For each order, a mail order bookseller charges a fixed processing fee

Question

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

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RaghavKhanna · Accepted Answer

Fees for an order of n books =   P + nS ; P = processing fees, S = shipping fees per book

Jan : P + S
Feb : P + 2S
Mar : P + 3S
Apr : P + 4S
May : P + 5S

St. 1: 
P + 3S - P - S = 1
=> 2S = 1
=> S = 1/2

Cannot determine P from it.
=>  St. 1 is insufficient.

St. 2: 
S + 2S + 3S + 4S + 5S = 7.5
=> 15S = 7.5
=> S = 1/2
Cannot determine P from it.
=>  St. 2 is insufficient.

St. 1 and St. 2 :  
We get S = 1/2
Cannot determine P from it.
=>  St. 1 and St. 2 together are insufficient.

Answer: E

yashikaaggarwal · Answer

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?

Solution:
(1) Rajeev's processing and shipping fees were $1 more for his order in March than for his order in January
Cost for 1 book = X(Processing+Shipping fees)
Cost for 3 books = X+1 (Processing+Shipping fees)
Cost of shipping 2 additional books = 1
But what's processing cost? (Insufficient)

(2) The total of Rajeev's shipping fees for the five orders was $7.50
No information regarding processing cost! (Insufficient)

Statement 1&2: No parameter given to determine the processing cost. (Insufficient)

IMO E

Posted from my mobile device

sambitspm · Answer

Kindly see the attachment. Now this question might take you some time as it takes time to form the equation based on the complete context of the question.

TIME: 02:15 
IMO E

rajatchopra1994 · Answer

Explanation:

Statement 1: March - Jan = P + 3S - P - S => 1
2S = 1,
S = 1/2 , Can't find value for P
Not Sufficient.

Statement 2: Jan + Feb + Mar + Apr + May = 7.5$
S + 2S + 3S + 4S + 5S = 7.5
15S = 7.5
S = 1/2 , Can't find value for P
Not Sufficient.

From 1 & 2,
Know, S = 1/2 ; Can't find P
Not Sufficient.

IMO-E

Rishab2409 · Answer

Kindly correct my understanding: I read the statements and deciphered that

(1) We have shipping fees as $.50, as the processing fees is fixed and the only difference would be of the variable fees (shipping fees). We have no information on processing fees. Insufficient.
 
(2) We are given that the total processing fees is $7.5 for 15 books, which boils down to $.5 per book. Again, we have no information on processing fees. Insufficient.

(1) + (2) We only have info on shipping fees and nothing on processing fees. Insufficient.

Answer (E)

egmat · Answer

Hi Rishab2409,

Good news: your final answer  E  is correct, and your logic for why is spot on. There's just one label to fix in Statement 2 so your understanding stays clean.

The mix-up:  In Statement 2 you called the  $7.50  the "total processing fees." It's actually the  total shipping fees  for the five orders. That's why your own line reads a little contradictory - you labeled it processing, then said you have no info on processing. Let me untangle it.

Each order costs  P + nS , where P is the fixed processing fee per order and S is the shipping fee per book.

-  Statement (1):  March - January = (P + 3S) - (P + S) = 2S =  $1 , so  S = $0.50 . P stays unknown.  Insufficient.  ✓ (your reasoning)
-  Statement (2):  The shipping units across the five orders are 1+2+3+4+5 =  15 , so total shipping =  15S  =  $7.50 , giving  S = $0.50  again. This tells us nothing about P.  Insufficient.  ✓

So both statements only pin down  S , and the question asks for the full total  5P + 15S  - which still depends on the unknown  P .

Why the combination still fails (two quick cases):  both statements hold as long as S =  $0.50 , no matter what P is.

- If  P = $1 : total = 5( 1 ) +  7.50  =  $12.50 
- If  P = $2 : total = 5( 2 ) +  7.50  =  $17.50

Same statements, two different totals -  not sufficient , even together. That's your E.

Bottom line: your conclusion is right - just remember the  $7.50  is  shipping , and the piece that's never given is the  processing  fee P.

Answer: E

For each order, a mail order bookseller charges a fixed processing fee

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For each order, a mail order bookseller charges a fixed processing fee

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