A cellular company's monthly data plan charges x dollars for the first

Question

A cellular company's monthly data plan charges x dollars for the first half-gigabyte of data, and then x/5 dollars for each additional quarter gigabyte of data used. Which of the following represents the amount a user would be charged, in dollars, for using g gigabytes of data in a month, if g is a positive integer?

A. 4gx/5

B. 3gx/5

C. 4x(g+1)/5

D. (4gx+3x)/5

E. (4x+gx)/5

A. 4gx/5
 
B. 3gx/5
 
C. 4x(g+1)/5
 
D. (4gx+3x)/5
 
E. (4x+gx)/5

danlew · Answer

D

Assuming g=2 gigabytes and x=$10, the total charge for 2 gigabytes=10+(10/5)*(2+4)=22
Substituting g=2 and x=10 in answer choices, only D gives us 22.

GMATinsight · Answer

g = Integer

now g = (1/2) + + 2 quarter gigabyte + 4*(g-1) Quarter gigabyte

Total Payment = x+ *(x/5) = x+(4g-2)*(x/5) = (4gx+3x)/5

Answer: option D

Sindbad · Answer

Decode the question:
1st two quarter will be charged@x/2 per quarter and then every subsequent quarter will be charged @x/5 per quarter.
Now for an integer total number(say N) of quarter will be 4N.

As per the question total no of data consumed =g(where g =>I+)
Hence total quarter of gb consumed = 4g

remove the first two quarters as the rates are different. Remaining => 4g-2
Total cost for 4g-2 = (4g-2)* x/5 ----(a)
Total cost for first 2 quarters = x ----(b)

User will be charged (a)+(b)
(4g-2)*x/5 +x => (4gx-2x+5x)/5=> (4gx+3x)/5 => option D

ScottTargetTestPrep · Answer

We are given that a cellular company's monthly data plan charges x dollars for the first half-gigabyte of data, and then x/5 dollars for each additional quarter-gigabyte of data used. If g gigabytes are used, we have:
 
x + (x/5) 
 
x + (x/5) 
 
x + (x/5)(4g - 2)
 
5x/5 + x(4g - 2)/5
 
(5x + 4xg - 2x)/5
 
(4xg + 3x)/5
 
Answer: D

stne · Answer

Is there anything wrong with the below approach :

2 half GB's make 1 gigabyte or there are one 1/2 GB and 2 quarter GB in 1 GB

1/2 GB cost is x dollars and quarter GB cost is x/5 dollars

cost of 1 GB = x+2(x/5) = 7x/5
cost of g GB = g* 7x/5

Answer =D

KarishmaB · Answer

This is incorrect.

Note that cost of the first GB is 7x/5 as you have calculated.
But the cost of every subsequent GB is 4*(x/5) (since only the first half GB costs x dollars). So the rest of the (g - 1) GB will be charged at 4x/5

Total = 7x/5 + 4(g-1)x/5
and this is (D)

Another option is to plug in as done by danlew above. I assumed the same values while solving it and the reason for it is this:

There is a denominator of 5 in x/5. I would like for it to be an integer. But I do not want it to be 1 and neither do I want g to be 1 (when we have such values, there is a higher probability that multiple expressions will give the answer and hence more values will need to be tried out).
Hence I will take g as 2 (the next integer) and x as 10 so that x/5 is an integer.

Note that with these values, total cost = 10 + 2*6 = 22 (a multiple of 11)
It is obvious that options (A) and (B) do not have a factor of 11. Neither does (C).
(D) gives us the answer.

Turkish · Answer

Why is the below equation wrong. Can you please help GMATinsight ?

X(G/2)+X/5(G/4)+X/5(G/4)--- reason x is charged on first half-gigabyte of data, which is G/2
 X/5 is charged on each additional quarter gigabyte of data used , which is G/4
Ans :- 3gx/5

stne · Answer

Thanks karishma, Had a gut feeling something was amiss

Though couldn't lay a finger on it. Too many variables confused me I guess. Thank you +1

kaushiksamrat · Answer

Not able to understand the logic behind half GB data correlation with 4 quarters.. need a basic detailed explanation to understand plz

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stne · Answer

let me see if I can explain

1 = 1/2 + 1/2 -- equation 1
Two halves make 1

1/2 =1/4 + 1/4 
Two quarters make = 1/2 ------ equation 2

hence putting the value of 1/2 from equation 2 in equation 1

1= 1/4 + 1/4 +1/4 +1/4

So there are 4 quarters in 1

Hence in 1 GB there will 4 quarters .

Hope this makes it clear. Feel free to ask if anything is still unclear.

Now can you tell in Half GB how many quarters there will be ?

kaushiksamrat · Answer

let me see if I can explain

1 = 1/2 + 1/2 -- equation 1
Two halves make 1

1/2 =1/4 + 1/4 
Two quarters make = 1/2 ------ equation 2

hence putting the value of 1/2 from equation 2 in equation 1

1= 1/4 + 1/4 +1/4 +1/4

So there are 4 quarters in 1

Hence in 1 GB there will 4 quarters .

Hope this makes it clear. Feel free to ask if anything is still unclear.

Now can you tell in Half GB how many quarters there will be ? 
Would like to understand the solution in detail. Why we didn't multiply g/2 with xtrme for first half of GB data

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stne · Answer

Dear kaushiksamrat,

Welcome to Gmat Club,hope you have a great learning experience here. Believe me you will find the best math teachers of the world here such as Bunuel and veritasprepkarishma, and others.

Now coming to the question in its original format :

For the first 1/2 GB cost is X dollars then for EACH quarter GB cost is x/5 dollars

So in First GB we have 1 half GB and 2 quarter GB which will cost x + 2(x/5) = 7x/5

Now for each additional GB the cost will be 4(x/5) as there are 4 quarter GB's in each additional GB.

So if a total of g GB's are used where g>1 then the cost will be :

for the 1 GB = 7x/5
for the rest GB= ( g -1) 4 (x/5)

So total cost = 7x/5 + ( g -1) *4 (x/5)

Please spend some time on this , you will get it .

hellosanthosh2k2 · Answer

Let us get rid of fractions 1/2 and 1/4 by multiplying by 4
so question will read as, for first 2 GB, it will cost x dollars and for each additional 1GB, it will cost x/5 dollars
how much cost for 4*g GB ?

x(first 2 GB) + (4g-2) *x/5 => (4gx + 3x)/5 => D

Ved22 · Answer

how did you get (2+4)?. Pls help

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A cellular company's monthly data plan charges x dollars for the first

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