3 more problems on LCM GCD

[vittalgmat]

Reposting these 3 problem on LCM and GCD coz that post had no replies.
Can the experts pls help me here.


G, M, and N are integers, M=X+6; G is the greatest common factor of M and N. G=?
1) N=2531
2) N=X+7

X and Y are positive integers. What is the maximum common divisor of X and Y?
a) X=Y+1
b) X is a multiple of 2

What is the greatest common factor of positive integers x and y?
1) The greatest common factor of and is 5
2) x and y are even

[papgust]

For 2nd,

What is the maximum common divisor of X and Y?

a) X=Y+1 -- This means that X and Y are consecutive integers. Then, the GCD is always 1 (Which is the maximum GCD)
Sufficient.

b) We don't know what Y is. Insufficient.

Answer: A


Can you check the 1st statement of 3rd question? It is not clear

[Stuart@KaplanGMAT]

Reposting these 3 problem on LCM and GCD coz that post had no replies.
Can the experts pls help me here.


G, M, and N are integers, M=X+6; G is the greatest common factor of M and N. G=?
1) N=2531
2) N=X+7

1) M could still have infinite values, and no relationship between M and N, so insufficient.

2) If M = X + 6 and N = X + 7, then M and N are consecutive integers. Therefore, their GCF is 1... sufficient!

2 is sufficient, 1 isn't: choose B.

What is the greatest common factor of positive integers x and y?
1) The greatest common factor of and is 5
2) x and y are even

Statement (1) is missing info (which is probably why it got ignored the first time around).

[vittalgmat]

Thanks everyone for the replies.
I could not find the rest of the problem either.. we will probably have to leave it as it is.

[pink_08]

2) If M = X + 6 and N = X + 7, then M and N are consecutive integers. Therefore, their GCF is 1... sufficient!

2 is sufficient, 1 isn't: choose B.


What if they are 0 and 1. There is no mention in the question that the integers are positive.

In that case how will 1 be the GCF.

So it should be C

[Stuart@KaplanGMAT]

2) If M = X + 6 and N = X + 7, then M and N are consecutive integers. Therefore, their GCF is 1... sufficient!

2 is sufficient, 1 isn't: choose B.


What if they are 0 and 1. There is no mention in the question that the integers are positive.

In that case how will 1 be the GCF.

So it should be C

You're correct!

I'm guessing the author of the question meant the answer to be B and just forgot about 0 issues.

[Stuart@KaplanGMAT]

2) If M = X + 6 and N = X + 7, then M and N are consecutive integers. Therefore, their GCF is 1... sufficient!

2 is sufficient, 1 isn't: choose B.


What if they are 0 and 1. There is no mention in the question that the integers are positive.

In that case how will 1 be the GCF.

So it should be C

You're correct!

I'm guessing the author of the question meant the answer to be B and just forgot about 0 issues.

Actually, I retract my previous statements.

0 is a multiple of all numbers except 0 (since 0/x = 0 for all values of x except 0).

So, even if our values are negative (which we usually don't think about when dealing with concepts such as GCF and LCM, which is why I think not stating we were dealing with positives was an oversight), the GCF will still be 1.

For example, if our numbers are -14 and -15,

-14 = 1*-14
-15 = 1*-15

so 1 would still be the GCF.