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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?

Re: A telephone station has x processors, each of which can process a maxi [#permalink]

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27 Oct 2015, 02:48

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

Kudos for a correct solution.

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. there has to be relation between x and y . means at what is the max value/min value of x that will take care of max. value of y .

Unless this relation is given we wont be able to solve the question .

1 ) only value of x is given . No relation between x and y is given . 2) value of y given

Together also no new information . hence E
_________________

Re: A telephone station has x processors, each of which can process a maxi [#permalink]

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27 Oct 2015, 04:11

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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?

Since we're looking for the number of calls the station can process, we are trying to find out if xy>500. Since the problem states (and even if they didn't, the specifics of the problem will also dictate) that x and y must be positive integers, we know x>=1, y>=1

(1) x = 600

If x is 600 and y is at least 1, then xy is at least 600.

SUFFICIENT

(2) 100 < y < 200

We know something about y and that x is at least 1, we know that the station can handle at least 100 calls but nothing else,

Re: A telephone station has x processors, each of which can process a maxi [#permalink]

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13 Jun 2016, 09:28

nicoguillenb wrote:

Why is everyone assuming that Y is a decimal. Isn't it possible that y < 0 ?? Therefore, A being insufficient.

Number of processed calls should be integer. You can't process 1.5 call by each processor. Moreover, number of processed calls can't be negative. Hence A is correct
_________________

There are 2 variables (x and y) in the original condition. In order to match the number of variables to the number of equations, we need 2 equations. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that C is the correct answer. Using the condition 1) and 2) at the same time, the correct answer may be C. However, since this is an integer question, one of key questions, we need to apply common mistake type 4(A). Then, using the condition 1), if x=600, xy=600>500 even if y is only 1. Hence, the answer is always yes and the condition is sufficient. Thus, the correct answer is A.

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

Kudos for a correct solution.

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, 2 processors can process 2y calls. 3 processors can process 3y calls.... And x processors can process xy calls.

We can write... REPHRASED target question:Is xy ≥ 500?

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

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