# Question: Is x less than 80 degrees?

## Comment on Is x less than 80 degrees?

### how can we assume that it is

How can we assume that it is the diameter ofthe circle? Also nowhere it is written that figure is not drawn to scale. Please explain ### "How can we assume that it is

"How can we assume that it is the diameter of the circle?"
The diameter is the longest chord in a circle. So, if the radius is 4, and statement 1 says that CB = 8 (i.e., twice the radius), then we can be certain that CB is the diameter of the circle.

"Also nowhere it is written that figure is not drawn to scale."
You might want to look a little more closely :-)

### I believe he is trying to

I believe he is trying to point out that the figure does not specify the center of the circle, since the diameter must run through the center we cannot be certain that CB is the diameter. ### It's not stated that CB is

It's not stated that CB is the diameter, that's correct. However, statement 2 tells us that CB is twice the radius, which means CB must be the diameter. And if CB is the diameter, we can be certain that it passes through the center of the circle.

### is that possible to say

is that possible to say statement 1 is sufficient even it yields x=90 which means x>80? ### Yes, it's still sufficient.

Yes, it's still sufficient. It all comes down to whether we can answer the target question with certainty.

Here, the target question is "Is x less than 80?"

Statement 1 essentially tells us that x = 90. So, our answer to the target question is "No, x is not less than 80."

Since we can answer the target question with certainty, statement 1 is sufficient.

Likewise, IF it were the case that statement 1 told us that x = 70, then the answer to the target question would be "Yes, x is less than 80." Since we could answer the target question with certainty, statement 1 would be sufficient. ### Honestly I am getting far

Honestly I am getting far more than the value I paid!

The information ignored was the value of the radius...

Thanks Brent