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In a certain order,the pretax price of each regular pencil was $0.o3,t

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In a certain order,the pretax price of each regular pencil was $0.o3,t  [#permalink]

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In a certain order,the pretax price of each regular pencil was $0.03,the pretax price of each deluxe pencil was $0.05,and there were 50% more deluxe pencils than regular pencils.All taxes on the order are a fixed percent of the pretax prices.The sum of the total pretax price of the order and the tax on the order was $44.10.What was the amount,in dollars,of the tax on the order?

(1) The tax on the order was 5% of the total pretax price of the order.
(2) The order contained exactly 400 regular pencils.


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Last edited by carcass on 03 Aug 2018, 11:11, edited 1 time in total.
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Re: In a certain order,the pretax price of each regular pencil was $0.o3,t  [#permalink]

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New post 20 Jul 2016, 00:11
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AbdurRakib wrote:
In a certain order,the pretex price of each regular pencil was $0.03,the pretex price of each deluxe pencil was $0.05,and there were 50% more deluxe pencils than regular pencils.All taxes on the order are a fixed percent of the pretex prices.The sum of the total pretex price of the order and the tax on the order was $44.10.What was the amount,in dollars,of the tax on the order?

(1) The tax on the order was 5% of the total pretex price of the order.
(2) The order contained exactly 400 regular pencils.


OG Q 2017 New Question(Book Question: 222)


As per question statement :
Price of Regular Pencil = 0.03/pencil
Price of Deluxe pencil = 0.05/pencil
# of Deluxe Pencil (D) in the Order = 50% More that # of Regular Pencil (R) => D = 1.5R
Also, there is a Tax (T) of a fixed percent on the pretex price (Total Price)
And finally : Total order value = 44.10
There fore we can write the equation :
0.05*D + 0.03*R + T = 44.10
(Huuufff .. this was too much data)
Now, we are asked to find the amount of Tax (T) on the order.

Lets see statement - 1 : The tax on the order was 5% of the total pretex price of the order.
So, from this we can deduce that 44.10 contains 5% of the tax in it.
So, 44.10 = 105% of (0.05*D + 0.03*R)
Lets call this 0.05*D + 0.03*R = X
44.10 = 105% of (X)
So we will get X
and on subtracting X from 44.10 we will get the Tax T
So statement - 1 is sufficient

Lets see statement - 2 : The order contained exactly 400 regular pencils
So R = 400
and from question statement D = 1.5R, we can get D also.
Plugging these values in equation
0.05*D + 0.03*R + T = 44.10, we can get T.
So statement - 2 is also sufficient ...

So answer Choice D.
Please note that we are NOT calculating any values ...

All this is just to get my first kudos on GMAT Club...
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Re: In a certain order,the pretax price of each regular pencil was $0.o3,t  [#permalink]

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New post 01 Jul 2016, 07:00
1
Let number of pencils (regular) be x.

From the first statement, regular to deluxe pencils would be in a ratio of 2:3.

We only need to know the number of any one of the pencils, as unit prices for each are already given.

First statement and second statement both can lead us to this.

Thus, I think the answer will be (D).
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Re: In a certain order,the pretax price of each regular pencil was $0.o3,t  [#permalink]

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New post 01 Jul 2016, 07:54
D

1 gives us tax of 22.
2.relation between regular and deluxe is given>compute the total revenue and subtract from 44 ,which is ur tax
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Re: In a certain order,the pretax price of each regular pencil was $0.o3,t  [#permalink]

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New post 20 Jul 2016, 06:01
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AbdurRakib wrote:
In a certain order,the pretex price of each regular pencil was $0.03,the pretex price of each deluxe pencil was $0.05,and there were 50% more deluxe pencils than regular pencils.All taxes on the order are a fixed percent of the pretex prices.The sum of the total pretex price of the order and the tax on the order was $44.10.What was the amount,in dollars,of the tax on the order?

(1) The tax on the order was 5% of the total pretex price of the order.
(2) The order contained exactly 400 regular pencils.


Should be pretAx, not pretex
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Re: In a certain order,the pretax price of each regular pencil was $0.o3,t  [#permalink]

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New post 20 Jul 2016, 06:26
GMATPrepNow wrote:
AbdurRakib wrote:
In a certain order,the pretex price of each regular pencil was $0.03,the pretex price of each deluxe pencil was $0.05,and there were 50% more deluxe pencils than regular pencils.All taxes on the order are a fixed percent of the pretex prices.The sum of the total pretex price of the order and the tax on the order was $44.10.What was the amount,in dollars,of the tax on the order?

