GMAT Math : Percents
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Example Questions
Example Question #11 : Percents
Statement 1: 
Statement 2: 
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
EITHER 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.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Assume Statement 1 alone.
If 
and
or
If 
Either statement alone answers the question.
Example Question #12 : Percents
Statement 1: 
Statement 2: 
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Assume both statements are true.
Case 1: 
Then 
Case 2:
Then 
In both situations, the conditions of the problem, as well as both statements, are true, but in one case, 
Example Question #3391 : Gmat Quantitative Reasoning
True of false: 
Statement 1: 
Statement 2: 
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT 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.
EITHER statement ALONE is sufficient to answer the question
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question
Similarly, 
Therefore,
or, equivalently,
or
If 
Example Question #13 : Percents
True or false: 
Statement 1: 
Statement 2:
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
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.
EITHER statement ALONE is sufficient to answer the question.
From Statement 1 alone, since 
This is enough to prove that 
From Statement 2 alone, since 
This is enough to prove that 
Example Question #1280 : Data Sufficiency Questions
Three candidates - Rodger, Stephanie, and Tina - ran for student body president. By the rules, the candidate who wins more than half the ballots cast wins the election outright; if no candidate wins more than half, there must be a runoff between the two top vote-getters. You may assume that no other names were written in.
Was there an outright winner, or will there be a runoff?
Statement 1: Rodger won 100 more votes than Stephanie and 210 more votes than Tina.
Statement 2: Tina won 25.9% of the votes.
BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.
STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.
BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.
EITHER STATEMENT ALONE provides sufficient information to answer the question.
STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.
BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.
For one candidate to have won the election outright, (s)he must win more than 50% of the votes.
Statement 1 alone does not prove there was an outright winner. For example, if Rodger got 211 votes, then Stephanie got 111 votes, and Tina got 1 vote; this makes Rodger's share of the votes
making Rodger the outright winner. But if Rodger got 500 votes, then Stephanie got 400 votes, and Tina got 290; Rodger got the most votes, but his share is
not the required share of the vote.
Statement 2 alone does not prove this either, since 74.1% of the vote was won by either Rodger or Stephanie, but it is not specified how this is distributed; Roger or Stephanie could have won 51%, with the remaining 23.1% won by the other, resulting in an outright winner. However, it is also possible that each won half this, or about 37%, resulting in a runoff between the two.
Now assume both statements are true. Let 
Since Tina won 25.9% of the vote, we can set up an equation:
This can be solved for 
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