LCM of 6,9,5 is 2*3*3*5 (we take both 3's from 9). Now for 6,9,15 its the same thing 2*3*3*5. Again even for 6,9,30 its 2*3*3*5. So we can find out the LCM Suff.

2: x must be 5 or 15. 3*3*5 or 3*3*5 for both. So again Suff.

LCM of 6,9, x can be calculated as 2*3*3*5 for both S1 and S2.
Manager
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Re: GMAT Prep Cat 1 questions [#permalink]  13 Jan 2008, 13:01
I'm not following how you are saying x must be 5, 15, or 30. Couldnt X be any factor of 30? I'm clear on the prime factoring part, but cant get off to the same start as you.

another question I got wrong:
if x is positive, is x>3?
1) (x-1)^2 > 4
2) (x-2)^2 > 9

I dont know how to make sense of the expressions once I break it out into components:
1) (x-3)(x+1)>0
2) (x-4)(x+1)>0

What do these expressions mean? Not making sense to me since they are inequalities, and not equal to 0.

thanks!
CEO
Joined: 29 Mar 2007
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Re: GMAT Prep Cat 1 questions [#permalink]  13 Jan 2008, 13:55
2
KUDOS
Manbehindthecurtain wrote:
I'm not following how you are saying x must be 5, 15, or 30. Couldnt X be any factor of 30? I'm clear on the prime factoring part, but cant get off to the same start as you.

another question I got wrong:
if x is positive, is x>3?
1) (x-1)^2 > 4
2) (x-2)^2 > 9

I dont know how to make sense of the expressions once I break it out into components:
1) (x-3)(x+1)>0
2) (x-4)(x+1)>0

What do these expressions mean? Not making sense to me since they are inequalities, and not equal to 0.

thanks!

Lets say X is 6, which is a factor of 30. Then the LCM of 6 and 6 would NOT BE 30. It would be 6. This is why we have to restrict the numbers to 5, 15 and 30. Actually it can be 10 as well I didn't include this number, but it doesnt change anything. Try any other factors of 30 but 5,10,15, and 30 and ul see that the LCM of 6 and whatever the number you chose is not 30. Same reasoning for S2.

if x is positive, is x>3?
1) (x-1)^2 > 4
2) (x-2)^2 > 9
sqrt both sides for s1 and s2

1: x-1>4 or x-1<-4 x>5 or x<-3 Since X is positive this is suff to tell us that x>3

2: x-2>3 or x-2<-3 --> x>5 or x<-1 Again since x is positive this is suff to tell us that x>3

D
Manager
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Re: GMAT Prep Cat 1 questions [#permalink]  13 Jan 2008, 14:09
kudos, thanks man.
Manager
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Re: GMAT Prep Cat 1 questions [#permalink]  13 Jan 2008, 18:04
D
i dont think we need to get in to values at all for finding an answer.
LCM of three nos is the LCM of (LCM of any two nos & the third number).
both statements give lcm of two nos and we know the third no, so we can find the answer.
VP
Joined: 22 Nov 2007
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Re: GMAT Prep Cat 1 questions [#permalink]  15 Jan 2008, 04:14
Dellin wrote:
D
i dont think we need to get in to values at all for finding an answer.
LCM of three nos is the LCM of (LCM of any two nos & the third number).
both statements give lcm of two nos and we know the third no, so we can find the answer.

very quickly, from both 1 and 2 it is clear that x has 5^1 as a different factor from 6 and 9 . thus lcm follows
SVP
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Re: GMAT Prep Cat 1 questions [#permalink]  27 Jan 2008, 19:01
doesnt x=10 also meet the condition of having 30 as a LCM with 6 ?

in this case, the LCM of 6,9 and 10 isnt the same as it is for 6,9 and 5, for example
Director
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Re: GMAT Prep Cat 1 questions [#permalink]  23 Feb 2008, 14:37
pmenon wrote:
doesnt x=10 also meet the condition of having 30 as a LCM with 6 ?

in this case, the LCM of 6,9 and 10 isnt the same as it is for 6,9 and 5, for example

But that is not what the question is asking.

if you know the LCM of 6 (or 9) and x, you can find the LCM of 6, x, and 9
Manager
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Re: GMAT Prep Cat 1 questions [#permalink]  23 Feb 2008, 17:38
YES FOR FIRST STATEMENT , EITHER X IS 5 OR 10 DOES'T CHANGE LCM FOR ALL THREE NUMBERS , SO THIS STATMENT IS SUFFICIENT AND SIMILARLY THE SECOND IS SUFF. TOO
Senior Manager
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Re: GMAT Prep Cat 1 questions [#permalink]  23 Feb 2008, 18:29
neeraj.kaushal wrote:
YES FOR FIRST STATEMENT , EITHER X IS 5 OR 10 DOES'T CHANGE LCM FOR ALL THREE NUMBERS , SO THIS STATMENT IS SUFFICIENT AND SIMILARLY THE SECOND IS SUFF. TOO

yep. clearly, D.
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Re: GMAT Prep Cat 1 questions   [#permalink] 23 Feb 2008, 18:29
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