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For each order, a certain company charges a delivery fee d t

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For each order, a certain company charges a delivery fee d t

by alanforde800Maximus » Wed May 16, 2018 4:12 am

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For each order, a certain company charges a delivery fee d that depends on the total price x of the merchandise in the order, where d and x are in dollars and


d = 3, if 0 < x <= 100

d = 3 + (x-100)/100, if 100 < x <= 500

d = 7, if x > 500

If George placed two separate orders with the company, was the total price of the merchandise in the two orders greater than $499?

(1) The delivery fee for one of the two orders was $3.
(2) The sum of the delivery fees for the two orders was $10.

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by alanforde800Maximus » Wed May 16, 2018 3:31 pm

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Hello Experts,

Can anyone help with this question?
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by Jeff@TargetTestPrep » Thu May 17, 2018 5:24 pm

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alanforde800Maximus wrote:For each order, a certain company charges a delivery fee d that depends on the total price x of the merchandise in the order, where d and x are in dollars and


d = 3, if 0 < x <= 100

d = 3 + (x-100)/100, if 100 < x <= 500

d = 7, if x > 500

If George placed two separate orders with the company, was the total price of the merchandise in the two orders greater than $499?

(1) The delivery fee for one of the two orders was $3.
(2) The sum of the delivery fees for the two orders was $10.
We need to determine whether the total price of the merchandise in two separate orders is greater than $499 or not.

Statement One Alone:

The delivery fee for one of the two orders was $3.

Thus we know price of one of the orders is at least $1 and at most $100. However, since we don't know anything about the other order, we can't answer the question. Statement one alone is not sufficient.

Statement Two Alone:

The sum of the delivery fees for the two orders was $10.

If the sum of the delivery fees was $10, it is possible that one order is at most $100 (thus has a delivery fee of $3) and the other order is at least $501 (thus has a delivery fee of $7). In this case the total price of the two orders will be greater than $499 since one of them is already greater than $499.

However, it is also possible that each of the orders has a price that is more than $100 but no more than $500.

So let's let a = price of the one order and b = price of the other order where both a and b are more than $100 but no more than $500. We can create the following equation:

3 + (a - 100)/100 + 3 + (b - 100)/100 = 10

(a - 100)/100 + (b - 100)/100 = 4

(a - 100) + (b - 100) = 400

a + b = 600

We can see that if each order is more than $100 but no more than $500, then the total price of the two orders is always $600, which is greater than $499.

Answer: B

Jeffrey Miller
Head of GMAT Instruction
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by [email protected] » Thu May 17, 2018 5:56 pm

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Hi alanforde800Maximus,

We're told that for each order, a certain company charges a delivery fee D that depends on the total price X of the merchandise in the order, where D and X are in dollars and
D = 3, if 0 < X <= 100
D = 3 + (X-100)/100, if 100 < X <= 500
D = 7, if X > 500
and George placed two separate orders with the company. We're asked if the total price of the merchandise in the two orders greater than $499. This is a YES/NO question and can be solved by TESTing VALUES. It's worth noting that - based on the 'pay scale' - the 'second level' fee would be between $3 and $7, inclusive (depending on the value of X).

1) The delivery fee for one of the two orders was $3.

Fact 1 tells us about just 1 of the 2 orders. With a fee of $3, we know that that first order cost between $0 and $100. However, we don't know anything about what the 2nd order cost.
IF... the 2nd fee was $3, then the total cost would be no more than $200 and the answer to the question would be NO.
IF... the 2nd fee was $7, then the total cost would be at least $500 and the answer to the question would be YES.
Fact 1 is INSUFFICIENT.

2) The sum of the delivery fees for the two orders was $10.

IF the two individual fees were $3 and $7, then the total cost would be at least $500 (since the $7 charge occurs when X is $500 or more) and the answer would be YES.

We do have to consider the possibility that both fees were from the 'second level'....
When
X=200, the fee is (3 + 1) = $4
X=250, the fee is (3 + 1.50) = $4.50
X=300, the fee is (3 + 2) = $5
X=400, the fee is (3 + 3) = $6
Etc.

With a total fee of $10, the total cost of the order will ALWAYS be at least $600 (you can pair any two values and the sum will always be at least that high), so the answer to the question WOULD be YES. In all possible situations, the answer to the question is YES.
Fact 2 is SUFFICIENT.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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