Practice GMAT Data Sufficiency Question
Return to the list of practice GMAT data sufficiency questions.
In 2003, a thennascent Internet search engine developed an indexing algorithm called GCache that retrieved and stored X million webpages per hour. At the same time, a competitor developed an indexing algorithm called HTMLCompress 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 GCache greater than three times the number of pages indexed by HTMLCompress?
 On a perhour basis in 2003, GCache indexed 1 million more pages than HTMLCompress indexed
 HTMLCompress 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 GCache" = X
"greater than three times" translates into: >3
"the number of pages indexed by HTMLCompress" = Y
Putting this together:
Was X > 3Y? 
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.
 Translate the information from Statement (1) into algebra:

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.
 Translate the information from Statement (2) into algebra:

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.
 With the information in Statement (1), we concluded that the original question can be boiled down to:
 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.
Return to the list of practice GMAT data sufficiency questions.