Shipping and processing DS problem

[praveen_gmat]

Hi,
For the question below:

For each order, a mail order bookseller charges a fixed processing fee and an additional shipping fee for each book in the order. Rajeev placed five different orders with this bookseller - an order for 1 book in January, an order for 2 books in February, an order for 3 books in March, an order for 4 books in April, and an order for 5 books in May. What was the total of Rajeev's processing and shipping fee for these five orders?

1) Rajeev's processing and shipping fees were $1 more for his order in March than for his order in January
2) The total of Rajeev's shipping fees for the five orders was $7.50

Is this not weird?
From statement 1, March + $1 = January, which means J-M = 1.
and if P is the fixed processing fee and A is the additional shipping fee, then
J=P + A
F=P+2A
M=P=3A

J - M = 1 = -2A ..?
How can the additional fee be negative?

[rishimaharaj]

Hello Praveen,

You're correct that each month's cost breaks down into a fixed portion and a variable portion:
Total Cost = Fixed Processing Fee + (Shipping Fee * Number of books)

Each month, the processing fee remains the same. So in Statement 1, where it says that the processing and shipping fees were $1 more for his order in March than for his order in January, it means:

January = Fixed + x
March = Fixed + (x + 1)

We can figure out from this that:
February = Fixed + (x + .5)
April = Fixed + (x + 1.5)
May = Fixed + (x + 2)

In regard to the answer, here's my attempt:

STATEMENT 1:
This doesn't mention anything about what the fixed cost is. We can figure out what all of the incremental costs are, but we don't have any information on what January costed and what the fixed cost is.
Insufficient.

STATEMENT 2:
This mentions what the total shipping is for the five orders, so we can break down what each month's shipping is, but we still don't have any information on what the fixed cost is.
Insufficient.

STATEMENT 1 & 2:
This is also insufficient because neither of the statements contain any information about the fixed portion of the cost.

The answer should be answer choice E.


Hope this helps!
--Rishi

[Whitney Garner]

1) Rajeev's processing and shipping fees were $1 more for his order in March than for his order in January

Is this not weird?
From statement 1, March + $1 = January, which means J-M = 1.

Hi praveen_gmat!

Be very careful when translating. My first question for you would be to re-read the question and ask yourself again, which should have been higher - March or January?

It says that the processing and shipping fees were HIGHER in March, so let's use the formula you derived (M+1=J) and test. If January had $5 for p&s fees, then March should have been $6, right? Plug this in: 6+1=5, or 7=5?? This cannot be quite right, so we must have an issue with our translation. And when you look at your rearranged expression (J-M=1) we can see the problem. The way you have it written, If I take Jan's fees and subtract Mar's, I get a 1. But that means J is larger than M - NOT what the question says. So how do we fix it??

If March is HIGHER than January, I need to add stuff to January's side in order to be able to call them equal. So I have to take January's fees and add $1 to make them as much as March's:

M = J + 1.

Now see if this helps the issue

Whit

[praveen_gmat]

Hi Whitney Garner,
I am so humbled by your detailed explanation. Thank you so much. My test is on 24th of this month. I am still in 550 levels. I want to get close to 700. Hope it works out for me.

Thank you again!

Praveen