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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

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.

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.

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.

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 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.

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

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 ANSWER D

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 ANSWER D

yep. clearly, D. _________________

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