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Director  Status: Been a long time guys...
Joined: 03 Feb 2011
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For each order, a certain company charges a delivery fee d  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 74% (02:12) correct 26% (02:21) wrong based on 422 sessions

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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. _________________ Originally posted by Marcab on 09 Dec 2012, 23:33. Last edited by Bunuel on 23 Jan 2020, 04:43, edited 2 times in total. Renamed the topic and edited the question. ##### Most Helpful Expert Reply Math Expert V Joined: 02 Sep 2009 Posts: 65764 Re: For each order, a certain company charges a delivery fee d [#permalink] ### Show Tags 4 4 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?

Notice that the highest charge for the delivery with the second formula is for x=500, thus it equals to d=3+(500-100)/100=$7. (1) The delivery fee for one of the orders was$3. The price of the merchandise for that order is less than or equal to 100, but we know nothing about the second order. Not sufficient.

(2) The sum of the delivery fees for the two orders was $10. If the delivery charges for the two orders are$3 and $7, then the price of the second merchandise must be more than or equal to$500, which means that the total price must be greater than $499. Sufficient. Now, if both delivery charges were calculated with the second formula, then we'd have $$(3+\frac{x_1-100}{100})+(3+\frac{x_2-100}{100})=10$$ --> $$x_1+x_2=600>499$$. So, we have that in both possible cases the total price of the merchandise in the two orders is greater than$499. Sufficient.

Hope it's clear.
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Re: For each order, a certain company charges a delivery fee d  [#permalink]

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1) Obviously insufficient. The other order could have any value.

2) We can easily create a situation for which the value is more than $499. So lets try to create a situation for which the value is lesser than$499 to prove insufficiency.

Sufficient

Notice that we can have a case when charges for both deliveries are calculated with the second formula, for example x1=$250 and x2=$350, in this case the total price still would be $10. _________________ Director  Joined: 29 Nov 2012 Posts: 672 Re: For each order, a certain company charges a delivery fee d [#permalink] ### Show Tags Bunuel 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?

Notice that the highest charge for the delivery with the second formula is for x=500, thus it equals to d=3+(500-100)/100=$7. (1) The delivery fee for one of the orders was$3. The price of the merchandise for that order is less than or equal to 100, but we know nothing about the second order. Not sufficient.

(2) The sum of the delivery fees for the two orders was $10. If the delivery charges for the two orders are$3 and $7, then the price of the second merchandise must be more than or equal to$500, which means that the total price must be greater than $499. Sufficient. Now, if both delivery charges were calculated with the second formula, then we'd have $$(3+\frac{x_1-100}{100})+(3+\frac{x_2-100}{100})=10$$ --> $$x_1+x_2=600>499$$. So, we have that in both possible cases the total price of the merchandise in the two orders is greater than$499. Sufficient.

Hope it's clear.

Thanks this was really helpful, I missed out on the second case. where there can be 2 values within the range of d=3
Manager  Status: struggling with GMAT
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Re: For each order, a certain company charges a delivery fee d  [#permalink]

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Bunuel 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? Notice that the highest charge for the delivery with the second formula is for x=500, thus it equals to d=3+(500-100)/100=$7.

(1) The delivery fee for one of the orders was $3. The price of the merchandise for that order is less than or equal to 100, but we know nothing about the second order. Not sufficient. (2) The sum of the delivery fees for the two orders was$10. If the delivery charges for the two orders are $3 and$7, then the price of the second merchandise must be more than or equal to $500, which means that the total price must be greater than$499. Sufficient.

Now, if both delivery charges were calculated with the second formula, then we'd have $$(3+\frac{x_1-100}{100})+(3+\frac{x_2-100}{100})=10$$ --> $$x_1+x_2=600>499$$.

So, we have that in both possible cases the total price of the merchandise in the two orders is greater than $499. Sufficient. Answer: B. Hope it's clear. Thanks Its really so helpful.I was confused of the statement 2.Now its clear Manager  Joined: 12 Dec 2012 Posts: 209 Concentration: Leadership, Marketing GMAT 1: 540 Q36 V28 GMAT 2: 550 Q39 V27 GMAT 3: 620 Q42 V33 GPA: 2.82 WE: Human Resources (Health Care) Re: For each order, a certain company charges a delivery fee d [#permalink] ### Show Tags Bunuel wrote: [b]Now, if both delivery charges were calculated with the second formula, then we'd have $$(3+\frac{x_1-100}{100})+(3+\frac{x_2-100}{100})=10$$ --> $$x_1+x_2=600>499$$ can you please clarify this part more? thanks in advance Intern  Joined: 24 Apr 2013 Posts: 40 Schools: Duke '16 Re: For each order, a certain company charges a delivery fee d [#permalink] ### Show Tags WOW! I didnt even know where to start i was off and in the end i took a guess and went for B Director  Joined: 29 Nov 2012 Posts: 672 Re: For each order, a certain company charges a delivery fee d [#permalink] ### Show Tags TheNona wrote: Bunuel wrote: [b]Now, if both delivery charges were calculated with the second formula, then we'd have $$(3+\frac{x_1-100}{100})+(3+\frac{x_2-100}{100})=10$$ --> $$x_1+x_2=600>499$$ can you please clarify this part more? thanks in advance Cross multiply you will get 300 + x1 - 100 + 300 + x2 - 100 = 1000 After we solve its 600... Manager  Joined: 12 Jan 2013 Posts: 137 Re: For each order, a certain company charges a delivery fee d [#permalink] ### Show Tags Marcab 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.

Right off the bat, you need to know if: 2*x > 499

1) This one tells you that one of the orders is >= 100, it's insufficient because the other order could be any value

2) This tells you that the total delivery was > 500 + (another value between 1 and 100, inclusive), because there are no other combinations of 3 and 7 other than 3 + 7 that yield 10. So this is clearly sufficient.

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Re: For each order, a certain company charges a delivery fee d  [#permalink]

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Marcab 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? Is x > 499? Quote: (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. 1) d = 3 for 1 of the orders. The other could be 3, or could be 7. x will vary. Insufficient. 2) d = 10 => x > 500 for d = 7 OR 10 = 3 + (x-100)/100 + 3 + (y-100)/100 => 10 = 6 + (x + y - 200)/100 => 1000 = 400 + x + y --> x+y=600>499 Sufficient. B is the answer. _________________ Put in the work, and that dream score is yours! Target Test Prep Representative G Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2800 Re: For each order, a certain company charges a delivery fee d [#permalink] ### Show Tags Marcab 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.

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GMAT 1: 600 Q46 V27 Re: For each order, a certain company charges a delivery fee d  [#permalink]

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Can we addd the tag "GMATPrep" if it is actually a GMAT Prep question? Just for people who intend to avoid prep questions. Thank you!
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Re: For each order, a certain company charges a delivery fee d  [#permalink]

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TheNightKing wrote:
Can we addd the tag "GMATPrep" if it is actually a GMAT Prep question? Just for people who intend to avoid prep questions. Thank you!

_________________ Re: For each order, a certain company charges a delivery fee d   [#permalink] 23 Jan 2020, 04:44

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