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?
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.
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.
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.
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
