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Math Expert V
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A cellular company's monthly data plan charges x dollars for the first  [#permalink]

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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

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GMAT 1: 720 Q48 V40 Re: A cellular company's monthly data plan charges x dollars for the first  [#permalink]

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2
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.
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Re: A cellular company's monthly data plan charges x dollars for the first  [#permalink]

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1
Bunuel wrote:
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

g = Integer

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

Total Payment = x+[4*(g-1)+2]*(x/5) = x+(4g-2)*(x/5) = (4gx+3x)/5

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Re: A cellular company's monthly data plan charges x dollars for the first  [#permalink]

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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
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Re: A cellular company's monthly data plan charges x dollars for the first  [#permalink]

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Bunuel wrote:
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

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)[(g - 1/2)/(1/4)]

x + (x/5)[4(g - 1/2)]

x + (x/5)(4g - 2)

5x/5 + x(4g - 2)/5

(5x + 4xg - 2x)/5

(4xg + 3x)/5

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Re: A cellular company's monthly data plan charges x dollars for the first  [#permalink]

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Bunuel wrote:
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

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

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Re: A cellular company's monthly data plan charges x dollars for the first  [#permalink]

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stne wrote:
Bunuel wrote:
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

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

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.
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Re: A cellular company's monthly data plan charges x dollars for the first  [#permalink]

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Why is the below equation wrong. Can you please helpGMATinsight?

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
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Re: A cellular company's monthly data plan charges x dollars for the first  [#permalink]

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VeritasPrepKarishma wrote:
stne wrote:
Bunuel wrote:
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

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

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.

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
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Re: A cellular company's monthly data plan charges x dollars for the first  [#permalink]

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ScottTargetTestPrep wrote:
Bunuel wrote:
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

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)[(g - 1/2)/(1/4)]

x + (x/5)[4(g - 1/2)]

x + (x/5)(4g - 2)

5x/5 + x(4g - 2)/5

(5x + 4xg - 2x)/5

(4xg + 3x)/5

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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Posts: 904
Re: A cellular company's monthly data plan charges x dollars for the first  [#permalink]

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kaushiksamrat wrote:
ScottTargetTestPrep wrote:
Bunuel wrote:
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

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)[(g - 1/2)/(1/4)]

x + (x/5)[4(g - 1/2)]

x + (x/5)(4g - 2)

5x/5 + x(4g - 2)/5

(5x + 4xg - 2x)/5

(4xg + 3x)/5

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

Sent from my SM-G935F using GMAT Club Forum mobile app

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 ?
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Re: A cellular company's monthly data plan charges x dollars for the first  [#permalink]

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stne wrote:
kaushiksamrat wrote:
ScottTargetTestPrep wrote:
[quote="Bunuel"]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

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)[(g - 1/2)/(1/4)]

x + (x/5)[4(g - 1/2)]

x + (x/5)(4g - 2)

5x/5 + x(4g - 2)/5

(5x + 4xg - 2x)/5

(4xg + 3x)/5

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

Sent from my SM-G935F using GMAT Club Forum mobile app

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 ?[/quote]
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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Re: A cellular company's monthly data plan charges x dollars for the first  [#permalink]

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kaushiksamrat wrote:

Would like to understand the solution in detail. Why we didn't multiply g/2 with xtrme for first half of GB data

Sent from my SM-G935F using GMAT Club Forum mobile app

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 .
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Re: A cellular company's monthly data plan charges x dollars for the first  [#permalink]

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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 Re: A cellular company's monthly data plan charges x dollars for the first   [#permalink] 31 Mar 2018, 05:14
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