(1) The tax on the order was 5% of the total pretex price of the order.
(2) The order contained exactly 400 regular pencils.


Should be pretAx, not pretex

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Re: In a certain order,the pretax price of each regular pencil was $0.o3,t  [#permalink]

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New post 23 Jul 2016, 07:31
3
(1) The tax on the order was 5% of the total pretax price of the order.
Let the total pretax price be x
then
x+0.05x=44.10
This will give is X and the tax amount !!
Sufficient

(2) The order contained exactly 400 regular pencils.
deluxe pencils = 1.5*regular pencils
deluxe pencils = 600
600*(0.05)+400*(0.03)+tax=44.10
this will give the variable tax

Therefore , D
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Re: In a certain order,the pretax price of each regular pencil was $0.o3,t  [#permalink]

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New post 30 Aug 2016, 09:54
1
In a certain order,the pretax price of each regular pencil was $0.03,the pretax price of each deluxe pencil was $0.05,and there were 50% more deluxe pencils than regular pencils.All taxes on the order are a fixed percent of the pretax prices.The sum of the total pretax price of the order and the tax on the order was $44.10.What was the amount,in dollars,of the tax on the order?

(1) The tax on the order was 5% of the total pretax price of the order.
Total PreTax Price =X
Tax = 5% of X= 0.05X
Total Cost (44.10) will be = Tax + PreTax Cost = X+ 0.05X ===> 1.05X
1.05X=44.10 (Sufficient)
FOR CURIOUS USERS
X = 44.10/1.05 ----> X =42
Tax= 5% of 42 = 2.10 $
SUFFICIENT

(2) The order contained exactly 400 regular pencils.
Regular Pencil = 400
Deluxe Pencil will be = 1.5 times x 400= 600
Prices are already given in the stimulus
(Price of regular + Price of Deluxe) + 5% of (Price of regular + Price of Deluxe) = 44.10
SUFFICIENT
FOR CURIOUS USERS:-
400 x 0.03 + 600 x 0.05 + {5% of (400 x 0.03 + 600 x 0.05) <---TAX} = 44.10
12+30+{2.10 <---TAX)= 44.10
44.10=44.10
Tax is 2.10
SUFFICIENT

Answer IS D



AbdurRakib wrote:
In a certain order,the pretax price of each regular pencil was $0.03,the pretax price of each deluxe pencil was $0.05,and there were 50% more deluxe pencils than regular pencils.All taxes on the order are a fixed percent of the pretax prices.The sum of the total pretax price of the order and the tax on the order was $44.10.What was the amount,in dollars,of the tax on the order?

(1) The tax on the order was 5% of the total pretax price of the order.
(2) The order contained exactly 400 regular pencils.


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Re: In a certain order,the pretax price of each regular pencil was $0.o3,t  [#permalink]

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New post 19 May 2017, 03:10
Ill keep it short and sweet:

(0.03) (n) (1+t/100) + (0.05) (1.5n) (1+t/100) = 44.10


(1) t = 5% --> (0.03) (n) (1+5/100) + (0.05) (1.5n) (1+5/100) = 44.10

we can figure out n and from there the amount of t



(2) n + 1.5n = 400, n = 160 --> (0.03) (160) (1+t/100) + (0.05) (1.5) (160) (1+t/100) = 44.10

we can figure out t and from there the amount of t



hopefully its correct :)
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Re: In a certain order,the pretax price of each regular pencil was $0.o3,t  [#permalink]

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New post 26 Jan 2018, 06:03
I got this one wrong and now I understand why it was wrong. My approach was close, but I made 1 critical mistake.

When creating the formula, I got 0.05*DT + 0.03*RT = 44.10, then because 50% more deluxe I multiplied by .5 next to .03.

So my formula is 0.05*DT + 0.015*RT = 44.10.
Statement 1 tells me to take out T, now I still have 2 variables to solve for (D and R) so I thought NF.
Statement 2 gives me D, still have 2 variables to solve for (R and T) so I thought NF. Then I assumed answer C.

My Question: I see now that I should not have counted D and R as two separate variables, but why is that? In the future, how can I know that for a question like this that Deluxe and Regular don't make 2 variables? I hope this question makes sense.
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Re: In a certain order,the pretax price of each regular pencil was $0.o3,t  [#permalink]

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New post 26 Jan 2018, 08:16
1
msurls wrote:
I got this one wrong and now I understand why it was wrong. My approach was close, but I made 1 critical mistake.

