The Accelera model graphics processor, working at its constant rate, w

Question

The Accelera model graphics processor, working at its constant rate, will perform \(6 × 10^9\) floating-point operations per second. If n Accelera model graphics processors will work simultaneously at this rate to perform a task which requires a total of \(1.2 × 10^{12}\) floating-point operations, what is the minimum value of n if the task will be completed in less than 1 minute?

A) 3

B) 4

C) 5

D) 6

E) 7

A) 3

B) 4

C) 5

D) 6

E) 7

harshtandel838 · Answer

Here’s my analysis regarding this problem:

Single accelera model works at constant rate of 6 * 10^9 fp operations per second.

Therefore in a minute it will work 60 * 6 * 10^9 op/sec 
(i.e 3.6 * 10^11 op/sec )

Now we can multiply the number of model to get the minimum number of models
And check whether ( result > 1.2 * 10^12)

For option A; 3 * 3.6 * 10^11 which equals 1.04 * 10^12. Here result is not greater than required value so ELIMINATE A

For option B; 4 * 3.6 * 10^11 which would result 1.44 * 10^12. Here result is greater than 1.2 * 10^12 which is the CORRECT anawer.

We would not consider for more number of models as we are required to find the minimum number of model.

So eliminate C, D and E.
B is the correct answer

Thanks 
Harsh Tandel

Posted from my mobile device

stne · Answer

Using

n *r *t =  work done

n *1*60 = 200

n= 3.33

Since  n  is an integer hence minimum  n   required is  4

Explanation:

Lets simply the problem

A man can do  6 * 10^9  work in  1  sec , At least how many such men are required to complete  1.2 * 10^{12}  work in less than  60  secs?

Let  6 * 10^9  be total work or  1 , then he finishes his total work in  1  sec. 
 
rate = work done / time taken , work done  = 1   time taken  =1 , hence  r= \frac{1}{1} =1  }

1.2 * 10^ {12} =  is  200  times  6 * 10^9

So final work is  200  times his individual work

Now we can put the values in our usual work equation.

n* {r} * t= 200  where  r  is the rate and  t   is the time taken to complete the work and  n  is the number of person's or machines required.

n* 1*60 = 200

n=3.33

Which means it will take  3.33  person's or machines to complete the work in  1   min.

To complete the work in less than a minute we will need more than  3.33  machines

And since we need the most minimum number of such machines , hence the minimum no. is 4.

Ans-B

Hope it's clear.

Lodz697 · Answer

This was my method:

(1.2 * 10^12)/(6*10^9 * n) = 60 --> work / rate = time (in secs)

n = 3.33

Minimum required --> 4

Purnank · Answer

Quick method-
1 graphic processor :   6*10^9   per sec. therefore for min =  60*6*10^9  =  360*10^9 
now there are such n graphic processors.

n*360*10^9 > 1.2*10^12

solve for n

n>\frac{10}{3 }

Therefore min of n = 4
  Answer is B.

The Accelera model graphics processor, working at its constant rate, w

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