Please explain

Q1. 1 is sufficient to answer the question at hand, since there is a general rule that the greatest common factor of two consecutive numbers is 1.

2 however is not enough, IMHO. Think of it this way:
a. j = 4 and k = 5 - in this case, jk = 20 and is divisible by 5, but the greatest common factor of j and k is 1.
b. j = 10 and k = 5 - now you get that jk = 50, which is again divisible by 5. However, the greatest common factor is 5.
This is why I believe that 1 is insufficient, so my answer is A. I may be missing smth here...


Q2. 1. I'd use picking numbers for this one.
a. take x = 0 and you get that 1/(x+1) = 1 and x/2 = 0, making 1/(x+1) > x/2
b. take x = 2 and you have 1/(x+1) = 1/3 = 0.33 and x/2 = 1. In this case, 1/(x+1) < x/2.
Since both cases comply with the rule that x is greater than equal to zero, 1 is insufficient.

2. The examples at 1 can be used to demonstrate that 2 is insufficient as well.

Put both stmts together and you get nothing: again, the examples at 1 are consistent with 0 <= x < 3. IMHO, it's E.

DanaJ wrote:Q1. 1 is sufficient to answer the question at hand, since there is a general rule that the greatest common factor of two consecutive numbers is 1.

2 however is not enough, IMHO. Think of it this way:
a. j = 4 and k = 5 - in this case, jk = 20 and is divisible by 5, but the greatest common factor of j and k is 1.
b. j = 10 and k = 5 - now you get that jk = 50, which is again divisible by 5. However, the greatest common factor is 5.
This is why I believe that 1 is insufficient, so my answer is A. I may be missing smth here...

You are right. 2 statement is in-sufficient.

DanaJ wrote:Q1. 1 is sufficient to answer the question at hand, since there is a general rule that the greatest common factor of two consecutive numbers is 1.

2 however is not enough, IMHO. Think of it this way:
a. j = 4 and k = 5 - in this case, jk = 20 and is divisible by 5, but the greatest common factor of j and k is 1.
b. j = 10 and k = 5 - now you get that jk = 50, which is again divisible by 5. However, the greatest common factor is 5.
This is why I believe that 1 is insufficient, so my answer is A. I may be missing smth here...


Q2. 1. I'd use picking numbers for this one.
a. take x = 0 and you get that 1/(x+1) = 1 and x/2 = 0, making 1/(x+1) > x/2
b. take x = 2 and you have 1/(x+1) = 1/3 = 0.33 and x/2 = 1. In this case, 1/(x+1) < x/2.
Since both cases comply with the rule that x is greater than equal to zero, 1 is insufficient.

2. The examples at 1 can be used to demonstrate that 2 is insufficient as well.

Put both stmts together and you get nothing: again, the examples at 1 are consistent with 0 <= x < 3. IMHO, it's E.

I Think DanaJ has answered both the questions correctly