# Practice GMAT Data Sufficiency Question

In 2003, a then-nascent Internet search engine developed an indexing algorithm called G-Cache that retrieved and stored X million webpages per hour. At the same time, a competitor developed an indexing algorithm called HTML-Compress that indexed and stored Y million pages per hour. If both algorithms indexed a positive number of pages per hour, was the number of pages indexed per hour by G-Cache greater than three times the number of pages indexed by HTML-Compress?
1. On a per-hour basis in 2003, G-Cache indexed 1 million more pages than HTML-Compress indexed
2. HTML-Compress can index between 400,000 and 1.4 million pages per hour
 A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D) EACH statement ALONE is sufficient. E) Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
1. Translate the final sentence, which contains the question, into algebra:
"the number of pages indexed per hour by G-Cache" = X
"greater than three times" translates into: >3
"the number of pages indexed by HTML-Compress" = Y

Putting this together:
Was X > 3Y?
2. Evaluate Statement (1) alone.
1. Translate the information from Statement (1) into algebra:
X - Y = 1 million
2. Since the original question states that "both algorithms indexed a positive number of pages per hour", the following inequalities must hold true:
X > 0
Y > 0
3. Simply knowing that X - Y = 1 million does not provide enough information to determine whether X > 3Y.
This can be seen via an algebraic substitution or by trying different numbers.
4. Trying Numbers
Let X = 10 and, therefore, Y = 9
10 is NOT > 3(9)
But, let X = 1.1 and, therefore, Y = .1
1.1 IS > 3(.1)
5. Algebraic Substitution
X - Y = 1 million
X = Y + 1 million
Plug this into the inequality we are trying to solve for:
Was X > 3Y?
Was (Y + 1 million) > 3Y?
Was 1 million > 2Y?
Was 500,000 > Y?
Was Y < 500,000?

Simply knowing that X - Y = 1 million does not provide enough information to determine whether Y < 500,000
6. Since different legitimate values of Y produce different answers to the question of whether X > 3Y, Statement (1) is not sufficient.
7. Statement (1) is NOT SUFFICIENT.
3. Evaluate Statement (2) alone.
1. Translate the information from Statement (2) into algebra:
400,000 < Y < 1,400,000
2. We know nothing about the value of X.
If X were 10 million, the answer to the original question was X > 3Y? would be "yes."
If X were 100,000, the answer to the original question was X > 3Y? would be "no."
3. Since different legitimate values of X and Y produce different answers to the question of whether X > 3Y, Statement (2) is not sufficient.
4. Statement (2) is NOT SUFFICIENT.
4. Evaluate Statements (1) and (2) together.
1. With the information in Statement (1), we concluded that the original question can be boiled down to:
Is Y < 500,000?
2. Statement (2) says:
400,000 < Y < 1,400,000
3. Even when combining Statements (1) and (2), we cannot determine whether Y < 500,000
Y could be 450,000 (in which case X = 1,450,000) or Y could be 650,000 (in which case X = 1,650,000). These two different possible values of X and Y would produce different answers to the question "Was Y < 500,000?" Consequently, we would have different answers to the question "Was X > 3Y?"
4. Statements (1) and (2), even when taken together, are NOT SUFFICIENT.
5. Since Statement (1) alone is NOT SUFFICIENT, Statement (2) alone is NOT SUFFICIENT, and Statements (1) and (2), even when taken together, are NOT SUFFICIENT, answer E is correct.