Question 1
Give the perimeter of 
Statement 1:
Statement 2:
- BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
- Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
- BOTH statements TOGETHER are insufficient to answer the question.
- Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
- EITHER statement ALONE is sufficient to answer the question.
Explanation: The perimeter of 
is equal to the sum of the lengths of the sides; that is, 
.
From Statement 1 alone, we get
we can add 
to both sides to get
However, without any further information, we cannot determine the actual perimeter.
A similar argument shows that Statement 2 alone gives insufficient information as well.
However, suppose we were to multiply both sides of the equation in Statement 1 by 2, then add both sides of Statement 2:
Divide both sides by 3:
Since
,
we can substitute 29 for 
and find 
:
While we cannot find 
or 
individually, this is not necessary; in the perimeter formula, we can substitute 29 for 
and 8 for 
:
.
is equal to the sum of the lengths of the sides; that is, .
From Statement 1 alone, we get
we can add to both sides to get
However, without any further information, we cannot determine the actual perimeter.
A similar argument shows that Statement 2 alone gives insufficient information as well.
However, suppose we were to multiply both sides of the equation in Statement 1 by 2, then add both sides of Statement 2:
Divide both sides by 3:
Since
,
we can substitute 29 for and find :
While we cannot find or individually, this is not necessary; in the perimeter formula, we can substitute 29 for and 8 for :
.