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

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).

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

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.

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

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

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!

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

Answer D

Posted from my mobile device

Solution:

Question Stem Analysis:

We need to determine the amount of sales tax on a certain order.

Statement One Alone:

If we let x = the total pretax price of the order, we can create the equation:

x + 0.05x = 44.1

1.05x = 44.1

x = 42

We see that the pretax price of the order was $42. Since the sales tax rate was 5%, the amount of sales tax was 42 * 0.05 = $2.10. Statement one alone is sufficient.

Statement Two Alone:

Since 400 regular pencils were sold, the number of deluxe pencils sold was 400 x 1.5 = 600. Therefore, the total pretax price of the order was 400 x 0.03 + 600 x 0.05 = 12 + 30 = $42. Since the total price of the order, including the sales tax, was $44.10, the amount of sales tax must be 44.1 - 42 = $2.10. Statement two alone is sufficient.

Answer: D

ScottTargetTestPrep
Thank you for your helpful reply. When I read this, I interpreted "All taxes on the order are a fixed percent of the pretax prices" to mean that there were different tax rates for the regular vs. deluxe. I would be so appreciative to learn how you knew it was just one fixed tax rate instead.

Dear woohoo921
you can translate:
.
as following, Total taxes = \(\frac{Fix}{100}\) * Pretax Amount

­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