In 2003, a then-nascent Internet search engine developed an indexing

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

Source: Platinum GMAT
Kudos for a correct solution.

(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

Source: Platinum GMAT

GMATinsight · Answer

Question : Is X > 3Y? Statement 1: On a per-hour basis in 2003, G-Cache indexed 1 million more pages than HTML-Compress indexed X = Y + 1 Million Y+1 Million may or may not be greater tha three times of Y depending on the value of Y. Hence, NOT SUFFICIENT Statement 2: HTML-Compress can index between 400,000 and 1.4 million pages per hour 0.4 Million < Y < 0.4 Million No relation of Y with X hence NOT SUFFICIENT Combining the two statements X = Y + 1 Million and 0.4 Million < Y < 0.4 Million i.e. X_{min} = 1.4 Million for Y = 0.4 Million i.e. X > 3Y and X_{max} = 2.4 Million for Y = 1.4 Million i.e. X < 3Y NOT SUFFICIENT Answer: Option E

kvazar · Answer

Questions can be rephrased to: is X > 3Y ?

(2) HTML-Compress can index between 400,000 and 1.4 million pages per hour
This statement looks simpler, start with it.
No information on G-cache (Y). Insufficient.

(1) On a per-hour basis in 2003, G-Cache indexed 1 million more pages than HTML-Compress indexed
X-Y = 1 mln.
We don't know if X/Y is 200k or 10m.
1. If Y is 200k, then X is 1,200 and X > 3Y, but
2. if Y is 10m, then X is 11m and X < 3Y.
Insufficient.

(1) & (2)
We are given a range in (2), let's test extreme cases, for statements to be sufficient all extreme cases should render the same answer to question in stem:

1. Min. if Y = 400k, then X = 1,4m X > 3Y
2. Max. if Y = 1,4m, then X = 2,4m X < 3Y
Insufficient.

Answer:

Show Spoiler

E

Bunuel · Answer

Platinum GMAT Official Solution: 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 thatX - 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.

lipsi18 · Answer

Is X>3Y? 
1. X=Y+1; not enough information given to find out Y+1 will greater than 3Y; so insufficient
2. Range of Y is given, no information is mentioned about X, so insufficient
Combining 1 & 2, we get :
Y= 400k; X=1400K therefore x>3Y
Y=1.4m; X= 2.4m therefore x<3Y

Hence not sufficient still

Hence answer is E
Thanks,

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