Data Sufficiency

please help needed

nafiul9090 wrote:please help needed

You chose option D, so I assume that you know how statement 2 is sufficient to answer..

I'll prove how statement 1 is not sufficient
Question : was the total price of the merchandise in the two orders > $499
Statement 1:
The delivery fee for one of the two orders was $3.
The maximum order price for that order = $100.

We don't know the delivery fee of the other order.
We will consider two extreme cases.

Min delivery fee that could be charged = $3, for which the max order price would be $100.

In this case the maximum total price of the two orders = $100 + $100 = $200 < $499 . Answer to the question "No"

Max delivery fee that could be charged = $7, for which the min order price would be = $500

In this case the maximum total price of the two orders = $100 + $500 = $600 > $499. Answer to the question "Yes".

There is no definite answer.
Hence the statement is insufficient.

Statement 1:
To get a $3 fee, the first order's price must have been between less than $100. With no additional information, we can determine that (1) is insufficient since:

Scenario A: Order #1 has price $1, delivery fee $3. Order #2 has price $1, delivery fee $3.

Scenario B: Order #1 has price $1, delivery fee $3. Order #2 has price $1,000, delivery fee $7

Both scenarios respect the delivery cost schedule and statement (1). However while in Scenario A the sum of prices is tiny, in Scenario B the sum of prices is greater than $499.

[spoiler](1) is not sufficient.[/spoiler]

Statement 2:
To determine sufficiency, do your best to answer the question in multiple ways without contradicting the statement. If multiple answers are achievable, you have insufficiency.

Scenario A: make the sum of prices large. The easiest way to get $10 total delivery fee is to have one order with a $3 fee and another with a $7 fee. This will allow us to avoid that big nasty fraction. This is easy: Order #1 has price $1, delivery fee $3. Order #2 has price $1,000 delivery fee $7. Sum of fees is $10 and sum of prices is greater than $499.

Scenario B: make the sum of prices small (hopefully smaller than $499). To make prices small while keeping delivery fees high (equal to $10), need to take advantage of the first tier since for very low prices, delivery is expensive (relative to order price). So we could have order #1 price $0.01 and delivery fee $3. However to get to $10 total delivery fee, we must either have a order #2 with price > 500 (delivery fee would be $7 taking total delivery to $10) or make Order #2 price = 500 (delivery fee from the middle tier would be 3+(500-100)/100 = $7, taking total delivery to $10). Either way, the total order price has to be greater than $499.

[spoiler](2) is sufficient.[/spoiler]

B is correct.