Yaj wrote:Points A, B and C are not on a line. Is AB > 12?

(1) Side AC has length 36
(2) Side BC has length 18

IMPORTANT: Since the 3 points are not on the same line, we know that the points create a TRIANGLE.

Target question: Is the length of side AB greater than 12?

Statement 1: Side AC has length 36
This statement tells us the length of 1 side of the triangle.
This information alone is not enough to determine whether or not side AB is longer than 12
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Side BC has length 18
This statement tells us the length of 1 side of the triangle.
This information alone is not enough to determine whether or not side AB is longer than 12
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
We now know the lengths of two sides of a triangle. So, we can use the following rule:
(difference between known sides) < third side < (sum of known sides)
So, (36-18) < third side < (36+18), which means: 18 < third side < 54
Since 18 < side AB < 54, side AB must be longer than 12
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

Hi Yaj,

Brent has provided a solid explanation for this question, so I won't rehash it here.

I can provide a bit more insight into this math concept though. It's called the "triangle inequality theorem" and you might see it 1 time in the Quant section. It's a rarer geometry rule, but it tends to show up more often when a Test Taker is doing well on the Quant.

The basic idea is that any two sides of a triangle, when added together MUST be greater than the third side. This rule applies to every combination of 2 sides in a triangle.

For example, a 3/4/5 triangle is a "real triangle" because...

3+ 4 > 5
3 + 5 > 4
4 + 5 > 3

Using this same rule, is it possible to have a 1/1/20 triangle???

No, this is not possible because...
1 + 1 is NOT > 20

In rarer versions of this rare question, you might be asked to find potential areas or perimeters of a triangle (and not just what the third side could be).

GMAT assassins aren't born, they're made,
Rich