A telephone station has x processors, each of which can process a maxi

Question

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.

(1) x = 600
(2) 100 < y < 200

BrentGMATPrepNow · Accepted Answer

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

Answer:  A

RELATED VIDEO
 https://www.youtube.com/watch?v=MyG1K3ee69w

TheKingInTheNorth · Answer

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.

(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

asethi · Answer

Total processor: x, and each can process y calls...

(1) x = 600
 600 processors can process 500 calls....sufficient
(2) 100 < y < 200
 In this case, X can be 2,3,4,5, so yes/no....insufficient

Ans: A

Rovers75 · Answer

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

MathRevolution · Answer

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.

felippemed · Answer

My two cents. Hope it helps :roll:

EyalFuhrer · Answer

X pro, each pro can handle Sufficient. 2. 100 inSufficient

GMATinsight · Answer

Answer: Option A

Video solution by  GMATinsight

https://www.youtube.com/watch?v=WT4Q69rVHPw

ScottTargetTestPrep · Answer

Solution:

We need to determine whether a certain telephone station can handle 500 calls given that it has x processors and each of which can process a maximum of y calls at any particular time, where x and y are positive integers. In other words, we need to determine whether xy ≥ 500.

Statement One Alone:
 
Since x = 600, and y ≥ 1, we see that xy ≥ 600 * 1 = 600, which means xy ≥ 500. Statement one alone is sufficient.

Statement Two Alone:
 
Statement two alone is not sufficient. For example, if x = 4 and y = 150, then xy = 600, which is more than 500. However, if x = 3 and y = 150, then xy = 450, which is less than 500.

Answer: A

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=IUFwcFHc9_0

Tanisha2819 · Answer

In this question, we are given that each processor could make a maximum of y calls, which means that if there are a total of x processors then maximum xy calls could be made but this is the maximum number beyond which no. calls could be made. We are not given anything about the minimum no of calls that a processor could make in this question so how can we assume that if there a total of 600 processors, then each of them are going to be make y no of calls, y is the at most no of calls any processor could make and not the least no of calls. It is totally possible that out of the 600 processors, 400 processors make 0 or no calls at all and the rest 200 processors make 1 call each, so there will be total of 200 calls. Till the time we are not given the minimum no of calls, each processor could make, we cannot make this assumption that each processor would make at least 1 call, thus Statement 1 should not be sufficient. Kindly clarify on this.

Bunuel · Answer

You're overanalyzing the situation. The question posed is, "CAN the station process all of the calls" and based on (1), since for any positive integer y, xy is at least 500, the answer is YES, it CAN.

CapnSal · Answer

What if out of the 600 processors, only 10 work? How can we assume that all processors work?

Bunuel · Answer

The problem states that "each" of the x processors can process up to y calls. The keyword "each" implies that every one of the x processors is functional and can handle up to y calls.

KarishmaB · Answer

x processors and each can handle y calls. Since both x and y are integers, it means each processor can handle at least 1 call at any given time. 
500 calls are sent.

(1) x = 600

There are more processors than calls. Each processor can handle at least 1 call. Hence 600 processors can easily handle 500 calls. 
Sufficient alone.

(2) 100 < y < 200

Each processor can handle between 100 to 200 calls. If there are 2 processors, then they cannot handle 500 calls. If there are 10 processors, they can easily handle 500 calls. 
Hence, not sufficient alone.

Answer (A)

bumpbot · Answer

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A telephone station has x processors, each of which can process a maxi

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