Practice GMAT Data Sufficiency Question
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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?
- On a per-hour basis in 2003, G-Cache indexed 1 million more pages than HTML-Compress indexed
- HTML-Compress can index between 400,000 and 1.4 million pages per hour
Correct Answer: E
- 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?
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Evaluate Statement (1) alone.
- Translate the information from Statement (1) into algebra:
X - Y = 1 million
- 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
- 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.
- 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)
- 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
- Since different legitimate values of Y produce different answers to the question of whether X > 3Y, Statement (1) is not sufficient.
- Statement (1) is NOT SUFFICIENT.
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Evaluate Statement (2) alone.
- Translate the information from Statement (2) into algebra:
400,000 < Y < 1,400,000
- 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."
- Since different legitimate values of X and Y produce different answers to the question of whether X > 3Y, Statement (2) is not sufficient.
- Statement (2) is NOT SUFFICIENT.
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Evaluate Statements (1) and (2) together.
- With the information in Statement (1), we concluded that the original question can be boiled down to:
Is Y < 500,000?
- Statement (2) says:
400,000 < Y < 1,400,000
- 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?"
- Statements (1) and (2), even when taken together, are NOT SUFFICIENT.
- 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.
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