Hi Yaj,

This DS questions asks us for side AB of an ISOSCELES triangle?

Fact 1: AC < BC/2
There's no numeric information here, so there's no way to answer the question.
Fact 1 is INSUFFICIENT

Fact 2: BC = 7
This doesn't tell us AB, but it does tell us something about the triangle. Since it's ISOCELES....

It's either 7 7 -
Or it's 7 - - in which the two blanks are the same
Fact 2 is INSUFFICIENT

Combined, we know that...
It's an ISOSCELES triangle
BC = 7
AC < 3.5
AB = ? but either matches AC or BC

Using the Triangle Inequality Theorem, we know that AB + AC MUST BE > 7

If AB = AC, then that WOULDN'T HAPPEN.

So, AB MUST = BC

Thus AB = 7

Final AnswerC

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

Hi Java_85,

Take a look at your work again.

Have you factored in:

1) That the triangle is ISOSCELES (we're told that in the prompt)
2) Every real triangle is based on the Triangle Inequality Theorem (so any 2 sides of the triangle that are added > 3rd side).

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

When you see statement 1, make sure you think about it for a bit. It turns out to be insufficient here, but it's still significant, because it determines exactly which sides are the congruent ones.

If the problem says this instead:

Yaj wrote:In isosceles triangle ABC, is AB = BC?

(1) AC < BC/2

(2) BC = 7

Thank You!

... then the answer is (a). Make sure you know why.

That's one way to do it.

If you haven't memorized that rule for triangles, you can also just try drawing the triangle both ways.

I.e., try drawing a triangle with sides x, x, and something that's less than half of x -- this will work just fine (you'll get a long skinny triangle, where the 2 congruent sides are the long ones).
Now try drawing a triangle with sides x, something that's less than half of x, and the same something that's less than half of x (or, equivalently, sides of y, y, and more than 2y). It won't work -- you won't be able to get the two short sides to join each other. They're too short to bridge the long side.

I'm not really capable of memorizing abstract rules like the one above, so this is how I'd go about doing it.