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A telephone station has x processors, each

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jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
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A telephone station has x processors, each

Post Mon Aug 07, 2017 9:32 am
A telephone station has x processors, each of which can process a maximum of y calls at any particular time, where x and y are positive integers. If 500 calls are sent to the station at a particular time, can the station process all of the calls?
(1) x = 600
(2) 100 < y < 200

Official Guide question
Answer: A

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GMAT/MBA Expert

Post Mon Aug 07, 2017 9:56 am
jjjinapinch wrote:
A telephone station has x processors, each of which can process a maximum of y calls at any particular time, where x and y are positive integers. If 500 calls are sent to the station at a particular time, can the station process all of the calls?
(1) x = 600
(2) 100 < y < 200

Official Guide question
Answer: A
Target question: Can the station process 500 calls?
This is a good candidate for rephrasing the target question.
Each INDIVIDUAL processor can process y calls.
So, x processors can process xy calls.
So....
REPHRASED target question: Is xy ≥ 500?

Aside: Here’s a video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100

Statement 1: x = 600
Since we're told that x and y are POSITIVE INTEGERS, the smallest possible value of y is 1
Even when y = 1, xy =(600)(1) = 600. So, the value of xy is AT LEAST 600.
In other words, xy ≥ 500
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: 100 < y < 200
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 1 and y = 101. in this case, xy = (1)(101) = 101. In other words, xy < 500
Case b: x = 10 and y = 101. in this case, xy = (10)(101) = 1010. In other words, xy ≥ 500
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

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