When creating the formula, I got 0.05*DT + 0.03*RT = 44.10, then because 50% more deluxe I multiplied by .5 next to .03.

So my formula is 0.05*DT + 0.015*RT = 44.10.
Statement 1 tells me to take out T, now I still have 2 variables to solve for (D and R) so I thought NF.
Statement 2 gives me D, still have 2 variables to solve for (R and T) so I thought NF. Then I assumed answer C.

My Question: I see now that I should not have counted D and R as two separate variables, but why is that? In the future, how can I know that for a question like this that Deluxe and Regular don't make 2 variables? I hope this question makes sense.


Hi

We CAN solve this question properly taking two different variables. Lets say number of regular pencils = x, number of deluxe pencils = y.
Total pretax price = 0.03x + 0.05y + T = 44.1, this is the first equation.
Given that deluxe pencils = 50% more than regular pencils, so y = 1.5x; this is the second equation.
We need three different equations to solve for three different variables, the third equation can be formed from either statement 1 or from statement 2.

However, to make it easier, we can already incorporate the fact that # of deluxe pencils = 1.5 * # of regular pencils. So if # of regular pencils = x, then # of deluxe pencils = 1.5x. And so total order price = 0.03x + 0.05*1.5x + T = 0.105x + T
This is an equation in two variables, we now need another equation to solve for the two variables. And the second equation will be provided from either statement 1 or statement 2.

So, you see, whether we solve it via 2 different variables or single variable for the kinds of pencils, its one and the same thing.
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Re: In a certain order,the pretax price of each regular pencil was $0.o3,t  [#permalink]

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New post 26 Jan 2018, 08:21
amanvermagmat wrote:
msurls wrote:
I got this one wrong and now I understand why it was wrong. My approach was close, but I made 1 critical mistake.

When creating the formula, I got 0.05*DT + 0.03*RT = 44.10, then because 50% more deluxe I multiplied by .5 next to .03.

So my formula is 0.05*DT + 0.015*RT = 44.10.
Statement 1 tells me to take out T, now I still have 2 variables to solve for (D and R) so I thought NF.
Statement 2 gives me D, still have 2 variables to solve for (R and T) so I thought NF. Then I assumed answer C.

My Question: I see now that I should not have counted D and R as two separate variables, but why is that? In the future, how can I know that for a question like this that Deluxe and Regular don't make 2 variables? I hope this question makes sense.


Hi

We CAN solve this question properly taking two different variables. Lets say number of regular pencils = x, number of deluxe pencils = y.
Total pretax price = 0.03x + 0.05y + T = 44.1, this is the first equation.
Given that deluxe pencils = 50% more than regular pencils, so y = 1.5x; this is the second equation.
We need three different equations to solve for three different variables, the third equation can be formed from either statement 1 or from statement 2.

However, to make it easier, we can already incorporate the fact that # of deluxe pencils = 1.5 * # of regular pencils. So if # of regular pencils = x, then # of deluxe pencils = 1.5x. And so total order price = 0.03x + 0.05*1.5x + T = 0.105x + T
This is an equation in two variables, we now need another equation to solve for the two variables. And the second equation will be provided from either statement 1 or statement 2.

So, you see, whether we solve it via 2 different variables or single variable for the kinds of pencils, its one and the same thing.


Thanks so much amanvermagmat ! That makes sense. Looks like I didn't think to eliminate "y" and convert it to x given that deluxe pencils = 50% more than regular pencils.

Thanks again.
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Re: In a certain order,the pretax price of each regular pencil was $0.o3,t  [#permalink]

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New post 26 Feb 2018, 05:15
mihir0710 wrote:
AbdurRakib wrote:
In a certain order,the pretex price of each regular pencil was $0.03,the pretex price of each deluxe pencil was $0.05,and there were 50% more deluxe pencils than regular pencils.All taxes on the order are a fixed percent of the pretex prices.The sum of the total pretex price of the order and the tax on the order was $44.10.What was the amount,in dollars,of the tax on the order?

(1) The tax on the order was 5% of the total pretex price of the order.
(2) The order contained exactly 400 regular pencils.


