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

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Question Stats: 62% (02:21) correct 38% (02:24) wrong based on 921 sessions

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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.

OG Q 2017 New Question(Book Question: 222)

Originally posted by AbdurRakib on 01 Jul 2016, 06:44.
Last edited by carcass on 03 Aug 2018, 11:11, edited 1 time in total.
Edited by Carcass
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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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44
1
3
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 ...

Please note that we are NOT calculating any values ...

All this is just to get my first kudos on GMAT Club...    Please be generous if this help...
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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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2
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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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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Top Contributor
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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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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Edited. 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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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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2
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

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.

OG Q 2017 New Question(Book Question: 222)

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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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1
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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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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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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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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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 ...

Please note that we are NOT calculating any values ...

All this is just to get my first kudos on GMAT Club...    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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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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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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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.

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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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

Posted from my mobile device
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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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1
S1937 wrote:
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

Posted from my mobile device

Hi S1937,

This may not be the fastest approach, but it is possible to use the weighted average mapping strategy to evaluate statement 2. (It's not relevant for statement 1.) We can treat the regular and deluxe pencils as the two groups being combined; these groups have average pretax prices of \$0.03 and \$0.05, respectively. If we call the number of regular pencils R and the number of deluxe pencils D, the question also tells us that D = 1.5R. When statement 2 tells us that R = 400, we then know that D = 600. Thus, 400 and 600 are the weights that we use for each group. Since the ratio of weights is 2:3, the ratio of the distances is also 2:3 (indicated by 2x and 3x on the diagram below), and here is how I would draw the weighted average mapping strategy: Since this is a Data Sufficiency question, I've really drawn more than you need to answer the question. Once you have the averages for each group, and the weights for each group, you know that you can solve for the weighted average. Since you know the total number of pencils, you can also calculate the total pretax price of all of the pencils. Then, if you see that you just need to subtract this from the sum of the tax and total pretax price to get the tax, you'll see that you have enough information to answer the question. So, statement 2 is sufficient.

While I'm here, I thought I would also leave my GMAT Timing Tips on how I recommend solving this question efficiently (the following links have growing lists of questions that you can use to practice each of these tips):

Use smart variables to represent unknowns: There are a variety of ways to set the question up, as shown in this thread, but you could consider doing it with up to 4 variables: T = tax (what we are solving for), P = total pretax price, R = number of regular pencils, D = number of deluxe pencils. I often recommend to students that they use more variables than they think they need to, if that helps them to see more clearly what is happening in the question.

Systems of linear equations: Using the above variables, you can get the following equations from the question itself:

P = 0.03R + 0.05D
D = 1.5R
P + T = 44.10

If we notice that these are 3 unique linear equations for 4 variables, we know that we could definitely solve for all 4 variables if we were given another unique linear equation. Each statement is sufficient, because each statement provides a 4th unique linear equation:

Statement 1: T = 0.05P (actually, this can be combined with the third equation above to form a system of 2 linear equations for 2 variables)
Statement 2: R = 400

Please let me know if you have any questions, or if you would like me to post a video solution!
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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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1
Let x be number of regular pencil anf T be the amount of tax
So 1.5x is number of delux pencil
\$44.10 = 0.03x + 0.05(1.5x) + T
44.10 = 0.105x + T

1) T = 5% of pretax price of the order
T = 0.05*(0.105x)
So x can be found by solving both equations and T can be determined
SUFFICIENT

2) x = 400
So T can be determined
SUFFICIENT

Posted from my mobile device
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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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souka92 wrote:
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 ...

Please note that we are NOT calculating any values ...

All this is just to get my first kudos on GMAT Club...    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

Hi souka92

The question stem says there were 50% more deluxe pencils than regular pencils.

D = R + 50% * R = R (1+50%) = 1.5R

To put in simple terms let the number of regular pencils be 10

if D has 50% more than R what is 50% of 10? it is 5.

so D = 10 + 5 = 15 Re: In a certain order,the pretax price of each regular pencil was \$0.o3,t   [#permalink] 22 Oct 2018, 13:11

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