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I agree, neither by itself gives you enough information. We're really only discussing C or E.

So, if you take the two statements and you make them AC + BC = AB + AC ( and I realize #2 is >, not =, but follow me for a second), you get AC + BC = AB + AC The AC on each side cancels out, so you have BC = AB. Because AB + AC is actually Greater than, since AC is the same, the difference must be in AB, which must be larger than BC, but we don't know how much larger.

We know AC is less than 10 because AC + BC = 10. A number + another number will always be less than the sum of the two numbers (as long as they're both positive).

AC can be anything up to (but not including) 10. It could be 9.9999999999999999999, and BC = 10 minus that (i'm not counting the 9's).

Because AB + AC > 10, AB + AC = 300 or AB + AC = 10.1. The point is we just don't know and together they're insufficient.

sset009 wrote:

\(A\) , \(B\) , and \(C\) are points on the plane. Is \(AB \lt 10\) ?

1. \(AC + BC = 10\) 2. \(AB + AC \gt 10\)

(C) 2008 GMAT Club - m09#34

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient * Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient * BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient * EACH statement ALONE is sufficient * Statements (1) and (2) TOGETHER are NOT sufficient

Couldnt understand the official explanation

_________________

------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

A ,B , and C and are points on the plane. Is AB<10 ?

1) AC+BC=10 2) AB+AC >10

Answer: E

Can someone pls explain this DS answer to me ? Do we assume that is a triangle? Maybe it is a straight line? If it is a triangle, then S1 is sufficient because the other side needs to less than ten. Thank you

Shldnt 1 be sufficient ? bcos if we make a triangle of these three points then triangle property says "The sum of the lengths of any two sides of a triangle must be greater than the third side" then AC+BC>AB since AB+BC=10 Hence AB<10

You're right if you think of it as a triangle, but a triangle is not the only option. The points are on a plane, and the points COULD be in a line and still on the same plane. If this happens, and say the points go A-C-B, then the distance between AB would be 10, not less than 10, so 1 is insufficient.

ritula wrote:

A, B , and C are points on the plane. Is AB<10 ?

1. AC+BC=10 2. AB+AC>10

Shldnt 1 be sufficient ? bcos if we make a triangle of these three points then triangle property says "The sum of the lengths of any two sides of a triangle must be greater than the third side" then AC+BC>AB since AB+BC=10 Hence AB<10

_________________

------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

You're right if you think of it as a triangle, but a triangle is not the only option. The points are on a plane, and the points COULD be in a line and still on the same plane. If this happens, and say the points go A-C-B, then the distance between AB would be 10, not less than 10, so 1 is insufficient.

ritula wrote:

A, B , and C are points on the plane. Is AB<10 ?

1. AC+BC=10 2. AB+AC>10

Shldnt 1 be sufficient ? bcos if we make a triangle of these three points then triangle property says "The sum of the lengths of any two sides of a triangle must be greater than the third side" then AC+BC>AB since AB+BC=10 Hence AB<10

At first glance, I also picked up A as an answer. Though, the trick here is to understand the fine difference between a line and plane and related peculiarities of both. I must remember it now! Thanks for posting such a nice question.
_________________

Stmt1: AC+BC = 10 Try to plot three points on a sheet of paper.You can either have a triangle or a line. - If you plot a triangle, it is clear that AB<10 (sum of any two sides will always be more than the third side). - If you plot a line using three points, and given that AC+BC = 10, we can conclude that C lies between A and B on the line. In other words, AC+BC=AB=10. So, in one case you get AB<10 and in other case you get AB=10. Thus INSUFFICIENT.

Stmt2: AB+AC > 10 (10.1 or 20, it doesnt matter. Both are greater than 10) 1+10 > 10 (AB=1, and is thus <10) 10+10 > 10 (AB=10 and is equal to 10) 2 values, thus INSUFFICIENT.

Lets combine the two statements now.

From stmt1, we have AC=10-BC. Put this is stmt2. That is AB + 10 - BC >10. We also know from stmt1 that AB can be either <10 or =10. You can now put AB=10 and AB=9 in equation above to see that both can be valid. Thus together the two statements are INSUFFICIENT. Hence, E.

PLease be generous in giving kudos incase you liked the explanation

Let the three points be anywhere. Since it is not mentioned that it is a triangle therefore we cannot use only Statement 1 using Statement 1 and 2 AB > AC and AB > 10 -BC the second is more interesting as we can start by having A,B and C in a straight line and as we move point B (or C, or A) we get various values of a triangle with values like AB > 10, AB>9 AB>8... so forth which makes both statements not sufficient