OG Q 2017 New Question(Book Question: 222)


As per question statement :
Price of Regular Pencil = 0.03/pencil
Price of Deluxe pencil = 0.05/pencil
# of Deluxe Pencil (D) in the Order = 50% More that # of Regular Pencil (R) => D = 1.5R
Also, there is a Tax (T) of a fixed percent on the pretex price (Total Price)
And finally : Total order value = 44.10
There fore we can write the equation :
0.05*D + 0.03*R + T = 44.10
(Huuufff .. this was too much data)
Now, we are asked to find the amount of Tax (T) on the order.

Lets see statement - 1 : The tax on the order was 5% of the total pretex price of the order.
So, from this we can deduce that 44.10 contains 5% of the tax in it.
So, 44.10 = 105% of (0.05*D + 0.03*R)
Lets call this 0.05*D + 0.03*R = X
44.10 = 105% of (X)
So we will get X
and on subtracting X from 44.10 we will get the Tax T
So statement - 1 is sufficient

Lets see statement - 2 : The order contained exactly 400 regular pencils
So R = 400
and from question statement D = 1.5R, we can get D also.
Plugging these values in equation
0.05*D + 0.03*R + T = 44.10, we can get T.
So statement - 2 is also sufficient ...

So answer Choice D.
Please note that we are NOT calculating any values ...

All this is just to get my first kudos on GMAT Club...
:P :P :P :P
Please be generous if this help...



Excuse my ignorance but there is something I don't understand. How do you come up with D=1.5R. The way I view is that Deluxe equal to Regular number plus half of the Deluxe, so D=R+ D/2. Can you please explain how you come up with D=1.5R?

Thank you
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Re: In a certain order,the pretax price of each regular pencil was $0.o3,t  [#permalink]

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New post 26 Feb 2018, 12:47
Statement I: Sufficient!
x = price of order (no tax)
1.05x = 44.10
x = 42
$ of tax = 2.10

Qty Regular pencil = R
Qty Delux pencil = D
D = 1.5R

0.05. 1.5R + 0.03R = 42
0.075R + 0.03R = 42
0.105R = 42
R = 400 (400 regular pencils)
D = 1.5 * 400 (600 delux pencils)


Statement II: Sufficient!

R = 400
D = 1.5 * 400 = 600

$ R = 400 * 0.03 = $12
$ D = 600 * 0.05 = $30

Total cost without tax = $42
Total tax cost = $2.10
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What was the amount, in dollars, of the tax on the order?  [#permalink]

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New post 14 Aug 2018, 16:03
In a certain order, the pretax price of each regular pencil was $0.03, the pretax price of each deluxe pencil was $0.05, and there were 50% more deluxe pencils than regular pencils. All taxes on the order are a fixed percent of the pretax prices. The sum of the total pretax price of the order and the tax on the order was $44.10. What was the amount, in dollars, of the tax on the order?

(1) The tax on the order was 5% of the total pretax price of the order.

(2) The order contained exactly 400 regular pencils.
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In a certain order,the pretax price of each regular pencil was $0.o3,t  [#permalink]

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New post 14 Aug 2018, 21:35
exgar26 wrote:
In a certain order, the pretax price of each regular pencil was $0.03, the pretax price of each deluxe pencil was $0.05, and there were 50% more deluxe pencils than regular pencils. All taxes on the order are a fixed percent of the pretax prices. The sum of the total pretax price of the order and the tax on the order was $44.10. What was the amount, in dollars, of the tax on the order?

(1) The tax on the order was 5% of the total pretax price of the order.

(2) The order contained exactly 400 regular pencils.


Please search before posting..

D=1.5R and let the tax be x
(0.03R+0.05D)(1+X/100)=44.10
(3R+5D)(100+X)=441000
We are looking for X(3R+5D)/100


(1) The tax on the order was 5% of the total pretax price of the order.
So X is 5..
105(3R+5D)=441000,
5(3R+5D)=441000*5/105=4200*5=21000
Ans 210
Sufficient


(2) The order contained exactly 400 regular pencil
So (3*400+5*600)(100+X)=441000...
X(3*400+5*600)=441000-(3*400+5*600)*100=441000-420000=21000
Ans 210
Sufficient
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Re: In a certain order,the pretax price of each regular pencil was $0.o3,t  [#permalink]

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New post 18 Aug 2018, 00:51
Hello gurus,
Can we solve this using weighted average formula or the mapping method?
I've got the solution from mathy way. But I've tried mapping on it to no avail.
Could mapping work here or is it off mapping?
I await your replies, JeffYin, @KarishmaB

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Re: In a certain order,the pretax price of each regular pencil was $0.o3,t &nbs [#permalink] 18 Aug 2018, 00:51
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