Data Sufficiency Pack 2, Question 1) The cost to ship...

st 1: 40+6(x+4-10)=220.... clearly sufficient, can solve for x

st 2: taking weighted avg: (40+x*6)/(x+10)=5.5... sufficient, no need to solve

ans: D

Hi All,

This DS question can be solved with traditional algebra or with a more strategic approach. To start, the prompt gives us information about cost, but asks us about the number of packages shipped. In these types of situations, it can be helpful to 'rewrite' the question. Here, we're asked if MORE then 35 packages were shipped. According to the shipping rates in the prompt, the first 10 packages cost a total of $40, while each additional package costs $6.

Thus 35 packages would cost...
$40 for the first 10 packages
$6 for each of the next 25 packages = $150
$40 + $150 = $190

So the prompt can be rewritten as "Does the shipping cost more than $190?" This is a YES/NO question.

(1) If 4 additional packages were shipped, then the retailer would have spent at least $220 on shipping on Monday.

Since we know what 35 packages would cost to ship, we can work 'back' from this information. According to the shipping rates, the extra 4 packages would account for 4($6) = $24.

"At least" $220 - $24 = "at least" $196

Since $196 is the minimum money spent on shipping, the answer to the question would be ALWAYS YES.
Fact 1 is SUFFICIENT.

(2) The average price of the packages shipped on Monday was $5.50

This Fact involves a great math 'shortcut' - The average price of the first 10 packages is $40/10 = $4/package. Since the cost of shipping an extra package becomes $6 after the first 10 packages are shipped, each additional package will INCREASE the average shipping price of all the packages.

For example

11 packages = ($40 + $6)/11 = 46/11 = 4 2/11
12 packages = ($40 + $12)/12 = 52/12 = 4 1/3
13 packages = ($40 + $18)/13 = 58/13 = 4 6/13
Etc.

This means that the average price will eventually become $5.50 exactly AND that there can be ONLY ONE way to get to that $5.50 average. That specific number of packages will get us the answer to the question, so this Fact is SUFFICIENT.
Fact 2 is SUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich

definitely needs to be read thoroughly...
in order to ship > 35 packages, the company needs to spend at least 40+25*6 = 190$.

1. if 4 more packages were shipped, then the total cost would be at least 220.
220-190=30. 30/6 = 5. so the company must have sent at least 36 packages. sufficient.

2. 190/35 = 38/7 = aprox 5.42 since we are told that the average price is 5.50, then definitely the company shipped more than 35 packages.
sufficient.

D